This paper gives an exposition of linear prediction in the analysis of discrete signals The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum The major part of the paper is devoted to all-pole models The model parameters are obtained by a least squares analysis in the time domain Two methods result, depending on whether the signal is assumed to be stationary or nonstationary The same results are then derived in the frequency domain The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra This also leads to a discussion of the advantages and disadvantages of the least squares error criterion A spectral interpretation is given to the normalized minimum prediction error Applications of the normalized error are given, including the determination of an "optimal" number of poles The use of linear prediction in data compression is reviewed For purposes of transmission, particular attention is given to the quantization and encoding of the reflection (or partial correlation) coefficients Finally, a brief introduction to pole-zero modeling is given

Linear prediction: A tutorial review

This paper describes the concept of adaptive noise cancelling, an alternative method of estimating signals corrupted by additive noise or interference. The method uses a "primary" input containing the corrupted signal and a "reference" input containing noise correlated in some unknown way with the primary noise. The reference input is adaptively filtered and subtracted from the primary input to obtain the signal estimate. Adaptive filtering before subtraction allows the treatment of inputs that are deterministic or stochastic, stationary or time variable. Wiener solutions are developed to describe asymptotic adaptive performance and output signal-to-noise ratio for stationary stochastic inputs, including single and multiple reference inputs. These solutions show that when the reference input is free of signal and certain other conditions are met noise in the primary input can be essentiany eliminated without signal distortion. It is further shown that in treating periodic interference the adaptive noise canceller acts as a notch filter with narrow bandwidth, infinite null, and the capability of tracking the exact frequency of the interference; in this case the canceller behaves as a linear, time-invariant system, with the adaptive filter converging on a dynamic rather than a static solution. Experimental results are presented that illustrate the usefulness of the adaptive noise cancelling technique in a variety of practical applications. These applications include the cancelling of various forms of periodic interference in electrocardiography, the cancelling of periodic interference in speech signals, and the cancelling of broad-band interference in the side-lobes of an antenna array. In further experiments it is shown that a sine wave and Gaussian noise can be separated by using a reference input that is a delayed version of the primary input. Suggested applications include the elimination of tape hum or turntable rumble during the playback of recorded broad-band signals and the automatic detection of very-low-level periodic signals masked by broad-band noise.

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Adaptive noise cancelling: Principles and applications

An overview of beamforming from a signal-processing perspective is provided, with an emphasis on recent research. Data-independent, statistically optimum, adaptive, and partially adaptive beamforming are discussed. Basic notation, terminology, and concepts are included. Several beamformer implementations are briefly described. >

Beamforming: a versatile approach to spatial filtering

A constrained least mean-squares algorithm has been derived which is capable of adjusting an array of sensors in real time to respond to a signal coming from a desired direction while discriminating against noises coming from other directions. Analysis and computer simulations confirm that the algorithm is able to iteratively adapt variable weights on the taps of the sensor array to minimize noise power in the array output. A set of linear equality constraints on the weights maintains a chosen frequency characteristic for the array in the direction of interest. The array problem would be a classical constrained least-mean-squares problem except that the signal and noise statistics are assumed unknown a priori. A geometrical presentation shows that the algorithm is able to maintain the constraints and prevent the accumulation of quantization errors in a digital implementation.

An algorithm for linearly constrained adaptive array processing

Fundamental developments in feedforward artificial neural networks from the past thirty years are reviewed. The history, origination, operating characteristics, and basic theory of several supervised neural-network training algorithms (including the perceptron rule, the least-mean-square algorithm, three Madaline rules, and the backpropagation technique) are described. The concept underlying these iterative adaptation algorithms is the minimal disturbance principle, which suggests that during training it is advisable to inject new information into a network in a manner that disturbs stored information to the smallest extent possible. The two principal kinds of online rules that have developed for altering the weights of a network are examined for both single-threshold elements and multielement networks. They are error-correction rules, which alter the weights of a network to correct error in the output response to the present input pattern, and gradient rules, which alter the weights of a network during each pattern presentation by gradient descent with the objective of reducing mean-square error (averaged over all training patterns). >

/pdf/30-years-of-adaptive-neural-networks-perceptron-madaline-and-3p7ko3fnas.pdf

30 years of adaptive neural networks: perceptron, Madaline, and backpropagation

A system consisting of an antenna array and an adaptive processor can perform filtering in both the space and frequency domains, thus reducing the sensitivity of the signal‐receiving system to interfering directional noise sources. Variable weights of a signal processor can be automatically adjusted by a simple adaptive technique based on the least‐mean‐squares (LMS) algorithm. During the adaptive process an injected pilot signal simulates a received signal from a desired “look” direction. This allows the array to be “trained” so that its directivity pattern has a main lobe in the previously specified look direction. At the same time, the array processing system can reject any incident noises, whose directions of propagation are different from the desired look direction, by forming appropriate nulls in the antenna directivity pattern. The array adapts itself to form a main lobe, with its direction and bandwidth determined by the pilot signal, and to reject signals or noises occurring outside the main lobe as well as possible in the minimum mean‐square error sense. Several examples illustrate the convergence of the LMS adaptation procedure to the corresponding Wiener‐optimum solutions. Rates of adaptation and misadjustments of the solutions are predicted theoretically and checked experimentally. Substantial reductions in noise reception are demonstrated in computer‐simulated experiments. The techniques described in this paper are applicable to signal‐receiving arrays for use over a wide range of frequencies.

Adaptive Antenna Systems

A system consisting of an antenna array and an adaptive processor can perform filtering in both the space and the frequency domains, thus reducing the sensitivity of the signal-receiving system to interfering directional noise sources. Variable weights of a signal processor can be automatically adjusted by a simple adaptive technique based on the least-mean-squares (LMS) algorithm. During the adaptive process an injected pilot signal simulates a received signal from a desired "look" direction. This allows the array to be "trained" so that its directivity pattern has a main lobe in the previously specified look direction. At the same time, the array processing system can reject any incident noises, whose directions of propagation are different from the desired look direction, by forming appropriate nulls in the antenna directivity pattern. The array adapts itself to form a main lobe, with its direction and bandwidth determined by the pilot signal, and to reject signals or noises occurring outside the main lobe as well as possible in the minimum mean-square error sense. Several examples illustrate the convergence of the LMS adaptation procedure toward the corresponding Wiener optimum solutions. Rates of adaptation and misadjustments of the solutions are predicted theoretically and checked experimentally. Substantial reductions in noise reception are demonstrated in computer-simulated experiments. The techniques described are applicable to signal-receiving arrays for use over a wide range of frequencies.

Adaptive antenna systems

Broadcasting protocols for video-on-demand continuously retransmit videos that are watched simultaneously by many viewers. Nearly all broadcasting protocols assume that the client set-top box has enough storage to store between 48 and 60 minutes of video. We propose to use this storage to anticipate the customer requests and to preload, say, the first 3 minutes of the top 16 to 20 videos. This would provide instantaneous access to these videos and also eliminate the extra bandwidth required to handle compressed video signal.We present two broadcasting protocols using partial preloading to eliminate this extra bandwidth. The first of these protocols, Polyharmonic Broadcasting with Partial Preloading (PHB-PP), partitions each video into between 20 and 160 segments of equal duration and allocates a separate data stream to each individual segment. Our second protocol, the Mayan Temple Broadcasting protocol, uses fewer data streams but requires more overall bandwidth.

/pdf/zero-delay-broadcasting-protocols-for-video-on-demand-2nlfffjrtq.pdf

Zero-delay broadcasting protocols for video-on-demand

The first part of this paper presents a new measure of sensitivity specifically applicable to the realization of a linear discrete system on a digital computer. It is also shown that the sensitivity of the eigenvalues to parameter inaccuracies in the realization depends strongly on the choice of state variables. From these considerations, a realization is obtained which is "best" for a large class of systems of interest with regard to minimizing storage requirements, arithmetic operations, parameter accuracy, and eigenvalue sensitivity. The second half of the paper considers the very practical problem of determining the number of bits accuracy required in the computer-stored parameters of the system to achieve satisfactory performance. For the realization found to be a best compromise, equations are obtained for determining these bit requirements. Examples are given showing the application of this realization to the computer implementation of a discrete filter, and a comparison is given to other possible realizations.

Eigenvalue sensitivity and state-variable selection

A method and means for creating the display illusion of "roughness" or "texture" in color patterns suitable for an raster scanned display surface by assigning different color values to pels (picture elements) in adjacent positions and then replicating the patterns automatically using the recurrent and sequential accessing of a concordance table. The real color of each pel of a textured pattern is a joint function of a color number stored in a refresh buffer driving the display surface for any given display matrix array pel position and the value of a predetermined subset of address bits which describe that pel position. The use of preselected pel position address bits for regulating texture is shown as applied to video lookup tables and refresh buffers as a singlelevel control and additionally to two or more video lookup tables for achieving a pattern hierarchy.

Patrick E. Mantey

Papers

Adaptive Antenna Systems

Adaptive antenna systems

Zero-delay broadcasting protocols for video-on-demand

Eigenvalue sensitivity and state-variable selection

Method and means for texture display in raster scanned color graphic