Showing papers on "Adaptive filter published in 1972"

Frequency Filter for Time Integrations

Abstract: A simple filter for controlling high-frequency computational and physical modes arising in time integrations is proposed. A linear analysis of the filter with leapfrog, implicit, and semi-implicit, differences is made. The filter very quickly removes the computational mode and is also very useful in damping high-frequency physical waves. The stability of the leapfrog scheme is adversely affected when a large filter parameter is used, but the analysis shows that the use of centered differences with frequency filter is still more advantageous than the use of the Euler-backward method. An example of the use of the filter in an actual forecast with the meteorological equations is shown.

Approaches to adaptive filtering

Abstract: The different methods of adaptive filtering are divided into four categories: Bayesian, maximum likelihood (ML), correlation, and covariance matching. The relationship between the methods and the difficulties associated with each method are described. New algorithms for the direct estimation of the optimal gain of a Kalman filter are given.

Stability and synthesis of two-dimensional recursive filters

Abstract: Two-dimensional recursive filters are conveniently described in terms of two-dimensional z transforms. The designer of these filters faces two fundamental problems, their stability and their synthesis. Stability is determined by the location of the zero-valued region of the filter's denominator polynomial. A conjecture based on a one-dimensional stability theorem leads to a useful empirical stabilization procedure. Two-dimensional recursive filters can be synthesized to approximate large varieties of desired two-dimensional pulse responses. A conformal transformation yields two-dimensional recursive bandpass filters from appropriately specified one-dimensional filters.

Linear program design of finite impulse response (FIR) digital filters

Abstract: The use of optimization techniques for designing digital filters has become widespread in recent years. Among the techniques that have been used include steepest descent methods, conjugate gradient techniques, penalty function techniques, and polynomial interpolation procedures. The theory of linear programming offers many advantages for designing digital filters. The programs are easy to implement and yield solutions that are guaranteed to converge. There are many areas of finite impulse response (FIR) filter design where linear programming can be used conveniently. These include design of the following: filters of the frequency sampling type; optimal filters where the passband and stopband edge frequencies of the filter may be specified exactly; and filters with simultaneous constraints on the time and frequency response. The design method is illustrated by examples from each of these areas.

Design techniques for two-dimensional digital filters

Abstract: The theory for designing finite-duration impulse response (FIR) digital filters can readily be extended to two or more dimensions. Using linear programming techniques, both frequency sampling and optimal (in the sense of Chebyshev approximation over closed compact sets) two-dimensional filters have been successfully designed. Computational considerations have limited the filter impulse response durations (in samples) to 25 by 25 in the frequency sampling case, and to 9 by 9 in the optimal design case. However, within these restrictions, a large number of filters have been investigated. Several of the issues involved in designing two-dimensional digital filters are discussed.

On the design of digital filters with coefficients of limited word length

Abstract: The cost of a digital filter, if implemented as a special-purpose computer, depends heavily on the word length of the coefficients. Therefore, it should be reduced as much as possible. On the other hand, a small word length causes large coefficient deviations that impair the wanted performance of the digital filter. The necessary word length may be reduced by choosing a suitable structure for the filter. Two methods for doing this will be presented, taking selective filters as a model. A further reduction of the word length may be won by optimizing the rounded filter coefficients in the discrete parameter space. A description of a modified univariate search will be given.

A simple design of maximally flat delay digital filters

Abstract: The problem of maximally flat delay design of recursive digital filters has been solved by Thiran, using a direct z-domain approach. In this paper, the solution is obtained in a much simpler way by making use of the familiar bilinear transform s of the variable z. A suitable continued fraction expansion available in the mathematical literature is shown to lead immediately to the required solution. The approach corresponds to the one used by Abele in transmission line filter design.

A unified treatment of recursive digital filtering

Abstract: Using the convolution integral, an integro-difference equation is derived for defining the input-output relation of a linear time-invariant filter. This equation is, in turn, used to obtain the various analog-to-digital filter transformations for the digitization of a continuous transfer function, with each transformation corresponding to a specific way of approximating the continuous time excitation.

Adaptive Decomposition of a Composite Signal of Identical Unknown Wavelets in Noise

Abstract: An algorithm is discussed which decomposes a noisy composite signal of identical but unknown multiple wavelets overlapping in time. The decomposition determines the number of wavelets present, their epochs, amplitudes, and an estimate of the basic wavelet shape. The algorithm is an adaptive decomposition filter which is a combination tion of three separate filters. One is an adaptive cross-correlation filter which resolves the composite signal from noise by an iteration procedure; this is followed by a wavelet extraction filter which ferrets out the basic wavelet form, and last there appears an inverse filter which achieves decomposition of the composite signal in the time domain. The decomposition algorithm can be applied to echoes and overlapping wavelets which might arise in radar, sonar, seismology, or electro-physiology. The proposed theory has been thoroughly simulated and selected experimental results are presented to demonstrate the technique. These include decomposition of brain waves evoked by visual stimulation.

Adaptive matched digital filter

Abstract: A real time digital filter with its transfer function being matched to a particular signal plus noise condition in a manner that causes the transfer function to adapt to changing signal plus noise conditions. A transversal type of digital filter is disclosed. A general purpose computer calculates coefficients of the filter by continuously monitoring the input signal plus noise in order to maintain the filter's transfer function at an optimum level in view of changing noise conditions.

A comparison of computations for spatial frequency filtering

Abstract: Three computational algorithms for performing spatial frequency filtering are compared and tradeoffs developed Although each method is defined by a convolution relation, the convolution computations are different Equal filter point-spread functions are assumed to effect the comparison If the filter point-spread function is nonzero only over a small area, then the computation tradeoff is simply the well-known comparison between direct convolution and the fast Fourier trsnsform (FFT) If the filter point-spread function is nonzero over a large area, then a recursive filter is competitive with the FFT Core memory requirements for this case are smallest with the recursive filter Experimental examples are given to illustrate the subjective evaluation problem

Digital filter to realize efficiently the filtering required when multiplying or dividing the sampling rate of a digital signal by a composite integer

Abstract: A digital filter employing a plurality of unit cells connected in cascade. Each unit cell includes a duplicating filter (typically a plurality of boxcar integrators connected in cascade). A switch is connected between the output of each duplicating filter and the output of the unit cell of which it is a part. The switch is operable to reduce the data rate to a submultiple of the input data rate to the associated duplicating filter, the sub-multiple being equal to the parameter R of the duplicating filter, where R is the number of points in the boxcar integrator impulse response when the duplicating filter is composed of boxcar integrators. In another form the switch is placed between the input to the unit cell and the input to the duplicating filter to increase the data rate and R in this latter situation is the multiple by which the data rate is increased. Two or more digital filters wherein the rate is reduced may be combined to form a band-pass filter or a bank of band-pass filters.

Correction to "Recursive and non-recursive realization of digital filters designed by frequency sampling techniques"

Abstract: The purpose of this correspondence is to correct some inaccuracies in the above paper. Specifically, we refer to the results in the Section "Linear Phase Type 2 Filters" (pp. 205-207). Although the results of that section are correct for the conditions stated, the constraints on phase delay and H_{(N-1)/2} are more restrictive than necessary. Therefore, we offer the following as a correction to the original section.

Vor receiver with adaptive filters and phase shifter for improved accuracy

Abstract: An improved VOR receiver which includes adaptive band pass filters for the 30 Hz reference and variable signals and an electronic phase shifter for shifting the variable and reference signals into phase coincidence, the amount of phase shift thus introduced being a measure of VOR bearing angle. The phase shifter is controlled by a feedback loop having a limiter which controls the rate of change of phase shift as a function of distance from the VOR station thereby reducing effects of scolloping in the beam of the VOR transmitter upon bearing indications.

Comments on "On the identification of variances and adaptive Kalman filtering"

Abstract: It has been found that a modification is required in the test proposed in a paper by Mehra. The purpose of this test is to tell whether or not identification is complete. This modification is described and an example showing the need for the modification is given.

Canonic realizations of second-order digital filters due to finite precision arithmetic

Abstract: Extending a procedure first used by Jackson, it is demonstrated that because of quantization after multiplications, practical realizations of second-order digital-filter sections are limited to 24 basic structures with the same transfer function.

Design and Simulation of Digital Filter Banks for Speech Analysis

Abstract: Short‐time spectrum analysis is the basis for many speech analysls systems. Although the fast Fourier transform is generally used to perform spectrum analysis on a general purpose computer, a bank of recursire digital bandpass filters may be the best approach for hardware realizations. This paper discusses the analysis and design of digital filter banks composed of equal‐bandwidth, equally spaced, bandpass filters. It is shown that significant improvement in the frequency response of the composite filter bank can be achieved by appropriate choice of the relative phases of the bandpass filters. Also discussed is an efficient general purpose computer simulation of a bank of recursire digital filters as required, for example, in a phase vocoder analyzer [Flanagan and Golden, Bell Syst. Tech. J. (Nov. 1966), This simulation uses the fast Fourier transform to compute filter outputs at a low sampling rate (approximately 100 Hz). For synthesis, the spectrum parameters are interpolated to a 10‐kHz sampling rate u...

Limit cycles in digital filters

Abstract: A study is made of the nonlinear phenomenon of limit cycles in digital filters implemented using fixed point arithmetic with product rounding. By investigating individually the different types of limit cycles, bounds are derived on the coefficients for second-order filters in the direct and canonic form that are more efficient than earner bounds. Then the results are extended to filters connected in cascade.

New linear smoothing formulas

Abstract: Formulas are given expressing the smoothed estimate of the state of a noisy linear system in terms of filtered estimates of the state, for both continuous and discrete time.

On frequency sampling digital filters

Abstract: It has been shown that the frequency sampling technique for the design of nonrecursive digital filters in conjunction with a search for optimum transition band samples yields good digital filter designs. It is shown that the frequency sampling technique is directly related to the Fourier series design and modifications are proposed for simplifying the design procedure.

z-transform analysis of nonuniformly sampled digital filters

Abstract: The paper presents a z transform analysis of digital filters operated with nonuniform sample periods. The analysis is applicable to filters using a mean-square definition of transfer function, e. g. moving-target-indicator filters, and also to conventional digital filters. The evaluation of the frequency response of such filters using the analytic results of the paper leads to considerable savings in computation time over direct simulation methods. Nonuniform sampling of conventional digital filters is shown to result in a reduction of the effective Nyquist frequency, although, within this limited frequency range, additional control of the frequency response is possible for certain filters. A pole-zero diagram may be drawn for a nonuniformly sampled filter, and allows comparisons to be made with the corresponding uniformly sampled case.

Numerical filter and digital data transmission system including said filter

Abstract: The invention relates to a digital filter which can be programmed, and a digital data transmission system employing automatic equalization of the transmission channel, said transmission system being adapted in such a manner that said digital filter can be used for the filter functions of transmitter and receiver.

Digital filter realizations using a special-purpose stored-program computer

Abstract: A special-purpose computer is organized to realize a second-order digital filter in a choice of 11 programming forms. Instructions for the forms are stored in a fast-access READ-ONLY memory. Also, a hard-wired multiplier is employed in the Arithmetic Unit to decrease computation time. The multiplier is organized into uniform functional blocks that are suitable for large-scale integration (LSI). A computer-aided design (CAD) program may be used to select the best filter programming form for a given filter transfer function D(z) . The CAD program also aids in the location of the binary point in the data registers of the computer.

Multilevel digital filter

Abstract: A multi-level digital filter system applicable to modems is provided. The incoming data is read serially into M shift registers and read out in parallel by M further shift registers under the control of an M-bit clock, where M=log2N and N is the number of levels. After appropriate conditioning by a logic control circuit, the parallel outputs are filtered separately by M digital shaping filters. The shaping filters each comprise a chain of shift registers the outputs of which are weighted by a resistor network and summed to produce a desired time response, which in an exemplary embodiment is the inverse Fourier transform of an ideal low-pass filter. Summing of the filter outputs produces an N-level signal.

On stochastic approximation and an adaptive Kalman filter

Abstract: The orthogonality between the innovations process and the one-step predicted state of a discrete-time Kalman filter is used to specify a stochastic approximation algorithm for simple, adaptive Kalman filtering. The filter is adaptive in the sense that on-line filter signals are used to train the gain matrix to its correct, steady-state form. The problem considered is one of training the gain matrix when the time-invariant plant dynamics are known, but the plant noise and observation noise covariance matrices are unknown. No direct identification of these covariances is required. Simulation results are presented to illustrate the simplicity and soundness of the proposed adaptive filter structure. The simplicity of the proposed adaptation method indicates that it might easily be implemented in real-time data or signal processing applications.

Digital Filter Realizations Using a Special-Purpose Stored-Program

Abstract: A special-purpose computer is organized to realize a second-order digital filter in a choice of 11 programming forms. In- structions for the forms are stored in a fast-access READ-ONLY memory. Also, a hard-wired multiplier is employed in the Arithmetic Unit to decrease computation time. The multiplier is organized into uniform functional blocks that are suitable for large-scale integra- tion (LSI). A computer-aided design (CAD) program may be used to select the best filter programming form for a given filter transfer function D(z). The CAD program also aids in the location of the binary point in the data registers of the computer.

System using adaptive filter for determining characteristics of an input

Abstract: An adaptive filter system for determining characteristics of an electrical input signal, such as resonant frequencies, anti-resonant frequencies, etc. which includes a plurality of anti-resonance circuits and/or resonance circuits coupled to an input signal, means for developing indicator signals indicate the deviation of the anti-resonant and/or resonant frequencies of the circuits from the anti-resonant and/or resonant frequencies of the input signal, and means for cross-correlating the output from at least one of the circuits with the indicator signals, and for generating correction signals as a function of the cross-correlation. The correction signals are fed to the circuits to vary the anti-resonant and/or resonant frequencies thereof so that the frequencies correspond to the respective resonant and/or anti-resonant frequencies in the input signal.

A slow approach to mechanizing a fast digital interpolation filter

Abstract: A digital data processor is mechanized using a given technology operating near its maximum speed. In order to digitally modulate this signal, the sampling rate of the information channel is increased and the data are smoothed by passing them through an interpolation filter. The faster sampling rate and higher speed interpolation filter appear to demand a change to a higher speed technology. This correspondence demonstrates that the slower technology can be carried through the interpolation filter stage.