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Showing papers on "Adaptive filter published in 1976"


Book ChapterDOI
01 Aug 1976
TL;DR: It is shown that for stationary inputs the LMS adaptive algorithm, based on the method of steepest descent, approaches the theoretical limit of efficiency in terms of misadjustment and speed of adaptation when the eigenvalues of the input correlation matrix are equal or close in value.
Abstract: This paper describes the performance characteristics of the LMS adaptive filter, a digital filter composed of a tapped delay line and adjustable weights, whose impulse response is controlled by an adaptive algorithm. For stationary stochastic inputs, the mean-square error, the difference between the filter output and an externally supplied input called the "desired response," is a quadratic function of the weights, a paraboloid with a single fixed minimum point that can be sought by gradient techniques. The gradient estimation process is shown to introduce noise into the weight vector that is proportional to the speed of adaptation and number of weights. The effect of this noise is expressed in terms of a dimensionless quantity "misadjustment" that is a measure of the deviation from optimal Wiener performance. Analysis of a simple nonstationary case, in which the minimum point of the error surface is moving according to an assumed first-order Markov process, shows that an additional contribution to misadjustment arises from "lag" of the adaptive process in tracking the moving minimum point. This contribution, which is additive, is proportional to the number of weights but inversely proportional to the speed of adaptation. The sum of the misadjustments can be minimized by choosing the speed of adaptation to make equal the two contributions. It is further shown, in Appendix A, that for stationary inputs the LMS adaptive algorithm, based on the method of steepest descent, approaches the theoretical limit of efficiency in terms of misadjustment and speed of adaptation when the eigenvalues of the input correlation matrix are equal or close in value. When the eigenvalues are highly disparate (λ max /λ min > 10), an algorithm similar to LMS but based on Newton's method would approach this theoretical limit very closely.

1,423 citations


Journal ArticleDOI
TL;DR: In this paper, an external specification of a digital filter is investigated via the internal structure of the filter using a state variable formulation, and conditions for minimizing this output noise are established and realizations which meet these conditions are constructed.
Abstract: Beginning with an external specification of a digital filter, structures which minimize roundoff noise are investigated. After fixing the probability of overflow through an l_{2} scaling procedure, roundoff noise is studied via the internal structure of the filter using a state variable formulation. An output noise variance formula in terms of the internal structure is derived. Conditions for minimizing this output noise are established and realizations which meet these conditions are constructed. A new set of filter invariants called second-order modes are defined and shown to play a definitive role in minimal noise realizations. From these invariants, for example, one can calculate the minimal output noise variance of a given external specification. Numerical results are given which compare these new filter structures with the usual parallel and cascade connections of second-order filters, both theoretically and through simulations. For narrow-band filters, these new structures can be orders of magnitude better (in terms of output noise variance). One drawback of these new structures is a large increase in the number of multipliers needed to realize them. However, by applying the theory to subfilters connected in parallel and cascade, a good compromise between output noise and number of multipliers is obtained.

774 citations


Journal ArticleDOI
TL;DR: A more substantial gain can be obtained in the direct realization of a uniform bank of recursive filters through combination of the polyphase network with a discrete Fourier transform (DFT) computer; savings in hardware result from the low sensitivity of the structure to coefficient word lengths.
Abstract: The digital filtering process can be achieved by a set of phase shifters with suitable characteristics. A particular set, named polyphase network, is defined and analyzed. It permits the use of recursive devices for efficient sample-rate alteration. The comparison with conventional filters shows that, with the same active memory, a reduction of computation rate approaching a factor of 2 can be achieved when the alteration factor increases. A more substantial gain can be obtained in the direct realization of a uniform bank of recursive filters through combination of the polyphase network with a discrete Fourier transform (DFT) computer; savings in hardware also result from the low sensitivity of the structure to coefficient word lengths.

420 citations


Journal ArticleDOI
TL;DR: This paper examines the major techniques for constraining the response of the adaptive processor, including methods of controlling the Response of the array in the absence of external interference, including angle domain techniques such as pilot signals, preadaption spacial filtering, and control loop spatial filtering.
Abstract: Initial applications of adaptive array theory to the radar sidelobe jamming problem ignored the problem of incidental cancellation of the desired signal returns. In more recent applications, longer transmitted waveforms have combined with returns from extended clutter and/or strong targets to create a more serious signal cancellation problem. There are several ways in which the adaptive processor can be constrained from responding to desired main lobe target returns while maintaining good cancellation of interference in the sidelobes. This paper examines the major techniques for constraining the response of the adaptive processor, including methods of controlling the response of the array in the absence of external interference. Time domain and frequency domain techniques are discussed. The majority of the discussion is devoted to angle domain techniques such as pilot signals, preadaption spacial filtering, and control loop spatial filtering. Analysis is presented showing the relationship between these techniques. Finally, examples are given showing the effects of these constraints as well as control of the quiescent array pattern.

388 citations


Journal ArticleDOI
01 Nov 1976
TL;DR: In this paper, an adaptive, recursive, least mean square digital filter is derived that has the computational simplicity of existing transversal adaptive filters, with the additional capability of producing poles in the filter transfer function.
Abstract: An adaptive, recursive, least mean-square-digital filter is heuristically derived that has the computational simplicity of existing transversal adaptive filters, with the additional capability of producing poles in the filter transfer function. Simulation results are presented to demonstrate its capability.

316 citations


Journal ArticleDOI
TL;DR: This paper compares the performance characteristics of three algorithms useful in adjusting the parameters of adaptive systems: the differential (DSD) and least-mean-square (LMS) algorithms, both based on the method of steepest descent, and the linear random search (LRS) algorithm, based on a random search procedure derived from the Darwinian concept of "natural selection.
Abstract: This paper compares the performance characteristics of three algorithms useful in adjusting the parameters of adaptive systems: the differential (DSD) and least-mean-square (LMS) algorithms, both based on the method of steepest descent, and the linear random search (LRS) algorithm, based on a random search procedure derived from the Darwinian concept of "natural selection." The LRS algorithm is presented here for the first time. Analytical expressions are developed that define the relationship between rate of adaptation and "misadjustment," a dimensionless measure of the difference between actual and optimal performance due to noise in the adaptive process. For a fixed rate of adaptation it is shown that the LMS algorithm, which is the most efficient, has a misadjustment proportional to the number of adaptive parameters, while the DSD and LRS algorithms have misadjustments proportional to the square of the number of adaptive parameters. The expressions developed are verified by computer simulations that demonstrate the application of the three algorithms to system modeling problems, of the LMS algorithm to the cancelling of broadband interference in the sidelobes of a receiving antenna array, and of the DSD and LRS algorithms to the phase control of a transmitting antenna array. The second application introduces a new method of constrained adaptive beamforming whose performance is not significantly affected by element nonuniformity. The third application represents a class of problems to which the LMS algorithm in the basic form described in this paper is not applicable.

280 citations


Proceedings ArticleDOI
01 Dec 1976
TL;DR: The purpose of this paper is to examine several Kalman filter algorithms that can be used for state estimation with a multiple sensor system and the data compression method is shown to be computationally most efficient.
Abstract: The purpose of this paper is to examine several Kalman filter algorithms that can be used for state estimation with a multiple sensor system. In a synchronous data collection system, the statistically independent data blocks can be processed in parallel or sequentially, or similar data can be compressed before processing; in the linear case these three filter types are optimum and their results are identical. When measurements from each sensor are statistically independent, the data compression method is shown to be computationally most efficient, followed by the sequential processing; the parallel processing is least efficient.

245 citations


01 Jul 1976

124 citations


Journal ArticleDOI
TL;DR: In this article, a theory for spectral transformations for two-dimensional digital filters is developed, and it is proved that these transformations take the form of stable 2D all-pass functions and that the result of spectral transformation is stable if the original transfer function is stable.
Abstract: A theory is developed for spectral transformations for two-dimensional digital filters. It is proved that these transformations take the form of stable two-dimensional all-pass functions and that the result of spectral transformation is stable if the original transfer function is stable. Emphasis is placed on formulating the transformations in a way which makes them easy to use for design, and it is shown that twodimensional spectral transformations offer a means of quickly obtaining new designs from previous ones. Included is a discussion of applications such as the design and realization of two-dimensional digital filters with tunable characteristics.

113 citations


01 Jan 1976

110 citations


Journal ArticleDOI
M.M. Sondhi1, Debasis Mitra
01 Nov 1976
TL;DR: In this article, the authors derived a broad range of theoretical results concerning the performance and limitations of a class of analog adaptive filters and proved the exponential convergence to zero of the norm ||r(t)|| with weak nondegeneracy requirements on x(t).
Abstract: We derive a broad range of theoretical results concerning the performance and limitations of a class of analog adaptive filters. Applications of these filters have been proposed in many different engineering contexts which have in common the following idealized identification problem: A system has a vector input x(t) and a scalar output z(t)=h'x(t), where h is an unknown time-invariant coefficient vector. From a knowledge of x(t) and z(t) it is required to estimate h. The filter considered here adjusts an estimate vector h^(t) in a control loop, thus d/dt h^= KF[z(t)-z^(t)]x(t) where z^(t) = h^'x(t), F is a suitable, in general nonlinear, function, and K is the loop gain. The effectiveness of the filter is determined by the convergence properties of the misalignment vector, r = h - h^. With weak nondegeneracy requirements on x(t) we prove the exponential convergence to zero of the norm ||r(t)||. For all values of K, we give upper and lower bounds on the convergence rate which are tight in that both bounds have similar qualitative dependence on K. The dependence of these bounds on K is unexpected and important since it reveals basic limitations of the filters which are not predicted by the conventional approximate method of analysis, the "method of averaging." By analyzing the effects of an added forcing term u(t) in the control equation we obtain upper bounds to the effects on the convergence process of various important departures from the idealized model as when noise is present as an additional component of z(t), the coefficient vector h is time-varying, and the integrators in a hardware implementation have finite memory.

Proceedings ArticleDOI
12 Apr 1976
TL;DR: A new digital filter bank design is proposed for the processing of speech waveforms where spectral pattern matching techniques are applicable and a distance metric is proposedfor comparing a spectral frame with previously derived reference patterns.
Abstract: A new digital filter bank design is proposed for the processing of speech waveforms where spectral pattern matching techniques are applicable. Outputs in decibels from the 30 channels of the filter bank are computed every 12 ms. Care has been taken to select a time window and filter center frequency and bandwidth values that take into account the acoustic characteristics of speech. A distance metric is proposed for comparing a spectral frame with previously derived reference patterns. The metric incorporates procedures for crude speaker/microphone normalization, signal level normalization, background noise normalization, and procedures for emphasizing differences in the region of spectral peaks.

Patent
04 May 1976
TL;DR: In this paper, the authors identify and analyse the parameters of an input signal that contains speech in the presence of simultaneously occuring near-stationary noise, pauses between speech intervals as well as the termination of such noise can be recognized.
Abstract: By identifying and analyzing the properties of the parameters of an input signal that contains speech in the presence of simultaneously occuring near-stationary noise, pauses between speech intervals as well as the termination of such noise can be recognized. When a pause interval containing noise is recognized, the parameters identified during such interval are used to set the parameters of an adaptive filter through which the input signal is passed during subsequent intervals of speech and until the noise terminates. During the time the input signal passes through the filter, the near-stationary noise is filtered out. In response to recognition of the termination of noise, the input signal is caused to by-pass the filter which is then prepared to accept the parameters of noise occuring in a subsequent pause.

Journal ArticleDOI
TL;DR: In this article, the sensitivities of the transfer function of a digital filter with respect to its coefficients are used to derive lower bounds on the roundoff noise output in the cases of L ∞ and L 1 ∞ scaling for fixed-point arithmetic.
Abstract: The sensitivities of the transfer function of a digital filter with respect to its coefficients are utilized to derive lower bounds on the roundoff noise output in the cases of L_{\infty} and L_{\infty} scaling for fixed-point arithmetic. General bounds are produced which apply to any filter structure if rounding is performed after multiplication and the filter has already been scaled. For the parallel and cascade forms, alternate bounds are derived which apply to rounding after multiplication or summation and which do not require prior scaling. The alternate bounds arethus independent (or nearly so) of pairing, ordering, and transposition. Examples are presented which show that the bounds are reasonably tight.

Patent
29 Mar 1976
TL;DR: In this article, an adaptive recursive filter is disclosed which comprises first and second adaptive transversal filters selectively coupled together to minimize the mean square error of the output data of recursive filter based upon observations of input data to the recursive filter.
Abstract: An adaptive recursive filter is disclosed which, in a preferred embodiment, comprises first and second adaptive transversal filters selectively coupled together to minimize the mean square error of the output data of the recursive filter based upon observations of input data to the recursive filter. Each transversal filter includes a tapped delay line with a variable weight on each tap. The output data of the recursive filter is developed by combining the outputs of the first and second transversal filters. The input data is applied to the first transversal filter, while the output data is applied to the second transversal filter. The output data is also combined with a reference signal to provide an error signal. A function of that error signal is utilized to update the weights of all of the taps in both transversal filters in order to cause the weights to automatically adapt themselves to minimize the mean square error of the output data of the recursive filter.

Journal ArticleDOI
TL;DR: A family of 2-D structures is presented for implementing2-D FIR digital filters designed by means of a transformation of a 1-D design that are computationally efficient for filters up to degree 50 x 50 and straightforward to program or build in hardware.
Abstract: A family of 2-D structures is presented for implementing 2-D FIR digital filters designed by means of a transformation of a 1-D design. These implementations are computationally efficient for filters up to degree 50 x 50 and are straightforward to program or build in hardware. Many details of the implementations are discussed such as its susceptibility to coefficient quantization and arithmetic roundoff. A comparison is made between these implementations and other implementations for 2-D FIR filters.

Journal ArticleDOI
TL;DR: It is demonstrated that the linearization algorithm is particularly well suited for recursive filter design, and the steepest descent and Newton methods are found to work rather poorly for this class of problems.
Abstract: The three gradient-based algorithms of 1) steepest descent, 2) Newton's method, and 3) the linearization algorithm are applied to the problem of synthesizing linear recursive filters in the time domain. It is shown that each of these algorithms requires knowledge of the associated recursive filter's first-order sensitivity vectors, and, in the case of the Newton method, second-order sensitivity vectors as well. Systematic procedures for generating these sensitivity vectors by computing the response of a companion filter structure are then presented. Using the ideal low-pass filter as a design objective, it is then demonstrated that the linearization algorithm is particularly well suited for recursive filter design. On the other hand, the steepest descent and Newton methods are found to work rather poorly for this class of problems. Reasons for these empirical observed results are postulated.

Patent
06 Aug 1976
TL;DR: In this paper, a dual channel receiver system for receiving polarized signals, which system reduces cross-interference between the signal channels by utilizing adaptive filter equalization means responsive to the input received signals and to error control signals for providing a plurality of weighting signals which are used to combine selectively with the inputs to reduce the errors, including particularly cross-polarization and noise errors therein.
Abstract: A dual channel receiver system for receiving polarized signals, which system reduces cross-interference between the signal channels by utilizing adaptive filter equalization means responsive to the input received signals and to error control signals for providing a plurality of weighting signals which are used to combine selectively with the input received signals to reduce the errors, including particularly cross-polarization and noise errors therein. The channels each include decision-directed error signal generating means for providing such error control signals. The system also includes means for preventing system failures wherein both received signals fade simultaneously under which conditions data reversal in the channels could occur and wherein one received signal fades under which condition the same data is produced in both channels.

Journal ArticleDOI
TL;DR: In this paper, the design considerations for charge-transfer split-electrode transversal filters are discussed, and the relationship of these parameters to filter performance and accuracy is described.
Abstract: Some of the design considerations for charge-transfer split-electrode transversal filters are discussed. Clock frequency, filter length, and chip area are important design parameters. The relationship of these parameters to filter performance and accuracy is described. Both random and tap weight quantization errors are considered, and the optimum filter length is related to tap weight error. A parallel charge-transfer channel, which balances both capacitance and background charge, and a coupling diffusion between split electrodes greatly improves accuracy. A one-phase clock is used to simplify the readout circuitry. Two off-chip readout circuits are described, and the performance of two low-pass filters using these readout circuits is given. Signal to noise ratios of 90 dB/kHz and an overall linearity of 60 dB have been achieved with this readout circuitry.

Journal ArticleDOI
TL;DR: In this paper, a synthesis technique is proposed for low sensitivity digital ladder filter networks, where the coefficient sensitivity of the magnitude transfer function |H(e^{f{omega}T}| is low valued throughout the passband.
Abstract: Digital ladder filter networks may be realized by applying simple transformations to the flow-graph network representation of continuous domain resistively terminated LC two ports. It is shown that such methods have the disadvantage that there does not exist a transformation with the three requirements that the entire imaginary s -plane axis map to the z -plane unit circle, that the resultant discrete network is stable and finally that the resultant discrete network be computationally realizable due to Its freedom from delay free loops. A synthesis technique is proposed for low sensitivity digital ladders. The conventional transformation that is applied to the LC filter prototype does lead to a stable structure with the required mapping property; the delay free loops are eliminated by straightforward flow-graph manipulation. The coefficient sensitivity of the magnitude transfer function |H(e^{f{\omega}T}| is low valued throughout the passband.

Journal ArticleDOI
01 Nov 1976
TL;DR: This paper presents a method of designing wave digital bandpass (BP) and bandstop (BS) filters whereby the center frequency and bandwidth can be independently controlled by simply changing the multiplier values.
Abstract: This paper presents a method of designing wave digital bandpass (BP) and bandstop (BS) filters whereby the center frequency and bandwidth can be independently controlled by simply changing the multiplier values. Also given are the canonic realizations for the BP and BS wave digital filters. This method of designing BP and BS wave digital filter results in a saving of coefficient registers.

Journal ArticleDOI
Keh Pann1, Y. Shin1
TL;DR: In this paper, the frequency spectrum of the filter is shifted along the frequency axis as a function of time without appreciable change in the spectrum shape, and the design is based on a given time-invariant filter with the desired spectrum shape.
Abstract: A linear time‐varying filtering process usually is realized by applying a number of time‐invariant filters to overlapping time regions of a trace and transitionally merging these different regions. We describe the design of a different type of linear time‐varying filter where the frequency spectrum of the filter is shifted along the frequency axis as a function of time without appreciable change in the spectrum shape. The design is based on a given time‐invariant filter with the desired spectrum shape. For long filter length, the design procedure is rather complicated. Furthermore, only a constant rate of frequency shift is possible. However, for many practical situations where the frequency shift over the filter length is much less than the bandwidth of the filter, the process of time‐varying filtering can be further simplified without appreciable frequency error. In fact, time‐varying filtering is achieved through modifying the complex signal representation of the original time invariant filter by a pre...

Patent
26 Nov 1976
TL;DR: A quadriphase shift keyed (QPSK) adaptive equalizer includes baseband inphase (I) and quadrature (Q) adaptive filters for receiving demodulated OPSK signals.
Abstract: A quadriphase shift keyed (QPSK) adaptive equalizer includes baseband inphase (I) and quadrature (Q) adaptive filters for receiving demodulated OPSK signals. The I and Q channel filters are designed to operate independent of each other and adapt their characteristics continuously in a predetermined manner in response to an incoming received QPSK signal, distorted in an unknown time varying manner.

Journal ArticleDOI
TL;DR: In this article, the authors examined the characteristics of this transformation in greater detail and discussed the range of parameters over which it can be useful, as well as the frequency mapping of the prototype filter response.
Abstract: In a recent paper by Oppenheim, Mecklenbrauker, and Mersereau [1] a class of variable cutoff linear phase digital filters has been proposed. The implementation of this class of filters is achieved by replacing a subnetwork in a prototype network such that it performs a frequency mapping of the prototype filter response. By varying a small number of coefficients in the subnetwork the frequency transformation can be varied. In this letter we examine the characteristics of this transformation in greater detail and discuss the range of parameters over which it can be useful.

Journal ArticleDOI
G. Maria1, M.M. Fahmy1
TL;DR: In this article, a new design technique for digital filters is proposed, which can be used to design digital filters whose response best approximates a prescribed magnitude and group delay response in the passband.
Abstract: A new design technique for digital filters is proposed. This technique can be used to design digital filters whose response best approximates a prescribed magnitude and group delay response. The proposed technique is well suited for the design of filters with constant group delay response in the passband.

Journal ArticleDOI
TL;DR: In this paper, a generalized Bessel filter and a generalized rational filter are considered and a number of special cases of Bessel-type filters are exploited to obtain a variety of filter responses.
Abstract: Bessel-type polynomials are defined and shown to be useful in constructing a variety of transfer functions in filter theory. A generalized Bessel filter and a generalized Bessel rational filter are considered and shown to include a number of special cases of Bessel-type filters. The greater flexibility of the generalized filters is exploited to obtain a variety of filter responses.

Patent
André Desblache1
15 Nov 1976
TL;DR: In this article, a new adaptive digital tuning filter for tracking a sinusoidal signal within a frequency band is described, in which the input signal representative of both the signal and noise is fed to a Hilbert transformer which provides the in-phase and quadrature components, x k and x k, respectively, of the signal.
Abstract: A new adaptive digital tuning filter for tracking a sinusoidal signal within a frequency band is described. The input signal representative of both said sinusoidal signal and noise is fed to a Hilbert transformer which provides the in-phase and quadrature components, x k and x k , respectively, of said sinusoidal signal. These components are applied to the input of a filter having a transfer function K where ##EQU1## WHERE φ = 2πFT, f is the tuned frequency of the filter, T is the signal sampling period and a is a constant close to unity. The output signals y x and y x of the filter are applied to a computing means which provides a frequency control signal e k such that e.sub.k = x.sub.k y.sub.k - y.sub.k x.sub.k The above value of φ is adjusted through a conventional gradient method where φ.sub.k + 1 = φ.sub.k + μe.sub.k and controls are provided to adjust φ in a direction to change e k toward zero. Application of the adaptive tuning filter to cancellation of the main component of phase jitter in a modem is also described.

Patent
23 Feb 1976
TL;DR: In this paper, a signal processing means and method of adaptively filtering input signals received at a terminal means in which the input signals include pulse signals and noise, with the pulse signals occurring at unknown times and having unknown durations.
Abstract: A signal processing means and method of adaptively filtering input signals received at a terminal means in which the input signals include pulse signals and noise, with the pulse signals occurring at unknown times and having unknown durations, which includes signal filtering means having a first input for receiving signals derived from the terminal means, a second input and an output, the signal filtering means having a controllable filter characteristic for passing signals from its first input to its output responsive to signals received at its second input, and a signal analyzing means having an input receiving signals derived from said terminal means and an output delivering signals which are responsive to signals received at its input, to the second input of said signal filtering means for controlling its filter characteristic, whereby the output of the signal filtering means delivers signals corresponding to the pulse signals of the input signals to said terminal means while minimizing delivery of noise signals received at said terminal means. The means and method utilizes orthogonal transformations of the input signals for processing the input signals and adaptively filtering the orthogonal signal components for providing at the output, pulse signals present in the input signal with reduction in the noise level. Walsh functions are utilized for filtering rectangular pulse signals while other orthogonal functions, including Fourier functions, are utilized for filtering non-rectangular pulse signals. The incoming signals are preferably converted to digital form and transformed by the orthogonal functions for adaptive filtering, after which the signals may be reconverted by an inverse transformation and delivered in digital or analog form. Rectangular pulse signals after being transformed back into the time domain, are further reconstructed by a thresholding operation providing the original DC level for the signal, together with the rectangular signals determined by the means and method of the invention to be present in the input signal.

Proceedings ArticleDOI
01 Apr 1976
TL;DR: A technique is presented for the design of stable two-dimensional recursive digital filters, where the stability of the resulting filters is guaranteed, and hence repeated application of cumbersome stability tests is obviated.
Abstract: A technique is presented for the design of stable two-dimensional recursive digital filters. The stability of the resulting filters is guaranteed, and hence repeated application of cumbersome stability tests is obviated. The transfer function of the filter is obtained from a one-dimensional prototype by applying a new transformation technique in the frequency domain. To illustrate the approach some design examples of low-pass filters are given.

Journal ArticleDOI
TL;DR: In this paper, a method for designing 2D recursive digital filters with circular symmetry and zero phase was proposed, based on transformations of the squared magnitude function of a 1D digital filter and on the stabilisation of the resulting digital filter.
Abstract: A method is proposed for designing 2-dimensional recursive digital filters with circular symmetry and zero phase. The method is based on transformations of the squared magnitude function of a 1-dimensional digital filter and on the stabilisation of the resulting digital filter. Design results are given.