This paper describes a set of 58 Matlab®-based speech processing exercises designed to give students and instructors hands-on experience with digital speech processing basics, fundamentals, representations, algorithms and applications. This result is achieved by providing working Matlab code using a LITE graphical user interface (GUI) for ease of use and understanding of the code. For each Matlab exercise we provide a brief description of the code and GUI structure, an explanation of key technical aspects of the solution, a description of the organization of the Lite Graphical User Interface, a scripted run of the software with an extensive set of speech files for processing, some results figures generated by the provided code, and a set of technical issues for further experimentation with the code. Our goal with these exercises is to provide a set of speech processing tools for the instructor and an extended set of speech processing exercises (denoted as “Issues for Further Experimentation”) that students can use to develop their understanding of the technical content of each speech processing exercise. This paper describes the resulting set of exercises and shows how they can be used to enhance the teaching and learning of digital speech processing.

This paper discusses the automatic quality assessment of echo-degraded speech in the context of teleconference systems. Subjective listening tests conducted over a carefully designed database of signals degraded by acoustic echo have been used to assess how this impairment is perceived and to determine which parameters have a significant impact on speech quality. The results have shown that, similarly to electric transmission line echo, acoustic echo is mainly influenced by echo delay and echo gain. Based on this observation, a mapping between these two parameters and the mean subjective score is devised. Moreover, a signal-based algorithm for the estimation of these parameters is described, and its performance is evaluated. The complete system comprising both the parameter estimators and the mapping function achieves a correlation of 94% between predicted and actual subjective scores, and can be employed as a non-intrusive monitoring tool for in-service quality evaluation of teleconference systems. Further validation indicates the operating range of the proposed quality assessment tool can be extended by proper retraining.

We propose a correlogram-based time delay estimation method using signals modeled as the output of the cochlea, where the low-level signal processing happens in the human auditory system. With a normalized correlogram that preserves time-delay patterns that are invariant to speech features such as formants, we employ two-dimensional template matching for time-delay estimation. Experimental results show that our method outperforms a traditional correlogram-based method as well as the GCC-PHAT, especially for short analysis windows in a moderately reverberant environment.

This paper presents a system approach to the residual echo suppression (RES) problem in a noisy acoustic environment. We propose a method that takes advantage of our existing robust acoustic echo cancellation system in order to obtain a residual echo estimate that closely resembles the true, noise-free residual echo. To achieve improved RES during strong near-end interference (e.g., double talk), a psychoacoustic postfilter is also used. The simulation results show that our RES based on the system approach outperforms a conventional estimation method. Comparing the postfiltered output to the unprocessed one indicates that our proposed RES approach can raise the PESQ score by more than half a point.

This paper addresses the problem of identifying impairment types that might be present in a speech signal. In particular, three acoustically induced degradation types that occur in teleconference systems are considered: acoustic echo, reverberation, and broadband noise, as well as combinations among them. The proposed system is double-ended (full reference) and is developed using a database of degraded full-band speech signals created according to a model for teleconference systems. A set of features obtained from both the degraded and non-degraded signals is proposed and shown to adequately capture information associated with each degradation type. A random forest classifier and a support vector machine are successfully employed, achieving a classification error below 2%. Such classifiers can be used to select an appropriate quality assessment tool for a given degraded signal.

Modern telepresence systems can deliver multimedia signals of unprecedentedly high quality of experience to the user. Setting and maintaining such services call for reliable and automatic tools for multimedia quality probing, in special those targeted at speech data along the transmission path. Most of the objective methods for sound quality assessment (QA) in the literature are intended for either speech signals of 4- to 8-kHz bandwidth or general audio until 24 kHz, but are not specifically designed for speech at high sampling-rates. This work approaches quality evaluation of full-band (24 kHz) high-quality speech corrupted by echo. A simple metric singled out from a standardized double-ended tool for audio QA is proposed as a solution for the problem at hand. Quality measures from a set of speech stimuli corrupted by echo under controlled conditions were obtained via listening tests to allow calibration and evaluation of the proposed method. Experimental results reveal an overall correlation of 0.94 between objective and subjective scores, even in the presence of moderate additive noise.

In this paper the design of a double-ended (intrusive) diagnostic tool for identifying five types of degradation in audio signals is reported. The impairment types taken into consideration are additive contamination with pink noise, occurrences of signal mutes, distortion by magnitude clipping, and the previous two types mixed with pink noise. As a simple solution to accomplish the established goal, a threshold-based hierarchical classification system is proposed, being completely defined from pre-processing of the input signals, passing through the estimation of a few characteristic features, up to data clustering criteria. Performance evaluation of the classifier is carried out via a validation database containing 60 impaired signals for each type of impairment, with five distinct degradation intensity levels. Considering the types and range of degradation levels considered in this work, excellent results are achieved, scoring above 96% of correctly classified data in the worst case. System performance in identifying mixed impairment types tends to deteriorate as the strength of the noise component increases.

This paper analyzes the ability of several measurements to quantify the reverberation effect in speech signals. We consider an intrusive scheme, in which the clean and reverberated signals are available, allowing one to estimate the corresponding room impulse response (RIR) signal. An artificial neural network (ANN) is trained for all features and used in a regression approach to estimate the human perceptual evaluation in a mean opinion score (MOS) 1–5 scale. Dimensionality reduction approaches are applied to generate a simpler ANN regression, establishing the most representative features for the problem at hand. A correlation level of 85% with subjective test scores was achieved by reducing the input-vector dimension from 10 to 3, including only the features of reverberation time, room spectral variance, and direct-to-reverberant energy ratio.

This paper constitutes an introduction to the field of quality evaluation of sound (speech and audio) signals. The need for such an assessment is inherent to modern communications: VoIP, mobile phone, or teleconference systems require meaningful measures of performance, which may ultimately assure good service or profitable business. A brief survey on subjective and objective evaluation methods is provided. Recent developments as well as new topics to be investigated are also addressed. Experiments are conducted to illustrate how to validate quality assessment methods.

We consider the problem of estimating the time-difference-of-arrival (TDOA) for audio source localization in noisy environments, defining a framework for statistical analysis in the phase domain which enables more reliable estimates. This is motivated by the fact that with complex sources, noise, and interfering signals, different frequency bands have significantly different signal-to-noise ratios, creating non-uniform distributions of errors in the phase measurements. Through a new method for analysis of the variations of the phase in frequency windows, we first estimate the signal-to-noise ratio for frequency, and then use it in a maximum-likelihood estimation of the time difference of arrival. We show that this corresponds to a generalization of the Phase Transform method (PHAT), and provides a theoretical justification of why it works so well. Numerical results show how the proposed technique compares favorably with PHAT.

We describe and analyze a comprehensive learning model to address issues such as consistency, convergence rate, and sample complexity in the general context of system identification. The learning model is based on unbounded loss functions, and it incorporates a measure of algorithmic deficiency. We define and use a novel formulation of algorithmic solution that is an extension of the empirical risk minimization method in the sense that it uses a generic notion of side information as opposed to the commonly used input/output observation of a system. Sufficient conditions for consistency as well as closed form expressions for exponential convergence rate and sample complexity of the identification algorithm are derived

Capacity analysis for channels with side information at the receiver has been an active area of interest. This problem is well investigated for the case of finite-alphabet channels. However, the results are not easily generalizable to the case of continuous-alphabet channels due to analytical difficulties inherent with continuous alphabets. In the first part of this two-part paper, we address an analytical framework for capacity analysis of continuous alphabet channels with side information at the receiver. For this purpose, we establish novel necessary and sufficient conditions for weak* continuity and strict concavity of the mutual information. These conditions are used in investigating the existence and uniqueness of the capacity-achieving measures. Furthermore, we derive necessary and sufficient conditions that characterize the capacity value and the capacity-achieving measure for continuous-alphabet channels with side information at the receiver.

In this second part of our two-part paper, we consider the capacity analysis for wireless mobile systems with multiple-antenna architectures. We apply the results of the first part to a commonly known baseband, discrete-time multiple-antenna system where both the transmitter and receiver know the channel's statistical law. We analyze the capacity for additive white Gaussian noise (AWGN) channels, fading channels with full channel state information (CSI) at the receiver, fading channels with no CSI, and fading channels with partial CSI at the receiver. For each type of channels, we study the capacity value as well as issues such as the existence, uniqueness, and characterization of the capacity-achieving measures for different types of moment constraints. The results are applicable to both Rayleigh and Rician fading channels in the presence of arbitrary line-of-sight and correlation profiles.

A sphere packing lower bound and a pairwise error upper bound are derived on error probability of space-time-frequency coded OFDM systems over multiple antenna block-fading channels. These bounds are useful in performance analysis and design of the codes. For example, the sphere packing bound provides a tool to investigate the performance limits of frequency-selective block-fading channels in terms of parameters such as number of antennas, coherence time, coherence bandwidth, delay constraint, and system bandwidth. Also, it can be used to specify the merit of a code in the sense of how far the code performs from fundamental limits. Comparisons with several known results are provided to support this assertion. On the other hand, the pairwise error upper bound can be used as a basis for a unified approach to analysis and design of space-time-frequency codes over any Rician or Rayleigh, block-fading channel in the presence of any type of correlation profile. Expressions for maxima of temporal diversity, spectral diversity, and spatial diversity are derived in terms of the system parameters. It is shown that under certain circumstances, one can not obtain the maxima of all types of diversities jointly. Moreover, the effect of system parameters and channel correlation profile on outage probability is investigated. Specifically, it is shown that unlike the spatial correlation, the temporal and spectral correlation does not affect the ergodic channel capacity (per dimension). However, they increase the variance of instantaneous channel capacity and hence, increase the outage probability.

We prove the uniqueness of the capacity-achieving input distribution for a noncoherent flat-fading channel (Rayleigh or Rician), subject to a second moment constraint. For this purpose, we first show the uniqueness and symmetry of the capacity-achieving output distribution. Then, we establish the assertion by proving that every fading channel is a bijective mapping from the space of symmetric, input distributions to the induced space of symmetric output distributions. This proof is constructive in the sense that for a given symmetric output distribution, one can uniquely determine the input distribution that induced such an output distribution.

We investigate the effect of system parameters on performance limits of space-time-frequency coded OFDM systems over block-fading channels. For this purpose, we obtain a sphere packing lower bound on average word error probability of space-time-frequency codes. This bound not only determines the merit of codes in the sense of error performance, but it also provides a tool to explore the performance limits of system in terms of parameters such as number of antennas, coherence time, coherence bandwidth, delay constraint, system bandwidth, and number of channel taps. It is also shown how these parameters affect the mean and the variance of instantaneous channel capacity, the outage probability, and the maximum achievable diversity of the system.

In this paper, we consider the problem of space-time coding over Rician channels in the presence of spatio-temporal correlation. We derive an upper bound on the pairwise word error probability (PWEP) of space-time codes and use it as a basis for a unified approach to analysis and design of space-time codes over any flat, Rician or Rayleigh, block-fading channel. Based on the statistical properties of a Rician channel, the high-signal-to-noise ratio (SNR) behavior of the bound is either exponential or rational. In the former case, design criteria for space-time codes are based on a Euclidean-distance-like measure. However, in the latter case, design criteria are based on a rank criterion together with a coding gain criterion. The analysis of the bound shows that the performance of rank-deficient codes can be highly degraded in the presence of spatio-temporal correlation, but the performance degradation is not severe for full-rank codes. These codes exhibit robustness against the channel correlation profile. Specifically, for channels with a nonsingular covariance matrix, the asymptotic performance of a full-rank code is proportional to its performance in the independent and identically distributed (i.i.d.) case. In the case that the only constraint on the codewords is a maximum energy constraint, we show that the set of rank-deficient codes forms a proper algebraic subset of measure zero in the affine space of space-time codes. Thus, any randomly selected code is full rank with probability one. Hence, in this case, the main challenge in space-time coding is not maximizing diversity but optimizing coding gain. However, optimizing the coding gain is computationally hard and there exists no satisfactory algorithm to solve this problem in general. On the other hand, when we constrain codewords to be from a finite alphabet or to satisfy particular algebraic structures, e.g., group codes, lattice codes, or coset codes, the problem might be tractable, but rank-deficient codes might be highly probable at high spectral efficiency.

We present a sphere packing bound (SPB) approach to investigate the performance limits of Rayleigh block-fading, multiple antenna systems. Specifically, we derive three sphere packing lower bounds, one tight, one loose, and one approximate, on average word error probability of space-time codes. These bounds provide us with intuition on how system parameters affect the performance limits [M. Fozunbal, S.M. Mclaughlin, and R.W. Schafer, 2002]. It is shown that the performance limits improve significantly for space-time codes that span a larger number of fading blocks. It is shown that the achievable diversity depends not only on the number of antennas and number fading blocks, K, but also on the block length, L, Moreover, it is shown that the block length, L, has a marginal effect on improving the performance limits and it is not possible to achieve arbitrarily small WEP by increasing L.

A sphere-packing bound (SPB) on average word-error probability (WEP) is derived to determine the performance limits of space-time codes on Rayleigh block-fading channels under delay and maximum energy constraints. Two other explicit bounds, a looser bound and a tight approximate bound, are also derived to provide more intuition on how the system parameters affect the performance limits. Moreover, it is shown that as the block length grows to infinity, the SPB converges to the outage probability, and the asymptotic behavior of performance limits is determined by the outage probability.

We present a multi-resolution space carving algorithm that reconstructs a 3D model of a visual scene photographed by a calibrated digital camera placed at multiple viewpoints. Our approach employs a level set framework for reconstructing the scene. Unlike most standard space carving approaches, our level set approach produces a smooth reconstruction composed of manifold surfaces. Our method outputs a polygonal model, instead of a collection of voxels. We texture-map the reconstructed geometry using the photographs, and then render the model to produce photo-realistic new views of the scene.

Motivated by our wavelet framework for error-control coding, we proceed to develop an important family of wavelet transforms over finite fields. Paraunitary (PU) filter banks that are realizations of orthogonal wavelets by multirate filters are an important subclass of perfect reconstruction (PR) filter banks. A parameterization of PU filter banks that covers all possible PU systems is very desirable in error-control coding because it provides a framework for optimizing the free parameters to maximize coding performance. This paper undertakes the problem of classifying all PU matrices with entries from a polynomial ring, where the coefficients of the polynomials are taken from finite fields. It constructs Householder transformations that are used as elementary operations for the realization of all unitary matrices. Then, it introduces elementary PU building blocks and a factorization technique that is specialized to obtain a complete realization for all PU filter banks over fields of characteristic two. This is proved for the 2 /spl times/ 2 case, and conjectured for the M /spl times/ M case, where M /spl ges/ 3. Using these elementary building blocks, we can construct all PU filter banks over fields of characteristic two. These filter banks can be used to implement transforms which, in turn, provide a powerful new perspective on the problems of constructing and decoding arbitrary-rate error-correcting codes.

The primary goal of this paper is to give examples of the recently developed (finite-field) wavelet coding method by studying the encoder and decoder for some half-rate codes. We propose a decoding methodology based on estimating the polyphase components of the channel error pattern. To demonstrate the striking computational savings of the wavelet coding method over alternatives, we show that bounded-distance decoding of the (24,12,8) Golay code requires only weight computations (or at the worst case, it needs a cyclic lookup table of table size 12). The simplicity and computational savings that finite field wavelets offer for the encoding and decoding of wavelet block codes indicate their powerful capacities for error control coding applications.

The recent rapid increase in applications of DSP has generated a need for technical personnel with a DSP background. Until recently, most DSP education has been at the graduate level, so many practicing engineers are developing a need for additional DSP education. At Georgia Institute of Technology, we are delivering an online continuing education course that is targeted at these engineers. The 12-week course is comprised of three interconnected tracks in DSP system theory, real-time implementation principles, and laboratory assignments with MATLAB and the latest fixed-point TI DSP chips. The course was designed after a needs analysis performed by Texas Instruments training specialists. It is intended specifically to provide a full semester's course in a way that is adapted to the schedules and circumstances of practicing engineers. We describe both the content of the course and the technology for delivering it online.

Digital still cameras use a single charge-coupled device (CCD) sensor array and a color filter array (CFA) to sample a full-color image. Thus, the measured image is an interleaving of the subsampled red, green, and blue images. The red and blue images are sampled at a lower rate, so if standard interpolation techniques are used, the reconstructed red and blue images will be missing some high-frequency information and could contain distortions from aliasing. This paper proposes a method of CFA interpolation that combines information from the green image with the subsampled red and blue images to attack these problems. The green high-frequency information is added to the interpolated red and blue images to increase the sharpness of the output and is also used to estimate the aliasing in the interpolated red and blue images, providing a means of reducing the appearance of the aliasing distortions.

Paraunitary filter banks are multi-rate filter realizations of orthogonal wavelet transforms. They are an important subclass of perfect reconstruction filter banks that provide a new framework for error control coding and decoding. This paper undertakes the problem of classifying all paraunitary matrices with entries from a polynomial ring, where the coefficients of the polynomials are taken from finite fields. It constructs Householder transformations that are used as elementary operations for the realization of all unitary matrices. Then, it introduces elementary paraunitary building blocks and a factorization technique that are specialized to obtain a complete realization for all paraunitary filter banks over fields of characteristic two (this is proved for the 2-band case, and a conjecture is applied for the proof of the M-band case, where M/spl ges/3). Using these elementary building blocks, we can construct all paraunitary filter banks over fields of characteristic two.

This paper presents an approach for the effective combination of interpolation with binarization of gray level text images to reconstruct a high resolution binary image from a lower resolution gray level one. We study two nonlinear interpolative techniques for text image interpolation. These nonlinear interpolation methods map quantized low dimensional 2 x 2 image blocks to higher dimensional 4 x 4 (possibly binary) blocks using a table lookup operation. The first method performs interpolation of text images using context-based, nonlinear, interpolative, vector quantization (NLIVQ). This system has a simple training procedure and has performance (for gray-level high resolution images) that is comparable to our more sophisticated generalized interpolative VQ (GIVQ) approach, which is the second method. In it, we jointly optimize the quantizer and interpolator to find matched codebooks for the low and high resolution images. Then, to obtain the binary codebook that incorporates binarization with interpolation, we introduce a binary constrained optimization method using GIVQ. In order to incorporate the nearest neighbor constraint on the quantizer while minimizing the distortion in the interpolated image, a deterministic-annealing-based optimization technique is applied. With a few interpolation examples, we demonstrate the superior performance of this method over the NLIVQ method (especially for binary outputs) and other standard techniques e.g., bilinear interpolation and pixel replication.

For several years, we have been teaching DSP as a first course in electrical and computer engineering at Georgia Tech. Such a dramatic rearrangement of the introductory material requires a new organization of topics and courses when teaching circuits and systems. In addition, the use of computer-enhanced course materials has a profound impact on the systems courses, which are quite mathematical and abstract in nature. This paper addresses some of the issues encountered when adopting a signal processing first approach.

We develop the theory of the wavelet transform over Galois fields. To avoid the limitations inherent in the number theoretic Fourier transform over finite fields, our wavelet transform relies on a basis decomposition in the time domain rather than in the frequency domain. First, we characterize the infinite dimensional vector spaces for which an orthonormal basis expansion of any sequence in the space can be obtained using a symmetric bilinear form. Then, by employing a symmetric, non-degenerate, canonical bilinear form we derive the necessary and sufficient condition that basis functions over finite fields must satisfy in order to construct an orthogonal wavelet transform. Finally, we give a design methodology to generate the mother wavelet and scaling function over Galois fields by relating the wavelet transform to a two channel paraunitary filter bank.

The cosine modulated filter bank is commonly used for the time-frequency decomposition of audio signals. For example, it is a basic element of the MPEG-1 and MPEG-2 audio coding standards. While this filter bank is not perfectly-reconstructing, it does provide for the cancelation of aliasing components that are introduced during the analysis decomposition. If the subband signals are to be processed, care must be taken to preserve the properties of the subband signals such that the aliased terms will be canceled successfully in the synthesis filter bank despite the modification of the subband signals. In this paper, a framework is provided for the generation and application of arbitrary FIR filters to signals that have been decomposed using the MPEG filter bank.

We designed a simple, lossless audio codec, called AudioPaK, which uses only a small number of integer arithmetic operations on both the coder and the decoder side. The main operations of this codec are polynomial prediction and Golomb-Rice coding, and are done on a frame basis. Our coder performs as well, or even better than most lossless audio codecs.

We discuss the problem of reconstruction of a high resolution image from a lower resolution image by a jointly optimum interpolative vector quantization method. The interpolative vector quantizer maps quantized low dimensional 2/spl times/2 image blocks to higher dimensional 4/spl times/4 blocks by a table lookup method. As a special case of generalized vector quantization (GVQ), a jointly optimal quantizer and interpolator (GIVQ) is introduced to find the corresponding code books for the low and high resolution image. In order to incorporate the nearest neighborhood constraint on the quantizer and also to obtain the desired distortion in the interpolated image, a deterministic annealing based optimization technique has been applied. With a small interpolation example, we demonstrate the superior performance of this method over nonlinear interpolative vector quantization (NLIVQ), in which the interpolator is optimized for a given input quantizer.

A nonexpansive pyramidal decomposition is proposed for low-complexity image coding. The image is decomposed through a nonlinear filterbank into low- and highpass signals and the recursion of the filterbank over the lowpass signal generates a pyramid resembling that of the octave wavelet transform. The structure itself guarantees perfect reconstruction and we have chosen nonlinear filters for performance reasons. The transformed samples are grouped into square blocks and used to replace the discrete cosine transform (DCT) in the Joint Photographic Expert Group (JPEG) coder. The proposed coder has some advantages over the DCT-based JPEG: computation is greatly reduced, image edges are better encoded, blocking is eliminated, and it allows lossless coding.

Video coding standards use the block-matching algorithm (BMA) and motion-compensated prediction to reduce temporal redundancies present in image sequences. Block matching is used since it is computationally efficient and produces a minimal representation of the motion field that is transmitted as side information. In order to build a robust coder the motion-estimation technique must be able to track motion in a noisy source. The approach presented in this paper uses spatio-temporal motion prediction, providing an accurate motion estimate even in the presence of noise. With this approach, noisy sources can be compressed efficiently and robustly in standard video coders (e.g., MPEG-1, MPEG-2, H.261, and H.263) with little increase in complexity.

In this paper we describe experiences gained from teaching an introductory electrical engineering course based on digital signal processing rather than the traditional first course in analog circuit theory. We discuss our motivation for teaching DSP first, before covering analog circuits and systems. We describe the style of the course and point out difficulties, as well as advantages, in the organization of basic material. At Georgia Tech and Rose-Hulman, this beginning course has been required of all computer engineering majors. Finally, we make some comments about extending this approach to encompass a wider range of students from other disciplines.

The MPEG audio standard has recently gained popularity for compressing high quality audio signals. In general, modifying or mixing MPEG signals requires decoding the MPEG signals into time-domain signals, processing the time-domain signals, and re-encoding the processed signals. In this paper, we present a psychoacoustically-based method for processing MPEG signals that eliminates significant portions of the encoding and decoding processes, resulting in reduced computational cost while maintaining perceptual audio quality.

Motion estimation plays an important role in video coding schemes by removing temporal redundancies that exist in image sequences. Motion information that is required in motion compensated prediction is transmitted as side information, as in forward motion estimation, or can be computed at the receiver in backward motion estimation. The former method has the advantage of more accurate prediction but, suffers in that the motion information is transmitted as side information. We introduce the motion transform (MT), a new motion estimation and compensation technique that does not require the transmission of motion vectors yet, performs well under a variety of conditions. In the proposed method, motion information is obtained in a bottom-up hierarchical fashion using a two-dimensional wavelet-like decomposition. By using a nonlinear non-expansive filter bank a hierarchical decomposition of the image allows coarse-to-fine motion compensation at the decoder without motion vector transmission.

This paper treats the problem of establishing bounds for the morphological filter by reconstruction class. Morphological filters by reconstruction, which are composed of openings and closings by reconstruction, are useful filters for image processing because they do not introduce discontinuities. The main contributions of this paper are: (a) to establish when the combination of openings by reconstruction is an opening by reconstruction (similarly for closing by reconstruction), and (b) to establish, for any filter by reconstruction, upper and lower bounds that are respectively a closing by reconstruction and an opening by reconstruction.

Perfect reconstruction (PR) filter banks have found numerous applications, and have received much attention in the literature. For linear filter banks, necessary and sufficient conditions for PR have been established for most practical situations. Recently, nonlinear filter banks have been proposed for image coding applications. These filters are generally simple, and produce better results than linear filters of same complexity. Nevertheless, the lack of general PR conditions limits these filters to cases where one of the filters is the identity. In this paper, we present a framework that allows, for the first time, the design of PR nonlinear filter banks including (non-trivial) filters on all channels. Although the framework does not include all nonlinear PR filter banks, it does include all previously published nonlinear filter banks, as well as all linear ones. This framework suggest new possibilities for the design of nonlinear PR filter banks.

A new digital signal processing (DSP) course designed to build students intuition about signals and systems is presented. The course makes extensive use of multi-media demonstrations to relate real-world signals and discrete-time systems to their mathematical descriptions. In addition to the numerous in-class demonstrations, weekly laboratory exercises have been developed to further strengthen the ties between DSP theory and real-world signals and systems. Many of the in-class demonstrations have been captured on the World Wide Web (WWW), so the students can explore them outside of class. In the near future, the WWW-based demonstrations will be packaged on a CD-ROM as an integral part of a new text.

Video coding standards use motion compensated prediction to reduce temporal redundancies. In general this is performed by computing motion vectors for predefined regions in the image (rectangular blocks), and transmitting these vectors as side-information. The motion transform (MT) provides a new motion compensation technique that does not require the transmission of motion vectors and yet, performs as well as forward motion estimation for many image sequences. In the MT, motion information is obtained in a bottom-up hierarchical fashion using a two-dimensional nonlinear filter bank. In this paper we elaborate on MT implementation details and discuss a new variation of the MT. Results obtained using MTs on typical image sequences are compared to results for the full search block matching algorithm (BMA).

This paper describes a new program in Digital Image Systems Science and Engineering that has just been initiated with the assistance of a grant from the Hewlett-Packard Company. This new initiative seeks to provide a coherent educational program in digital image systems that is readily accessible to students in electrical and computer engineering, computer science, and other technical fields. A key feature of the program is the extensive use of computer technology to provide hands-on laboratory experience, classroom demonstrations, and on-line educational support materials.

This paper introduces a class of rank-order-based template matching criteria that are multiplier-free and independent of the dc variations of the image. The core component of these criteria is a grayscale morphological hit-or-miss transform (GHMT). Experimental results show that the GHMT features sharp and robust indications in the presence of Gaussian noise. The idea of the GHMT is used to develop more general forms of matching criteria that are robust to both Gaussian and impulsive noises.

Sampling and reconstruction are usually analyzed under the framework of linear signal processing. Powerful tools like the Fourier transform and optimum linear filter design techniques, allow for a very precise analysis of the process. In particular, an optimum linear filter of any length can be derived under most situations. Many of these tools are not available for non-linear systems, and it is usually difficult to find an optimum non-linear system under any criteria. The authors analyze the possibility of using non-linear filtering in the interpolation of subsampled images. They show that a very simple (5/spl times/5) non-linear reconstruction filter outperforms (for the images analyzed) linear filters of up to 256/spl times/256, including optimum (separable) Wiener filters of any size.

Pyramid image coding is a natural coding scheme for applications where progressive transmission is desired. In this kind of coder, versions of the original image at several resolution levels are formed by successive filtering and subsampling. Then, beginning from the coarsest image, the image is used to produce an estimate for the next (higher resolution) level and the error is coded and transmitted. While expansive pyramids (e.g., Burt's Laplacian pyramid) are usually less efficient, non-expansive pyramids tend to produce ringing (e.g., subband/wavelet) and/or blocking (e.g., DCT). We introduce a non-expansive pyramid that does not, produce ringing or blocking effects. Instead, the main artifact is texture removal. The simulations have produced images with entropies in the range of 0.2 to 1.5 bpp, with SNR figures similar to or better than JPEG at equivalent rates. The proposed coder has several attractive features, including 8 bit integer operations only, a perfect reconstruction mode, progressive transmission and an interesting progressive computation property.>

The paper extends Kosravi and Schafer (1994) which introduced the notion of normalized min correlation (NMC) as a new criterion for template matching applications. The NMC features low complexity and robustness with respect to Gaussian noise. It is also independent of the local average of the image, which is a desired property in many template matching applications. However, its sensitivity to impulsive noise increases with the size of the template. The paper introduces two different modifications of the NMC which are robust with respect to both Gaussian and impulsive noise. The performance of the new modifications are examined in motion estimation applications. As a different way of looking at the NMC, the notion of grayscale hit-or-miss transform is introduced. This is an extension of the binary hit-or-miss transform to grayscale.>

Previous research has shown that the homomorphic filtering procedure combined with analysis-by-synthesis excitation coding is a promising alternative to linear predictive coding (LPC) for low bit rate vocoding. In particular, static vector excited and dynamic vector excited homomorphic vocoders have been designed. In this work, the performances of recently developed homomorphic vocoders are evaluated through formal subjective listening tests, using a variation of the paired acceptability rating method. The subjective test results show that the vocoder framework using analysis-by-synthesis excitation analysis is capable of producing good speech quality at 4.8 kb/s or lower.>

An iterative algorithm for computing a family of piecewise-constant approximations of images in scale space with variable resolution is presented. The algorithm is a modification of an iterative adaptive smoothing algorithm proposed by P. Saint-Marc et al. (1991). The modification improves the behavior of the algorithm when weak edges are present in the image. Edge information computed from the image is incorporated into the adaptive smoothing approach. The added iterative step does not introduce a significant amount of computation, and the employment of only local operators makes it well suited for a parallel hardware implementation. The edges extracted must be two pixels wide and exhibit high connectivity. A morphological edge operator is presented to fulfil these requirements.>

A theoretical lower bound on the number of points required in the decomposition of morphological structuring elements is described. It is shown that the decomposition of an arbitrary N-point structuring element will require at least (3 ln N/ln 3)points. Using this lower bound it is possible to find the optimal decompositions (in terms of the minimum number of unions or the minimum number of points) for all one-dimensional connected line segments. L-dimensional rectangles may be decomposed by optimally decomposing the L one-dimensional line segments that describe the rectangle.>

An efficient dynamic excitation modeling which emphasizes either the pitch-dependent periodic nature or the more random nature of the sound sources depending on the voicing state of the speech signal is applied to the homorphic vocoder. In this excitation modeling scheme, the cepstral peak value is used as the basis for classifying a given speech segment into three different classes: voiced, unvoiced, and mixed. Different excitation modeling strategies are used for the different classes. The algorithm is simulated, and clear improvement in the speech quality is shown.>

A LISP based system is described for performing the automatic manipulation and analysis of morphological expressions. The system is capable of four types of symbolic manipulations: expression simplification, equivalent-form generation, signal-property analysis, and dual-form generation. The different types of knowledge that need to be represented in such a system include morphological system knowledge, signal and structuring element knowledge, and knowledge about the interaction of signals and morphological systems. As integral components of the analysis system, signals and structuring elements are represented by abstract classes which are distinguished by their properties. In addition, actual structuring elements are also represented and may be used with both abstract signals and abstract structuring elements. The interaction of signals, structuring elements, and systems is determined by a collection of morphological rule bases.>

The basic theory and applications of a set-theoretic approach to image analysis called mathematical morphology are reviewed. The goals are to show how the concepts of mathematical morphology geometrical structure in signals to illuminate the ways that morphological systems can enrich the theory and applications of multidimensional signal processing. The topics covered include: applications to nonlinear filtering (morphological and rank-order filters, multiscale smoothing, morphological sampling, and morphological correlation); applications to image analysis (feature extraction, shape representation and description, size distributions, and fractals); and representation theorems, which shows how a large class of nonlinear and linear signal operators can be realized as a combination of simple morphological operations.

A novel homomorphic vocoder producing good quality speech at 4.8 kb/s is presented. In this homomorphic vocoder framework, the real cepstra containing vocal tract information are vector quantized and the excitation signals are obtained applying an analysis-by-synthesis method using a weighting filter which is derived from the cepstrum. Informal listening tests show that this vocoder is fully competitive with the code-excited linear predictive coder in producing good-quality speech at 4.8 kb/s.>

Burg's maximum entropy method has been used with success in spectral estimation. This paper is an attempt to generalize the maximum entropy method to the deconvolution of positive signals from a finite set of linear measurements. In this paper, we also investigate the existence of a solution to the deconvolution problem using a geometric approach. By formulating the deconvolution problem as an unconstrained optimization problem, our procedure will provide the maximum entropy deconvolved positive signal when it exists. Otherwise, the algorithm diverges.

This paper summarizes some applications of morphological erosions, dilations, openings, and closings to image edge-detection, cleaning of impulsive-noise, median-filtering, region-filling, skeletonization, and 2-D shape recognition.

This paper introduces different types of nonstationary constrained iterative image restoration algorithms. The adaptivity of the algorithm is introduced by the constraint operator which incorporates properties of the response of the human visual system. The properties of the visual system are represented by noise masking and visibility functions. A new way of computing the masking function is also introduced. The proposed algorithms are general and can be used for any type of linear constraint and distortion operators. The algorithms can also be used to restore signals different than images, since the constraint operator can be interpreted as adapting to the local signal activity.

This paper introduces a general formulation of constrained iterative restoration algorithms in which deterministic and/or statistical information about the undistorted signal and statistical information about the noise are directly incorporated into the iterative procedure. This a priori information is incorporated into the restoration algorithm by what we call "soft" or statistical constraints. Their effect on the solution depends on the amount of noise on the data; that is, the constraint operator is "turned off" for noiseless data. The development of the new iterative algorithm is based on results from regularization techniques for stabilizing ill-posed problems.

This paper presents a summary of a unified theory, based upon mathematical morphology, of all translation-invariant and increasing systems. Examples of such systems are morphological transformations of signals, order-statistics filters and some linear shift-invariant filters. Our theoretical research showed that every such system can be uniquely represented by the minimal elements of its kernel and realized as a minimal combination of morphological erosions.

This paper introduces a new iterative image restoration method which is capable of restoring noisy, blurred images by incorporating a priori knowledge about the image and noise statistics into the iterative procedure. The iteration equation consists of a prediction part which is based on a noncausal image model description and an innovation part which is weighted by a gain factor. The gain is computed using a linear MSE optimization procedure and is updated at each step of the iteration. This image restoration scheme can be interpreted as an iterative procedure with a statistical constraint on the image data.

This paper reports on a preliminary study of applying single-channel (scalar) and multichannel (vector) 2-D linear prediction to color image modeling and coding. Also, the novel idea of a multi-input single-output 2-D ADPCM coder is introduced. The results of this study indicate that texture information in multispectral images can be represented by linear prediction coefficients or matrices, where as the prediction error conveys edge-information. Moreover, by using a single-channel edge-information we obtained, from original color images of 24 bits/pixel, reconstructed images of good quality at information rates of 1 bit/pixel or less.

This paper presents a preliminary study on using Mathematical Morphology to represent and code a binary or a grey-tone image by parts of its skeleton, a thinned version of the image. An image can be uniquely decomposed into skeleton components, and then reconstructed by dilating these components. Since, for a certain category of imagery, the skeleton components possess a lower entropy than the original image, a run-length or entropy coding scheme can be used to achieve representation or transmission of the image at a lower information rate than originally required.

We use the lossy electric transmission-line analog model of the vocal tract to study the acoustics of speech produced in a hyperbaric helium-oxygen atmosphere. The analysis extends previous work by including more completely the effects of the wall vibration, glottal, and radiation impedances, and by analyzing the formant bandwidths and amplitudes in addition to the formant frequencies. It shows that (1) the classic Fant and Lindquist formula somewhat overstates the formant frequency shift when glottal and radiation effects are included; (2) the lower formant bandwidths increase by much more than commonly assumed; and (3) the upper formant amplitudes are higher relative to the lower formants in helium speech than in normal speech. These results are useful in developing advanced helium speech enhancement algorithms.

This paper describes a study that has been conducted on potential ways of estimating a signal coming from a specific source in a noisy reverberant room. That is, the desired signal is corrupted by reverberation and also signals coming from other sources, which may have similar spectral or statistical characteristics to the desired signal. By using an array of microphones and minimizing the effects of the undesired sources with the LMS algorithm, some significant improvements can be made. The results of some computer simulations will be presented, and their application to "in-situ" acoustic noise measurements will be discussed.

The extrapolation of a bandlimited signal from observations taken over a finite interval is an important problem in applications such as spectral estimation and image processing. The extrapolation of bandlimited analog signals is fundamentally different, however, from the band-limited extrapolation of discrete time sequences. Specifically, as has been previously noted, a unique solution to the discrete problem does not exist. In this paper, this fact is demonstrated in a new and convincing way. In particular, two methods are presented for constructing a sequence which, in the frequency domain, is band-limited to an arbitrary cutoff frequency and which, in the time domain, is equal to zero over an interval of arbitrary length. The importance of the existence of these multiple solutions to the general extrapolation problem is emphasized and questions are raised regarding the need for additional constraints in the discrete band-limited extrapolation problem.

This paper analyses the error behavior of iterative deconvolution algorithms when the distorting system has a frequency response that has negative real part or has a finite number of isolated zeros. The existence of these zeros at a finite number of discrete frequencies results in an inability of the deconvolution algorithm to restore the lost information at these frequencies with a small number of iterations. A new algorithm is suggested that incorporates multiple distorted versions of the signal and results in a restoration error that approaches zero with a small number of iterations.

This paper is concerned with the use of 2-D linear prediction for image segmentation. It begins with a brief summary of the mathematics involved in 2-D linear predictive analysis of arbitrarily-shaped regions. Then, it introduces a 2-D LPC distance measure based on the error residual of 2-D linear prediction. Finally, it describes how the above results can be applied to image segmentation using a simple cluster seeking algorithm. The results indicate that arbitrarily-shaped image regions can be well identified and clustered using as features their 2-D LPC parameters.

From a single transient test we determine all of the parameters of a vented-box loudspeaker system. A complete electroacoustical circuit representation is thus obtained from the time-domain test using digital signal processing techniques. First, we apply the pencil-of-functions technique [5] to the digitally recorded response and determine the impedance-function coefficients of the circuit. Next, using the relationships between the impedance coefficients and the circuit parameters, we show that every circuit parameter can be computed without resorting to simultaneous nonlinear equations.

This paper is a preliminary report on a study of the application of two-dimensional linear prediction in image quantization. The study has focused on three major concerns: implementation of an adaptive linear predictor, adaptive quantization of the prediction error signal, and the adaptive predictive coding of density (logarithm of intensity) images. The results of the study indicate that through the use of adaptive prediction and quantization, a high level of image fidelity can be obtained for both intensity and density images at information rates well below one bit/pixel.

In this paper the problem of contrained deconvolution is related to the minimization of a functional. By applying the conjugate gradient algorithm of optimization theory to this minimization an efficient iterative algorithm for deconvolution is developed. This algorithm is then extended to perform constrained deconvolution and the performance of the new algorithms is compared with other published algorithms.

In a recent paper a time-domain method for the measurement of the parameters of a loudspeaker-driver was described. Here we extend the technique to the more interesting problem of measuring the parameters of a vented-box loudspeaker system. We use the pencil-of-functions technique, and show that all of the loudspeaker system parameters can be determined straightforwardly from a single time-domain test. Results of computer simulation, demonstrating the effectiveness of the two-step approach, namely, identification of the impedance function by pencil-of-functions method and therefrom the computation of the physical parameters, is given in the paper. Results of experimental studies are expected to follow in the future.

A new method for the measurement of the Thiele-Small small-signal parameters of a loudspeaker driver is described. The technique is based on an analysis of the time domain voltage response of the voice coil circuit to a current step of excitation. It is demonstrated that the method can be implemented with a digital computer using the technique of linear predictive analysis. The method is simple and can be implemented with a micro-processor configuration.

There has recently been considerable interest in iterative deconvolution algorithms. Some of these algorithms seek to improve performance by incorporating á priori knowledge of the components of a convolution. For example, incorporation of both positivity and finite interval constraints tends to automatically introduce an extrapolation of the bandwidth. A question which naturally arises concerns the effect of noise on the performance of such algorithms. In this paper we describe an experimental evaluation of the effect of noise using synthetic data. Results of extensive tests are presented and some suggestions for mitigating the effects of noise are offered.

In a pulsed-doppler radar system the return signal is naturally viewed as a sequence of samples of one or more complex sinusoids plus noise. We have studied several digital processing techniques for estimating a short-time spectral representation of such signals as well as digital techniques for estimating the frequency of a single dominant spectral component. Techniques considered include: (1) Discrete short-time Fourier analysis followed by peak-picking and median smoothing to remove errors. (2) Short-time maximum entropy spectrum estimation incorporating adaptive noise suppression. (3) A new recursive algorithm based on recursive computation of the short-time auto-correlation function. The relative merits of each technique are discussed and examples of performance are given.

The purpose of this study was to assess the effects of LPC/CVSD tandem connections and to investigate ways of improving performance. In the case of the CVSD-to-LPC connection, the CVSD quantizing noise severely affects the estimate of LPC coefficients, thereby distorting the spectral representation. An averaging technique was shown to reduce the average spectral distance from the noiseless case; however, no statistically significant perceptual advantage was measured. In the LPC-to-CVSD connection, it was found that modest improvements can be measured both in signal-to-noise ratio and perceptually, by modifying the phase in LPC synthetic speech before CVSD coding.

It is shown that a number of well known iterative deconvolution algorithms are closely related members of a general class. This point of view leads to new understanding of previous approaches and to a new algorithm that incorporates both a finite interval constraint and a positivity constraint on the output of the deconvolution process. Examples are given to illustrate performance on gamma-ray spectra.

When speech is coded using a differential pulse-code modulation system with an adaptive quantizer, the digital code words exhibit considerable variation among all quantization levels during both voiced and unvoiced speech intervals. However, because of limits on the range of step sizes, during silent intervals the code words vary only slightly among the smallest quantization steps. Based on this principle, a simple algorithm for locating the beginning and end of a speech utterance has been developed. This algorithm has been tested in computer simulations and has been constructed with standard integrated circuit technology.