Describes a special purpose, very high speed, digital deterministic Boltzmann neural network VLSI chip. Each chip has 32 physical neural processors, which can be apportioned into an arbitrary topology (input, multiple hidden and output layers) of up to 160 virtual neurons total. Under typical conditions, the chip learns at approximately 5*10/sup 8/ connection updates/second (CUPS). Through relatively minor (subsequent) modifications, the authors' chips can be 'tiled' in multi-chip modules, to make multi-layer networks of arbitrary size suffering only slight communications delays and overhead. In this way, the number of CUPS can be made arbitrarily large, limited only by the number of chips tiled. The chip's high speed is due to massively parallel array computation of the inner products of connection weights and neural activations, limited (but adequate) precision for weights and activations (5 bits), high clock rate (180 MHz), as well as several algorithmic and design insights.>

A computational image analysis model that resembles the functioning of the brain is introduced. The multiple-channel neural network model consists of three stages: multiple-channel representation, neural network classification and spatial context correction. The model is implemented and applied to the problem of texture analysis. Gabor filters are involved to represent the textural patterns. Low misclassification rates are obtained. Composite textural images are also applied to the system and accurately segmented images are obtained. The usefulness of the model is demonstrated.>

Multichip modules permit highly efficient implementation of tiled architectures. If the tiles are implemented in submicron CMOS, extremely highly computation rates can be achieved, but power dissipation becomes the principal factor limiting achievable levels of integration and performance. Some examples of tiled architectures are described. The feasibility and advantages of reduced voltage operation for reducing energy per operation in power constrained environments are discussed.>

Alternative implementations are presented for the frequency-domain LMS (least-mean-square) adaptive filter first introduced by Narayam and Peterson (1981). The implementation suggested there was a bank of bandpass filters implemented by the discrete Fourier transform (DFT). One of the present implementations is based on the recent paper of B. Widrow et al. (1987) that shows that it is possible to compute the DFT by using the LMS steepest-descent algorithm of Widrow and Hoff. This new implementation is very modular. and requires fewer computations for large filter lengths. This is because the transform part requires O(2N) computations per input sample where N is the filter length while the conventional method of taking FFTs requires O(N log N) computations per input sample. Some results of analysis of convergence are presented. Simulations of practical applications of frequency-domain LMS adaptive filters are carried out to determine its suitability, and comparisons are made with simulations using the FFT. A similar structure cannot be suggested for real data. Instead, a frequency-sampling implementation is proposed, using the recursive computation of the discrete Hartley transform.>

A neural network model, called SPAN (space partition network), is presented. This model differs from most of the currently seen neural networks in that it allows a network to adapt its structure by adding neurons, killing neurons, and modifying the structural relationships between neurons in the network. An adaptive vector quantization source-coding system based on SPAN is proposed. The major advantage of using SPAN as the codebook of a vector quantizer is that SPAN can capture the local context of the source signal space and map onto a lattice structure. A fast codebook-searching method utilizing the local context of the lattice is proposed, and a coding scheme, called the path coding method, for eliminating the correlation buried in the source sequence is introduced. The performance of the proposed coder is compared to an LBG (Y. Linde, A. Buzo, and R.M. Gray, 1980) coder on synthesized Gauss-Markov sources. Simulation results show that, without using the path coding method, SPAN yields performance similar to an LBG coder; however, if the path coding method is used, SPAN displays a much better performance than the LBG for highly correlated signal sources.>

A novel algorithm for dynamically adapting the size of neural networks is proposed. According to the measures to be defined, a neuron in the network will generate a new neuron when the variation of its weight vector is high (i.e. when it is not learned) and will be annihilated if it is not active for a long time. This algorithm is tested on a simple but popular neural network model, Self Organization Feature Map (SOFM), and implemented in software using a double linked list. Using this algorithm, one can initially put a set of seed neurons in the network and then let the network grow according to the training patterns. It is observed from the simulation results that the network will eventually grow to a configuration suitable to the class of problems characterized by the training patterns, i.e. the neural network synthesizes itself to fit the problem space.>

The authors describe a direct, fast, and efficient method of implementing time-domain block LMS (least mean squares) adaptive FIR (finite impulse response) filtering using radix-2 decomposition of the input data but no transforms. The same method can be applied to the implementation of time-domain block LMS adaptive FIR filters where the weight vector is updated in the transform domain and of frequency-domain block LMS adaptive FIR filters. The method is well suited to implementation on DSP (digital signal processing) architectures based on multiply-accumulate. Computational complexity comparisons show that the block length and number of weights can be traded for reduction in computational complexity and that the method is the most efficient for block lengths less than about 16, for a typical filter length. >

A new adaptive algorithm is proposed to give an unbiased and high resolution frequency estimate of sinusoids in white noise. Base on the normalized Least-Squares (LS) lattice algorithm and the inverse power iteration method, the eigenvector associated with the minimum eigenvalue of the signal covariance matrix is estimated in the algorithm. The zeros of the "eigenvector polynomial" thus obtained are all on the unit circle and at the angles of the sinusoid frequencies. It is an adaptive realization of the Pisarneko's "harmonic retrieval" method. But differing from the adaptive method proposed by Thompson where the eigenvector is obtained through a gradient search in a constrained optimization formulation, in the new method the eigenvector is computed by an inverse power iteration. It enjoys all the advantages of the normalized LS lattice such as fast computations, low round-off noise and an easy stability check, etc. as well as fast convergence rate of the inverse power iteration method. Computer simulation results are shown.

The existing echo cancellation methods are primarily based on the LMS adaptive algorithm. Despite the fact that the LMS echo canceller works better than its predecessor-the echo suppressor, its performance can be substantially improved if the Recursive LS (RLS) algorithm is used instead. However the αp2operations (p: filter order) per sample required prevents the RLS algorithm from being used in this and many other applications where the filter order is relatively high. The computational complexity of the RLS has recently been brought down to αp by exploiting the shifting structure of the signal covariance matrix. Two fast algorithms, namely the LS lattice and the "fast Kalman", are used here. Comparisons between the two fast LS algorithms and the LMS gradient algorithm are made and the performance difference is demonstrated. Two important problems in voice echo cancellation: the flat delay estimation and the near-end speech detection, are approached novelly through a minimum-mean-squared-error flat delay estimator and a likelihood near-end speech detector. Simulation results are very satsifactory.

A reduction on the number of multiplies per point is achieved for narrowband filtering when frequency sampling filters are used. Agarwal and Cooley [4] tabulated some optimal block size segments of long sequences when convolving them with a short sequence by FFT methods. In this paper we describe how, by using block lengths of twice the filter's length (which is not the optimum size for filters of order > 4), and by utilizing frequency sampling filters, the number of multiplies per point is reduced over that obtained with other filters using the optimum block length. We also show that by doing a decimation (i.e. reducing the sampling frequency) in the frequency domain, we then only have to compute a short IDFT, as compared with decimating in the time domain after the long block sized IDFT has been computed.

The architecture of a real time processing system to study and compare a number of different speech processing algorithms is described. The system consists of a front-end processor, a fast arithmetic processor and a diagnostic/download processor. The arithmetic processor is based on bit-slice bipolar microprocessor devices. It has a dual bus structure with a dual ported data memory and employs horizontal type microprogramming with a writable control store. A variable rate clock is used to avoid pipeline delays in data paths; the effective computation rate is about 5 million instructions per second. Input-output operations are done by the front-end processor in conjunction with a double buffered I/O memory. The user program is loaded into the control store from a host system using the download processor which also provides extensive debugging capabilities. Three different algorithms-a Linear predictive coder (LPC), an Adaptive Transform Coder, (ATC) and a wave form coder--have been implemented on the system. The performance of the processor with respect to these algorithms will be discussed.

The Adaptive Line Enhancer (ALE) was first introduced by Widrow and has since been used in applications such as noise cancellation, coherent interference rejection, detection and estimation of sinusoid(s) in white noise, etc. In this paper, a Complex Adaptive Line Enhancer (CALE) is adopted to process complex-valued signals in their analytic form. The performance and asymptotic behavior of the CALE in cases of single and multiple sinusoid(s) in white noise are investigated in detail. It is shown that the frequency estimation obtained by CALE in the case of a single sinusoid is unbiased and independent of the bulk delay, Δ, the predictor length, L, and the Signal-to-Noise Ratio (SNR). If a conventional real ALE is used, this result, in general, cannot be obtained. A precise analysis is made for the case of two sinusoids. It is shown that an optimal choice of Δ, exists. For more than two sinusoids, an approximation is used to derive more insight into the analytical structure of a CALE. An intuitive explanation for the optimal choice of Δ, is given. Simulation results are also shown.

THE SIGNAL PROCESSING SPECIALIST WHO USES A COMPUTER TO MODEL SIGNAL NETWORKS OR ANALYZE DIGITIZED DATA SPENDS CONSIDERABLY MORE TIME PROGRAMMING THAN DOING THE ANALYSIS. A PROTOTYPE SIGNAL PROCESSING LANGUAGE WAS DEVELOPED WHICH SUPPORTS THE TYPES OF OPERATIONS TYPICALLY DESIRED BY THE SPECIALIST, WHILE REQUIRING LITTLE PROGRAMMING KNOWLEDGE. THE USER HAS AVAILABLE A VARIETY OF ARITHMETIC MODES, PRECISIONS, OPERATORS, SIGNAL SOURCES (INCLUDING EXTERNAL DATA), FILTERS, ANALYSIS TOOLS AND OUTPUT FORMATS. THE PACKAGE ALLOWS ON-LINE MODIFICATION OF THE NETWORK AND PROCESS DESCRIPTIONS, GIVING THE FLEXIBILITY NEEDED FOR INTERACTIVE ANALYSIS.

The analytic form of speech signals has been generated by combining the real-valued speech with its imaginary-valued discrete-Hilbert-transformed counter-part. Instead of using an 8th order real-valued linear prediction to analyze its spectral components, a 4th order complex-valued linear prediction is used. Furthermore, a fast and closed-form rooting procedure is adopted to extract the roots (i.e., bandwidth and frequency information of the speech formants) of the obtained 4th order polynomial of the corresponding inverse filter. The numerical complexity and convergence problems are thus avoided and the computational load is greatly reduced. Promising results in both spectral and pitch estimation are shown. Its advantages in efficient speech coding are discussed.

Narrow band digital notch filters have their poles near the unit circle. As the sampling rate is increased, the poles move towards z = +1. Implementing such filters requires long registers to overcome the sensitivity and roundoff errors. A filter structure based on digital incremental computers is proposed, which has low sensitivity and roundoff errors, and simple hardware implementation. The filter structure can be directly used on differentially pulse-code modulated signals. Hard-ware multipliers are not required as the poles approach z = +1, and excellent results can be obtained using multipliers with very short word lengths, or with small size read-only memories.

Roundoff noise and limit cycle oscillations due to postmultiplication rounding can seriously limit the application of recursive digital filters in practice, particularly for poles near the unit circle or near z = +1. Rounding is usually performed by zero memory quantizers. "Second-order quantizers" are introduced, which can be used for implementing recursive digital filters with practically no roundoff errors or limit cycle oscillations. Based on the idea of changing the transfer function used to compute roundoff errors, these quantizers save the low-order bits to correct the product at future iterations. For several pole locations, this can be done with minimal amount of extra hardware.

A digital bandpass filter-bank for demodulating a wideband frequency multiplexed signal into a specified number of uniform narrow band channel outputs, and conversely for modulating a set of channel inputs into a composite frequency multiplexed signal, can be realized efficiently by the combination of a suitable transform processor and a weighting network. The design and implementation of these filter-banks for different types of input-ouput configurations such as complex signals at both the wideband and narrow band sides, real signal at the wideband side and complex signals at the narrow band side, and real signals at both ends are discussed. Applications in telecommunications (TDM-FDM translators), speech processing (phase vocoders), signal analysis and detection (spectrum analyzers) and other signal processing systems are also described.

AnN-point discrete Fourier transform (DFT) algorithm can be used to evaluate a discrete cosine transform by a simple rearrangement of the input data. This method is about two times faster compared to the conventional method which uses a2N-point DFT.

A complete solution is given to the problem of finding the number of distinct quadratic residues for a composite modulus. Two specific applications of this result are described. The first one concerns the efficient implementation of chirp filters. It is shown that by an optimum choice of the number of taps, the number of multiplications required to realize a transversal chirp filter can be greatly reduced. Secondly, an algorithm for the computation of DFT, based on chirp filtering, is discussed. It has the potential of being faster than the FFT in certain cases and, in addition, requires less storage for the sine-cosine values.