A highly efficient 2D convolutional algorithm based on the Discrete Hirschman Transform (DHT), known as DHT-Conv, has recently been developed. This method demonstrates superior performance compared to FFT-based convolution (FFT-Conv) in terms of computational complexity. In this paper, we implement DHTConv on Field Programmable Gate Arrays (FPGA) and evaluate its hardware performance on both Altera and Xilinx FPGA devices. The results from the Altera device indicate that our DHTConv significantly outperforms FFT-based convolution, yielding over 22% savings in real computations and approximately 5% in latency. Additionally, the results from the Xilinx FPGA board show that DHTConv requires fewer hardware resources compared to FFTConv, achieving over 16% savings in LUTs, 48% savings in flip-flops, and 61% savings in DSP blocks.

The Fast Fourier Transform (FFT)-based convolution is the most popular fast convolution algorithm. In past work, we developed the Discrete Hirschman Transform (DHT)-based convolution. When compared to the FFT-based convolution, our DHT-based convolution can reduce the computational complexity by a third. Recently, we developed a comprehensive DFT algorithm where every calculation is natively real-valued (RV) dot products. In this paper, we first apply the natively real-valued DFT to linear convolution. We call this method the RV-based convolution. The arithmetic analysis reveals that it efficiently reduces the operation counts. The algorithm is fast regardless of length.

Because mathematics classes are often taken at different locations, including high schools and 4-year schools, the math background of students in introductory electrical & computer engineering classes can vary significantly. We have addressed this by a careful restructuring of the circuits course “Intro to EE” taken by computer engineering students, as well as students in other non-EE majors. This course covers DC circuits, information circuits (filters), and AC circuits. These topics introduce material that is covered in multiple courses required for EE students. We have structured this course so that we cycle through analysis techniques for each type of circuit, which allows students to reinforce their previous knowledge. AC circuits are covered as a special case of information circuits. We have published an e-book that we have used for several years. The format of the e-book allows us to include video, interactive questions, and most importantly detailed examples that include even minor steps. We are exploring options for moving our textbook content to a standalone e-book to be used with a Learning Management System (LMS), such as canvas. The restructuring of the course to focus on fundamentals supports student success and early identification of weaknesses in math backgrounds.

With the best basis function that compactly describes a discrete-time signal, the Discrete Hirschman Transform (DHT) has been proved to perform better than the Discrete Fourier Transform (DFT) in terms of high resolution and computational complexity. It is reasonable to develop fast algorithms for the DHT computation since the DHT has applied to multiple signal processing applications. In this letter, we propose a split-radix DHT (SRDHT) including mathematical decomposition and comparison of computation complexity. The SRDHT is computationally superior to the DFT and performs more efficiently than our previously developed radix-2/-4 DHTs, with further reduced arithmetic operations. We regard this proposed SRDHT as a more attractive candidate to compute the DHT for those existing and future Hirschman-based applications.

The Discrete Hirschman Transform (DHT) is more computationally attractive than the Discrete Fourier Transform (DFT). Based on its derived linear convolution, we have confirmed that the DHT-based convolution filter shows its superiority in reducing computations conditionally, while compared with the conventional DFT-based convolution filter in our previous work. Since the DHT-based convolution has many configurations depending on parameter choices, we conjecture that there should be an optimal case for the largest reduction in computations. In this paper, for the DHT-based convolution, we express the requirement in real computations and propose an approach of how to determine the optimal parameters to reduce computations. We further compare the computational load of the optimal DHT-based convolution with that of other popular convolutions. Moreover, its reduction in clock cycles has also been estimated using a Digital Signal Processor (DSP) TMS320C5545. Results indicate that the optimal DHT-based convolution can reduce real computations (multiplications by 9.09%-50% and additions by 1.12%-51.09%) and clock cycles, according to the input length and filter size, except for some cases with identical performance to the radix-2 FFT-based competitor.

A Fast linear convolution algorithm based on the Discrete Hirschman Transform (DHT) provides increased hardware flexibility and reduced computational complexity compared to those based on the Fast Fourier Transform (FFT). This DHT convolution can be realized by block-processing filters. We propose a hardware-efficient structure to implement the DHT convolution filter. A digital data example is used to discuss its improvement in computational complexity. Observation indicates that our proposed DHT convolution filter either enjoys the same peak performances as its FFT competitor, or even reduces more computational load with a slightly larger output size. This performance can be further enhanced using alternative DHT-based methods.

The efficiency can be significantly improved if the attacker uses interesting points to perform Correlation Power Analysis (CPA). The prerequisite for this is that the attacker knows the positions of interesting points. However, it is difficult for the attacker to accurately find the locations of interesting points if he only has a small number of power traces. In this paper, we propose a Frequency based Interesting Points Selection algorithm (FIPS) to select interesting points under the condition that the attacker only has a very small number of power traces. Moreover, an error tolerant Single Interesting Point based CPA (SIP-CPA) is proposed. Experiments on AES algorithm implemented on an AT89S52 single chip and power trace set of DPA contest v1 of DES algorithm implemented on the Side Channel Attack Standard Evaluation Board (SASEBO) show that, our SIP-CPA can significantly improve the efficiency of CPA.

In [1] we developed a new uncertainty measure which incorporates Rényi entropy instead of Shannon entropy. This new uncertainty measure was conjectured to be invariant to the Rényi order α > 0 for the case of the optimizer signals of Hirschman Uncertainty (Picket Fence functions whose lengths are a perfect square). In this paper, we prove this invariance, and test whether this invariance is predictive in the problem of a simple texture classification for digital images. In the preliminary results, we find that it certainly influences the recognizer performance. Specifically, we find that the recognition performance does not depend significantly on the Rényi parameter α. We hope that these results will be extended to other problems where Rényi entropy is used.

The traditional Heisenberg-Weyl measure quantifies the joint localization, uncertainty, or concentration of a signal in the phase plane based on a product of energies expressed as signal variances in time and in frequency. Unlike the Heisenberg-Weyl measure, the Hirschman notion of joint uncertainty is based on the entropy rather than the energy [1]. Furthermore, as we noted in [2], the Hirschman optimal transform (HOT) is superior to the discrete Fourier transform (DFT) and discrete cosine transform (DCT) in terms of its ability to resolve two limiting cases of localization in frequency, viz pure tones and additive white noise. We found in [3] that the HOT has a superior resolution to the DFT when two pure tones are close in frequency. In this paper, we improve on that method to present a more complete spectral analysis tool. Here, we implement a stationary spectral estimation method using compressive sensing (in particular, Iterative Hard Thresholding) on HOT filterbanks. We compare its frequency resolution to that of a DFT filterbank using compressive sensing. In particular, we compare the performance of the HF with that of the DFT in resolving two close frequency components in additive white Gaussian noise (AWGN). We find the HF method to be superior to the DFT method in frequency estimation, and ascribe the difference to the HOT's relationship to entropy.

The traditional Heisenberg-Weyl measure quantifies the joint localization, uncertainty, or concentration of a signal in the phase plane based on a product of energies expressed as signal variances in time and in frequency. Unlike the Heisenberg-Weyl measure, the Hirschman notion of joint uncertainty is based on the entropy rather than the energy [1]. Furthermore, its definition extends naturally from the case of infinitely supported continuous-time signals to the cases of both finitely and infinitely supported discrete-time signals, and, as we noted in [2], the Hirschman optimal transform (HOT) is superior to the discrete Fourier transform (DFT) and discrete cosine transform (DCT) in terms of its ability to separate or resolve two limiting cases of localization in frequency, viz pure tones and additive white noise. In this paper we implement a stationary spectral estimation method using an orthogonal matching pursuit method whose dictionary members are constructed from the combination of HOT-based and DFT atoms (elements) [3] in combination with the interpolating procedure developed in [4]. We call the resulting algorithm the smoothed HOT-DFT periodogram. We compare its performance (in terms of frequency resolution) to Quinn's smoothed periodogram. In particular, we compare the performance of the HOT-DFT with that of the DFT in resolving two close frequency components in additive white Gaussian noise (AWGN). We find the HOT-DFT to be superior to the DFT in frequency estimation, and ascribe the difference to the HOT's relationship to entropy.

Traditional techniques for damage detection in civil infrastructures that are based on the global vibration response of the system are limited in their capabilities to detect damage. Because damage detection based on the global vibration response relies on global parameters to describe the dynamic behavior of local structural elements, it suffers from limiting factors such as poorly-formed aggregate system models, very low signal to noise ratio, unrealistic boundary conditions. An alternative to the use of global detection techniques is the use of an adaptive local analysis technique based on the local response of the structure. This is achieved using wavelet packet decomposition at the sensor outputs and interpreting this decomposition as a subband framework for a bank of adaptive beamformers. The beamformer adaptive processors guaranties the maximization of the output SNR and in the same time allows for spatial selectivity and a highly directive vibration response in the structure. Scanning the structure over time produces a detailed vibration signature of the structure. The structural damage can be localized with high probability by comparing two vibration signatures before and after the damage occurs.

This paper proposes a causal approach to adaptive estimation of time-frequency localized signals using Adaptive Notch Filters (ANF). By adaptively estimating the envelope of each sinusoidal component, it is possible to specify the tracking quality and restart the ANF unit whenever the tracked sinusoid disappears, as well as preventing the ANF from ldquotrackingrdquo non-existent sinusoids (the frequency mis-lock situation). Employing multiple ANFs allows an efficient approach to tracking time-frequency localized signals such as speech.

In this paper a new block LMS algorithm is introduced. This algorithm is based on a fast HOT convolution developed by our group. We call our algorithm the block HOT-DFT LMS algorithm. Our algorithm uses the premise that the filter size is much smaller than the block size. Our developed algorithm is very similar to the block DFT LMS algorithm, but provides a reduced computational complexity of about 30%. The computational efficiency of the block HOT-DFT LMS algorithm is verified and its convergence analysis is analyzed.

We propose in this paper a novel modification of the popular Adaptive Notch Filter (ANF) to improve the tracking of time-varying frequencies. Unlike previous algorithms, our new method incorporates a modeling of frequency variation directly into the cost minimization procedure. Our results show a notable improvement in the frequency estimation performance over earlier methods, and comparisons over a few examples show the general effectiveness of our approach.

In this paper, we derive a "convolution theorem" suitable for the Hirschman optimal transform (HOT), a unitary transform derived from a discrete-time, discrete-frequency version of the entropy-based uncertainty measure first described by Hirschman (1957). We use the result to develop a fast block-LMS adaptive filter which we call the HOT block-LMS adaptive filter. This filter requires slightly less than half of the computations that are required for the FFT block-LMS adaptive filter. The simulations show that the convergence rates of both the HOT and FFT block-LMS adaptive filters are similar.

A new approach for the clear air velocity estimation in weather radar is presented. A combination of nonparametric with parametric spectral analysis allows us to identify and extract multiple processes caused by different scatterer types within a single radar resolution volume. An example of clear air observed using an S-band dual polarization radar is presented. Heretofore, migrating birds and wind-blown insects that are mixed within each resolution volume caused such data to be unusable for meteorological interpretation. In this paper, we construct power spectral densities of polarimetric variables. We use the polarimetric spectral densities to differentiate the scatterer types within the observed radar resolution volume. We demonstrate how our combination of non-parametric and parametric spectral analysis can be used to retrieve the true wind velocity in situations with severe contamination by biological scatterers.

Adaptive filter implementations require real-time conversion of coefficients to canonical signed digit (CSD) or similar representations to benefit from multiplierless techniques for implementing filters. Multiplierless approaches are used to reduce the hardware and increase the throughput. This paper introduces a novel hardware implementation method that converts two's complement numbers to their CSD representations using a fixed number of shift and logic operations. As a result, we can greatly reduce the power consumption and area requirements for hardware implementation of DSP algorithms in which coefficients are not known a priori. Because all CSD digits are produced simultaneously, the conversion speed and thus the throughput are improved when compared to overlap-and-scan techniques such as Booth's recoding.

Echoes detected by polarimetric weather radar in clear air contain signals from air and biological scatterers. Discriminating the various scatterer types from a composite echo is challenging due to variability in scatterres' quantity, azimuthal dependences of their polarimetric properties, and uneven mixing in resolution volumes. We use polarimetric spectral densities to estimate the volume content by constructing two dimensional (2D) histograms. The dimensions used to form image are Doppler velocity and polarimetric variable. The assimilation of these histograms in azimuth results in a 3D-azimuthal-spectral-histogram (3DASH). This representation allows us to use transparency for small occurrences to visualize the 3D-signatures of dominant content. The scatterer types have distinguishable signatures in 3DASH due to their diverse physical shapes, scattering properties, different headings, and speeds. 3DASH can help to understand what constitutes the polarimetric averages of the resolution volume. 3DASH can help provide resources for establishing intrinsic polarimetric values/functions for different types of biological scatterers, which are necessary for scatterer classification algorithms.

Implementation of digital signal processing (DSP) algorithms in hardware, such as field programmable gate arrays (FPGAs), requires a large number of multiplications. In this paper, we introduce a novel multiplier structure that converts from 2's complement to canonical signed digit (CSD) representation in real time. The proposed algorithm increases the number of zero partial products (which can be simplified by shift operations) to approximately 66.7% compared with 50% for modified Booth's recoding. Also, the proposed hardware structure reduces the non-zero partial products to a minimum, and consequently the number of arithmetic operations in the carry-save structure is reduced. So, our proposed hardware decreases both the time required for multiplication and the power consumption of the multiplier. Furthermore, because the proposed structure uses real time CSD recoding, and does not require a fixed value for the multiplier input to be known a priori, the proposed multiplier can be used to implement digital filters with non-fixed filter coefficients, such as adaptive filters.

The adaptive Volterra filter has been successfully applied in nonlinear acoustic echo cancellation (AEC) systems and nonlinear line echo cancellation systems, but its applications are limited by its required computational complexity and slow convergence rate, especially for systems with long memory length. In this paper, by leveraging a multi-channel configuration of the Volterra filter and the sampling theory for nonlinear systems, we extend linear sub-band delay-less adaptive filter techniques to develop an efficient sub-band implementation of the adaptive Volterra filter. The developed sub-band configuration of the adaptive Volterra filter can greatly improve the convergence rate and reduce the computational complexity of nonlinear echo cancellers, which is shown by analyses and simulations.

In this paper, we discuss the sub-space based blind nonlinear channel equalization problem. The conditions required for exciting the zero force equalizer and an MMSE equalizer based on the sub-space algorithm are given. Using these conditions, we propose several efficient sub-space-based blind nonlinear channel equalization algorithms. These provide: 1) a blind zero force equalizer for a nonlinear channel whose linear portion has maximum memory length, 2) an MMSE equalizer for a nonlinear channel whose nonlinear distortion is weak and 3) an MMSE equalizer for a nonlinear channel whose linear part has minimum memory length while the inputs to the linear and nonlinear parts are uncorrelated to each other. Our proposed algorithms are more efficient than currently available methods and work over a broader range of channels. As a result, our algorithms have significant practical application.

Most available control algorithms for active noise control (ANC) require identification of the secondary path. This estimation not only increases the control system complexity, but it can add to the residual noise power and even cause the adaptive system to diverge when the identification is not sufficiently close to the real system. We use a geometrical analysis of the filtered-x LMS algorithm to introduce a new ANC algorithm for a single frequency and narrowband noise where no identification of the secondary path is required. We then extend our new ANC algorithm without secondary path identification to the active control of broadband noise through the use of a sub-band ANC implementation. When compared to other available control algorithms requiring no secondary path identification, our method possesses a simple structure, good performance, and a reasonable convergence rate. Simulation results confirm the effectiveness of our proposed algorithms.

We describe a new gust front detection method using functional template correction (FTC) and entropy. The new method provides better boundaries than does a previously developed method by our group (V. DeBrunner and E. Matusiak, 2003). Our proposed method described in this paper requires only one template for detection, thereby reducing the computational complexity and so yielding an algorithm that is more suitable for real time detection than that previously developed one.

In this paper we propose a novel image restoration method that effectively combines a particle filter with wavelet shrinkage to achieve robust performance against inhomogeneous noise mixtures. Specifically, the particle filter acts to suppress outlier-rich components of the noise while, in a subsequent step, the wavelet domain shrinkage attenuates any remaining, less heavily tailed noise components. We present late breaking preliminary examples demonstrating excellent rejection of salt-and-pepper like Cauchy noise mixed with additive white Gaussian noise (AWGN). Although limited in scope, these preliminary results suggest that the combination of particle filters with more traditional restoration techniques is a powerful approach that can provide a new dimension of flexibility for addressing noise mixtures involving difficult nonlinear and non-Gaussian components.

The constrained minimum output variance method (CMOV), which is also known as the constrained minimum output energy method (CMOE), has been applied to directly blind equalize a linear channel and proven effective with white inputs (Tsaisanis et al. (1999)). It is believed that the method introduced in Tsaisanis can work for a linear system with colored source. In this paper, we correct this misunderstanding, and prove that a colored input will cause the equalizer to incorrectly converge. Consequently, we introduce a new blind channel equalizer algorithm based on the CMOV, but with different constraints. Our proposed algorithm works for channels with either white or colored input, and performs equivalently to the trained minimum mean-square-error (MMSE) equalizer under high SNR. Our proposed algorithm may be regarded as a generalized version of the CMOV in Tsaisanis. However, unlike CMOV, the proposed method exploits the input sequence statistics. As a result, the proposed method performs better than the original CMOV even when the input is white.

We derive the minimum entropy estimation (MEE) method from information theory to show the similarity of this method to the maximum likelihood method for the linear regression problem. The result is a nonparametric-based identification technique that can be applied in any case with iid noise that outperforms estimators in this case, including the popular LS method and a recently-developed (and limited) version of the MEE. Performance-wise, the MEE method is comparable to the expectation-maximization (EM) method. Its application to FIR system identification produces a very efficient implementation of this technique.

Adaptive filtering is a widely used technique in active noise control (ANC). In order to make the adaptive filter in an FXLMS (filtered-x LMS) ANC system stable, the reference signal must pass through an estimation filter whose phase response is within /spl plusmn/90/spl deg/ of the phase of the secondary path. In this paper, we study the quantization effects on the filter phase response and the relationship between the phase response and the location of the zeros and poles. In addition, we propose a filter structure and nonuniform quantization method in which we quantize the filter coefficients so they each contain a small number of nonzero bits, based on the distance of the zeros/poles to the unit circle, to guarantee that the /spl plusmn/90/spl deg/ allowable phase deviation is met - greatly reducing the implementation cost. We combine these ideas with that of multiplierless implementations of adaptive FIR filters to realize an efficient active noise control using field programmable gate arrays or other digital hardware.

The adaptive nonlinear predistorter is an effective technique to compensate the nonlinear distortion existing in a digital communication system. In this paper, we first apply the recently developed nonlinear filtered-x LMS and adjoint nonlinear LMS algorithm to design an adaptive Hammerstein nonlinear predistorter for a high power amplifier (HPA) preceded by a linear system. Compared with the adaptive Hammerstein nonlinear predistorter with either direct learning or indirect learning, our developed adaptive nonlinear predistorter is computationally efficient and can be easily implemented via DSP hardware and software. By exploring the robustness of our proposed algorithm and the statistical properties of our virtual filter, we further simplify the adaptive Hammerstein nonlinear predistorter to further reduce the computational complexity and implementation cost. Simulation results confirm the effectiveness of our proposed algorithm.

The nonlinear predistorter is an effective technique to compensate the nonlinear distortions existing in a digital communication system. However, available adaptive nonlinear predistorters are either based on the indirect learning algorithm, or are complicated in structure and computation. In this paper, we propose a novel adaptive nonlinear predistorter based on a direct learning algorithm: the adjoint nonlinear LMS algorithm. Because of the direct learning algorithm, our adaptive predistorter outperforms the other nonlinear predistorters that are based on the indirect learning method in the sense of mean square error (MSE). Moreover, compared with any other adaptive nonlinear predistorter based on the direct learning architecture, our predistorter has a simpler structure and lower computational complexity. Simulation results show the effectiveness of our nonlinear adaptive predistorter.

We develop an algorithm suitable for convolving two finite length sequences of uneven length that is more efficient than its FFT-based competitor. In particular, we present a method for computing a fast linear convolution of the finite length sequences h and x where the length of x is much greater than the length of h using the Hirschman optimal transform (HOT). When compared to the most efficient methods using the DFT and its fast FFT implementation, our method can reduce the computational complexity by a third.

We propose a method for designing a filter to meet a set of specifications, which can be implemented with reduced area. Our approach combines a prefilter implementation structure whose function has been developed over the years with our previously reported variable precision technique for intelligently quantizing the filter coefficients. Our area-efficient structure uses frequency masking with a single filter model to give good performance with low order and low coefficient sensitivity. Our method does use a novel connection of a simple prefilter structure used in a frequency masking technique to give good designs for the previously unattainable wide-band filter designs. The technique also gives designs with superior (very sharp) transition regions. Both types produce filters that efficiently use digital circuitry, leading to space-efficient designs that are significantly smaller than would otherwise be the case. Some examples are given to demonstrate the effectiveness of our design.

We propose a method for designing a filter to meet a set of specifications, which can be implemented with reduced area. Our approach combines a prefilter implementation structure whose function has been developed over the years with our previously reported variable precision technique for intelligently quantizing the filter coefficients. Our area-efficient structure uses frequency masking with a single filter model to give good performance with low order and low coefficient sensitivity. Our method does use a novel connection of a simple prefilter structure used in a frequency masking technique to give good designs for the previously unattainable wide-band filter designs. The technique also gives designs with superior (very sharp) transition regions. Both types produce filters that efficiently use digital circuitry, leading to space-efficient designs that are significantly smaller than would otherwise be the case. Some examples are given to demonstrate the effectiveness of our design.

The quantification of signal localization simultaneously in time and in frequency is fundamental to a variety of signal processing applications where time-frequency analysis is to be performed on nonstationary signals. In this paper, we develop novel joint localization measures defined on equivalence classes of finitely supported discrete-time signals. These measures bear strong analogies to the well-known continuous-time Heisenberg-Weyl inequality. In particular, they are invariant to signal translations and modulations and admit an intuitive interpretation in terms of the temporal and spectral variance of the signal energy. The new measures are used to design optimal wavelet quadrature mirror filter banks that exhibit improved localization relative to the Haar and Daubechies analysis filters.

This paper introduces a sub-band adaptive algorithm that avoids the signal path delay, and so can be used in an adaptive active control (feedback) system. A side effect of this algorithm is that it still causes extra delay in the error path due to the analysis filter bank. Even though the delay along the error path has only a slight influence on the steady-state behavior, it does decrease the system bounds of stability. We propose an error path delay compensation method that alleviates this problem. Simulation results are presented to illustrate the efficiency of the new adaptive algorithm.

Accurate estimation of the number of textured regions that are present in an image is one of the most difficult aspects of the unsupervised texture segmentation problem. In this paper we introduce a new approach for estimating the number of regions in an image without a priori information. Using a novel discrete-discrete uncertainty measure defined on equivalence classes of signals, we design a localized separable 2-D wavelet transform. By clustering in a feature space defined by the wavelet coefficients computed over disjoint blocks in the image, we obtain high quality estimates for the number of textured regions present in an image. Compared to a previously reported algorithm based on the eight-point Daubechies wavelet, this new approach tends to produce clusters with improved between-cluster separations.

We determine all signals giving equality for the discrete Hirschman uncertainty principle. We single out the case where the entropies of the time signal and its Fourier transform are equal. These signals (up to scalar multiples) form an orthonormal basis giving an orthogonal transform that optimally packs a finite-duration discrete-time signal. The transform may be computed via a fast algorithm due to its relationship to the discrete Fourier transform.

We have previously developed an uncertainty measure that is suitable for finitely-supported (N samples) discrete-time signals. A specific instance of our measure has been termed the "discrete Hirschman (1957) uncertainty principal" in the literature, and we have adopted this terminology for our more general measure. We compare the optimal signals of this discrete version to the already determined optimal signals of the (continuous-time) Hirschman uncertainty principal. From our comparison, we conclude that a basic premise in signal processing, that if we sample densely enough, the discrete-time case directly corresponds to the continuous-time case, is not correct in this instance. The arithmetic of N, which seems to have no analog in continuous time, is crucial to the construction of the Hirschman optimal discrete representation. We suggest that more work in this important area be performed to determine what impact this has, and to find out how widespread this problem may be.

Unsupervised segmentation of weather images into features that correspond to physical storms is a fundamental and difficult problem. Treating an infrared satellite image as a Markov random field, the Kolmogorov-Smirnov distance between the local distribution of spatial statistics and the global statistics of classified regions is used to segment the image using a relaxation algorithm. An outlier class is utilized to capture as yet unclassified pixels. We demonstrate the results of different initialization methods on the final segmentation and point out where the method is deficient.

We use a new uncertainty measure, H/sub p/, that predicts the compactness of digital signal representations to determine a good (non-orthogonal) set of basis vectors. The measure uses the entropy of the signal and its Fourier transform in a manner that is similar to the use of the signal and its Fourier transform in the Heisenberg uncertainty principle. The measure explains why the level of discretization of continuous basis signals can be very important to the compactness of representation. Our use of the measure indicates that a mixture of (non-orthogonal) sinusoidal and impulsive or "blocky" basis functions may be best for compactly representing signals.

A fully adaptive infinite impulse response notch filter in cascade form is proposed to detect and track multiple time-varying frequencies in additive white noise. Based on transformations for digital filters in the frequency domain, the filter results in a minimal number of parameters. In addition, a simple adaptive algorithm with good tracking and convergence properties is obtained by using all-pass filters and truncating the gradient. Computer simulations are included to verify the competitive performance of this filter under a wide range of conditions. From this analysis, we conclude that our new design is computationally simple, achieves rapid convergence, and is consequently a good choice in many non-stationary environments.

We describe a system for still image compression that uses several transform sets in a multiple bases realization algorithm. Our algorithms reduce the number of encoded transform coefficients 20% beyond DCT-only compression. We extend these algorithms to use several newly developed lapped orthogonal transform (LOT) bases, resulting in useful algorithms for low bit rate (high compression) operation without blocking effect.

This paper describes the use of a new, multiple use laboratory facility in DSP education at the University of Oklahoma. The facility, funded by a combination of NSF grant money, industrial donations and university funds supports the teaching of signal and image processing, telecommunications and multimedia courses. This unique combination of related areas has fostered significant faculty and department interaction to support the strong telecommunications industry in the region. In fact, the laboratory was chosen as the model laboratory for the joint OU/OSU program in Telecomputing.

We derive a two-microphone directional and adaptive broadband array for use in hearing aids. The array contains only two directional microphones to satisfy the cosmetic constraints which are most likely to be accepted by hearing aid wearers. Our proposed processing method is a modification of Widrow (1975) et al.'s narrowband MMSE algorithm which does not generate a reference signal. The required frequency separation is performed using a multirate filter bank. The distance between two microphones is 12 cm. When the signals are split into four narrower bands, an SNR improvement of 9.2 dB and an intelligibility-weighted directivity index of 8.9 dB are obtained. Only 8 weights (2 for each band) need to be updated and thus the approach is much simpler when compared with other methods.

This paper develops algorithms for using the lapped orthogonal transforms (LOT) in the multiple bases representation (MBR) of non-stationary signals. We have previously developed speech algorithms using nonlapped mixed transforms. The major motivation for using lapped orthogonal transforms is their ability to eliminate blocking effects which show up as discontinuities in the reconstructed signal at the block boundaries. In addition, LOT based transforms improve the transform coding gain considerably. We test and compare the performance of the LOT in MBR algorithms that use a previously developed cascade structure to our newly developed parallel structure. We also discuss different dominant component (DC) picking strategies and introduce some new methods. Results and subjective evaluations are provided for real speech signals.

We describe a system for still image compression which uses several lapped orthogonal transform (LOT) sets in a multiple bases realization (MBR) algorithm, the recursive residual projection (RRP) algorithm. Newly developed RRP algorithms are shown to reduce the number of encoded transform coefficients 20% beyond the discrete cosine transform (DCT)-only compression standard, JPEG. These algorithms still suffer from the problem of block-discontinuities at the boundaries of the segmented image. We extend these algorithms to use several newly developed LOT bases, which result in useful algorithms for low bit-rate (high compression) operation. We see that our proposed methods have superior % MSE for equal numbers of coefficients when compared to several transform coding methods.

A faster, more cost effective test for evaluating spindle motors is described. This test is significant in proving the efficacy of the potentials of artificial neural networks in industrial situations. The use of a self-organizing adaptive resonance structure following an input reduction network is studied. This network extracts the information about the motor power spectral density which is vital to the motor classification. Some heuristic rules are developed to help guide the test designer. Classification shapes are examined to determine the influence of the neural network on the motor classification.>

Uses the Pareto optimal multi-criterion optimization method to design low sensitivity state-space digital filters for the parallel form and cascade form structures. The designs balance the desire to match a desired filter response with the desire to produce a low sensitivity filter. Some work on direct form II designs which solidifies some previous work is shown. The authors find that pole/zero cancellation pairs added to a desired direct form II filter are Pareto optimal.>

Multicriterion optimization methods for determining low-sensitivity digital filters for a given structure are considered. Pareto optimal as well as min/max methods are considered. It is shown that the methods yield low sensitivity designs via the presented computer algorithms. Filter scaling can be directly incorporated in the designs.>

The convergence of previously described output error identification procedures is examined. The convergence analysis uses the eigeninformation of the parameter correlation matrix (really its inverse, the Fisher information matrix) for the identified structure. Convergence rates are important in digital adaptive equalizer design, for example. The eigeninformation of the parameter information matrix related the system sensitivity and numerical conditioning in a manner which provides insight into the identification process. An interesting sideline of this work is that balanced-coordinate state-space structures appear to consistently have good information properties. The relevant eigeninformation is combined in a proposed scalar convergence time constant. An important result is that identification of the usually identified direct form II parameters (the standard ARMA parameters) does not necessarily yield the fastest parameter convergence for the system being identified.>

The authors investigate the usefulness of structures with high parameter sensitivities for the purpose of increasing the convergence rate of parameter identification algorithms. In particular, they examine two SISO (single input, single output) structures: the direct form II and the dual generalized Hessenberg representation. A Gauss-Newton identification procedure is presented for implementing parameter identification from impulse response data. The authors then present a sensitivity analysis and provide some illustrative examples.>

A reasonable coefficient sensitivity measure for state-space recursive, finite-wordlength, digital filters is the sum of the L/sub 2/ norm of all first-order partials of the system function with respect to the system parameters. This measure is actually a lower bound approximation to the output quantization noise power. A gradient-based method for sensitivity minimization of direct-form II (infinite-impulse) filters is given. ARMA (autoregressive moving-average) sensitivity gradients are shown to consist also of ARMA auto- and cross-covariances, facilitating closed-form efficient evaluations. Some examples show the effectiveness of this procedure. The use of the design method in other filter forms is considered.>

The sensitivity of a Direct II form digital filter can be reduced by a factor of up to 10. This is achieved by providing additional degrees of freedom in the Direct II form by increasing the order. To maintain the original system function to be implemented, this corresponds to the addition of cancelling pole-zero pairs. The location of the latter influences the overall sensitivity function. As a measure of sensitivity the sum of L2norms of all first order partials of the system function is used. It is shown that this measure is particularly attractive because it can be evaluated efficiently and in closed form. This results from breaking down the sensitivity measure in terms of ARMA auto- and cross-covariances.