Showing papers on "Filter design published in 1971"

New automatic equaliser employing modulo arithmetic

Abstract: The limitations of present automatic and adaptive equalisers stem from the use of feedforward transversal filters. These drawbacks may be obviated by using a feedback transversal filter, the inverse filter, but this is only suitable for limited use since it can be an unstable circuit. It is shown that modulo arithmetic may be used in the inverse filter to eliminate completely the possibility of instability, and a very simple automatic or adaptive equalisation system is presented. Some interesting properties of the modulo inverse filter are included.

Phase-Only Complex-Valued Spatial Filter*

Abstract: A new type of phase-only filter is described for wave-front construction, in which both the amplitude and phase information necessary to construct an arbitrary image over a limited field are encoded. It is shown that this phase-only filter can duplicate the performance of an ideal complex-valued spatial filter (a filter that controls both amplitude and phase transmittance). This phase-only filter controls the amplitude transmittance by the use of a modulated high-frequency phase carrier that diffracts a controlled amount of light into the image. This type of filter is particularly useful in the implementation of computational wave-front construction, because the maximum spatial frequency that must be plotted is associated with the image and not the carrier. The performance of the filter is examined both numerically and experimentally.

Real-Time Tracking Filter Evaluation and Selection for Tactical Applications

Abstract: Five important tracking filters that are often candidates for implementation in systems that must track maneuvering vehicles are compared in terms of tracking accuracy and computer requirements for tactical applications. A rationale for selecting among these filters, which include a Kalman filter, a simplified Kalman filter, an ?-s filter, a Wiener filter, and a two-point extrapolator, is illustrated by two examples taken from the authors' recent experience.

Computational requirements for a discrete Kalman filter

Abstract: How practical is a Kalman filter? One answer to this question is provided by the computational requirements for the filter. Computational requirements-computational time per cycle (iteration) and required storage-determine minimum sampling rates and computer memory size. These requirements are provided in this paper as functions of the dimensions of the important system matrices for a discrete Kalman filter. Two types of measurement processing are discussed: simultaneous and sequential. It is shown that it is often better to process statistically independent measurements in more than one batch and then to use sequential processing than to process them together via simultaneous processing.

Techniques for Designing Finite-Duration Impulse-Response Digital Filters

Abstract: Several new techniques for designing finite-duration impulse-response digital filters have become available in the past few years. The motivation behind three design techniques that have been proposed are reviewed here, and the resulting designs are compared with respect to filter characteristics, ease of design, and methods of realization. The design techniques to be discussed include window, frequency-sampling, and equiripple designs.

Recursive and nonrecursive realizations of digital filters designed by frequency sampling techniques

Abstract: A great deal of work has been done recently on techniques for optimally designing finite duration impulse response (FIR) filters. One of these techniques, called frequency sampling, is a method for designing a digital filter from a set of samples of the desired filter frequency response. In this paper we present a unified discussion of the various types of frequency sampling designs and show how to realize them, both recursively and nonrecursively.

Signal Versus Noise Characteristics of Filtered EMG Used as a Control Source

Abstract: A common method of initially processing surface-detected electromographic (EMG) activity is to differentially amplify, rectify, and then smooth (using a low-pass filter) the rectified activity. The output of the filter exhibits a mean value slightly obscured by ripple. Both the mean value and ripple increase with increasing muscle contraction. The mean value can be called the signal while the ripple, undesirable when only the signal is desired, can be called noise. The SNR depends, at least, upon the contraction level, type of smoothing filter, and the amount of smoothing for the particular filter. This defined SNR is important in signal communication problems of both a design and a theoretical nature.

Recursive digital filters for biological signals

Abstract: Digital filters achieve their frequency-selective properties by operating on the values of a sampled-data signal. After outlining an important design method for such filters, two classes of recursive digital filter of particular value for the processing of biological signals are described in some detail. These are applied to the recovery of an ECG waveform from wide- and narrowband contaminating noise.

A Comb-Line Elliptic Filter

Abstract: The design of a new type of elliptic filter, particularly suitable for narrow-band low-loss applications at VHF and UHF, is presented. The filter is derived from a lumped-element bandpass prototype by replacing the lumped inductors, which are normally the main contributory factors to the loss, by a comparatively low-loss distributed network. The latter consists of an n-wire digital line short-circuited at one end, the length of which is i/8 or less. An experimental elliptic filter of fifth order was constructed at 136.6 MHz with a pass bandwidth of 5 MHz, having 60-dB points at /spl plusmn/ 7 MHz from midband. The measured insertion loss of 1.1 dB is lower than that of a comparable lumped-element filter by a factor of at least 3,5:1. It compares favorably also with a comb-line filter, both in terms of loss and physical size.

Optimal mismatched filter design for radar ranging, detection, and resolution

Abstract: In a multiple-target environment a radar signal processor often uses weighting filters that are not matched to the transmitted waveform. In this paper the mean-square range-estimation error, the detection Signal-to-noise ratio (SNR), and the effects of sidelobes are expressed in terms of the impulse response of an arbitrary mismatched filter. It is desired to find that impulse response that results in the minimum range-estimate variance subject to preassigned constraints on the side-lobes and the detection SNR. It is shown that for detecting the radar target and estimating its range, the form of the optimum filter is a modified transversal equalizer. If only detection is required, the optimum filter reduces to the transversal equalizer. Certain parameters upon which the solution depends can be found by solving a nonlinear programming problem. Numerical results are given for an interesting class of transmitted waveforms.

Structure of optimum receiving filters in data transmission systems (Corresp.)

Abstract: It has been observed by several authors that a number of different optimum receiving filters (corresponding to different criteria of goodness) for sampled-data transmission systems can be factored as a product of a matched filter and a periodic filter with the period equal to the sampling frequency. By a simple argument it is shown in this correspondence that any reasonable criterion of goodness will lead to an optimum filter that has this form.

Return-difference matrix properties for optimal stationary Kalman-Bucy filter

Abstract: A strikingly simple characterisation of the optimal stationary Kalman-Bucy filter is obtained in terms of the return-difference matrix for the associated feedback system. The spectral factorisation of the observation spectral-density matrix is shown to generate directly the appropriate return-difference matrix. This leads to a physical interpretation of the mechanism by which signal and noise are separated, which could form the basis of an approach to filter design.

Multiple-constraint adaptive filtering

Abstract: An algorithm is derived for multichannel time‐series data processing, which maintains specified initial multiple filter constraints for known signal or noise sources while simultaneously adapting the filter to minimize the effect of the unknown noise field. Problems of implementing the technique such as convergence, determination of a starting filter, and comparison of results with conventional filters are discussed and illustrated with data from a vertical seismic array. The procedure is shown to be stable and obtains approximately 3–4 db gain in S/N improvement over conventional Wiener filtering in the band 1 to 3 hz.

Filter Distortion and Intersymbol Interference Effects on PSK Signals

Abstract: The combined effects of filter distortion and the associated intersymbol interference on coherently detected biphase and quadriphase PSK signals are studied in white Gaussian noise. A determination is made of the system performance degradation from matched-filter detection resulting from the use of a linear channel model that focuses attention on the critical filters in the communication link. The critical filters that affect performance consist of transmission filters in the transmitter and/or transponder, receiver predetection filters, and data filters associated with the detector. Numerical results for adjacent symbol interference are given for detection using both integrate-and-dump filters as well as more general data filters, particularly an undumped 2-pole Butterworth data filter. The numerical results include symmetrical band limiting, broad-band filtering with a frequency offset, mismatched data filtering, cascaded filter chains, and the effects of pure phase distortion.

Variable bandpass dynamic noise filter

Abstract: A variable bandpass filter for a dynamic noise filtering effect that reduces the perceptible noise in an audio reproduction system. The variable bandpass filter responds to peak signal levels in relatively high and relatively low frequency portions of the audio spectrum to automatically and independently vary high and low frequency cutoff points for the filter in correspondence with the level of signals at those frequencies. Low distortion and wide dynamic range is achieved in a filter configuration which comprises a forward signal path and a reverse signal path, each having a variable integration response provided by temperature compensated and linearized field-effect transistor circuits. The integration response of the two paths imparts a high and low frequency filtering effect. A further constant gain feedback path establishes a uniform middle frequency amplification for the variable bandpass filter.

Design of digital filter banks for speech analysis

Abstract: A bank of bandpass filters is often used in performing short-time spectrum analysis of speech signals. This paper is concerned with the analysis and design of digital filter banks composed of equally spaced bandpass filters. It is shown that significant improvement in the composite filter bank response can be achieved by proper choice of the relative phases of the bandpass filters. The results are extended to more general filter bank configurations.

Automatic tuning electric wave filter

Abstract: A band pass filter for use in RF transmitting or receiving apparatus comprises a plurality of resonant stages coupled through variable apertures whose areas are dependent on the tuning adjustment of the resonant stages whereby a substantially constant bandwidth and insertion loss are achieved over the tuning range. Tuning is effected by a servomechanism responsive to the conditions of phase and signal level at the input and output ports of the filter. The phase and signal level are sensed through directional couplers at the input and output ports of the filter. The couplers at the filter input and output act as matching sections, thereby minimizing losses.

New Design Equations for a Class of Microwave Filters (Correspondence)

Abstract: New approximate design equations for a class of microwave bandpass filters are presented. The filters are 1) dual forms of half-wave parallel-coupled resonator filters, 2) one form of interdigital filter, and 3) dual forms of direct-coupled stub filters. The advantages derived from using the new equations are 1) exact realization of the specified design bandwidth and 2) improved pass-band voltage standing-wave ratio (VSWR) response in the vicinity of band edge. Experiments data are presented for a trial filter design having 7 resonators, 40-percent bandwidth, and passband VSWR of 1.2.

The Kalman-Bucy Filter as a True Time-Varying Wiener Filter

Abstract: The notion is exploded that to build a Kalman-Bucy filter, one needs to know the whole structure of the signal generating process. It is shown that the filter is constructible knowing precisely those covariances required to construct a Wiener filter, and no more, and that the filter is independent of the particular models of the processes generating these covariances. Performance of the Kalman-Bucy filter does depend on the models, however. Results are also obtained for the smoothing problem.

Optimum digital filtering and inverse filtering in the frequency domain

Abstract: Two distinct filters are developed in the frequency domain which represent an attempt to increase the resolution of fine structure contained in the signal whilst keeping the expected filtered noise energy within reasonable bounds. A parameter termed the White Noise Amplification is defined and used together with a measure of the deconvolved pulse width in order to provide a more complete characterisation of the filters. Each of the two main types of frequency domain filters discussed varies in properties with respect to a single adjustable parameter. This may be contrasted with a time domain Wiener filter which in general has three variables: length, delay and an adjustable noise parameter or weight. The direct frequency domain analogue of the Wiener filter is termed a gamma-Fourier filter, and is shown to have properties which span the range from those of a spiking filter with zero least square error at one extreme, to those of a matched filter at the other extreme of its variable parameter's range. The second type of filter considered—termed the modulated Gaussian filter—is similarly shown to be a perfect spiking filter at one extreme of its parameter range, but adopts the properties of an output energy filter at the other extreme.

On Synthesis of Filters

Abstract: A general classification of reactive ladder filters with real transmission zeros is given which is based on the extreme frequency behavior of port impedances and on types of design polynomials of the characteristic and effective transmission functions. It is shown that this classification provides an ordered algorithm for automatic realization of ladder structures which can be used to construct a logical development of appropriate computer programs. The bilinear frequency transformation is extended to all filter classes for a synthesis procedure entirely in the transformed plane. Accuracy limitations of this method are discussed and reasons for them are pointed out. A recently developed method of filter synthesis is proposed, which does not require high accuracy working in a computer because it operates throughout with simple factors which are never multiplied into polynomials. A design example of a through-supergroup filter is offered which demonstrates limitations of standard synthesis procedures.

Shaping filter representation of nonstationary colored noise

Abstract: The problem of determining a shaping filter for nonstationary colored noise is considered. The shaping filter transforms white noise into a possibly nonstationary random process (having no white noise component) with a specified covariance function. A set of conditions to be satisfied by the covariance function leads to the determination of a shaping filter. The shaping filter coefficients are simply related to the solution of a matrix Riccati equation. In order to formulate the Riccati equation, basic results concerning the mean-square differentiability of a random process are developed. If the Riccati equation can not be defined, an autonomous (zero-input) shaping filter may be easily determined.

System for spectrum analysis including digital filter with variable sampling rate

Abstract: A system for analyzing the frequency spectrum of an input signal includes a digital filter, the center frequency of which is varied by changing the sampling rate. The output signal of the digital filter is squared in a detector circuit; and the output signal of the detector circuit is fed to an integrator circuit. The integration time is varied inversely proportional to the center frequency of the digital filter to obtain a signal representative of the power spectrum of the input signal.

Digital filters with poles via the FFT

Abstract: A method is presented that uses the fast Fourier transform (FFT) to compute the output of an infinite-impulse-response digital filter. This method uses the summability of infinite-length geometric sequences to account for the aliasing that is inherent in using the discrete Fourier transform (DFT) to calculate convolutions. Previous procedures that use the FFT to realize recursive digital filters require that the filter have a large number of poles and zeros before the FFT method offers a computational advantage over the direct implementation of the filter. The technique presented here is competitive with direct filter implementation.

Linear minimum-variance estimation and control in systems with state-dependent noise

Abstract: A recursive, minimum-variance linear filter and controller is derived for systems in which white state-dependent noise appears in the system dynamics and measurements. The filter without control is a generalization of the Kalman filter and possesses many of its desirable properties. First, the discrete form of the filter is derived. By taking a formal limit, a continuous filter with convergence in distribution to an Ito representation is obtained. The concept of a perfect controller is given, showing the formal duality of the filter and controller with the stochastic controller derived by Wonham. Finally, some of the properties of the filter-controller system are illustrated through the use of a scalar example. It is shown that a filter-controller designed by neglecting the state-dependent noise can destabilize a dynamically stable system.

Probability Weighting of Spatial Filters

Abstract: The optimum spatial filter for the detection of randomly located patterns is discussed. When the signal-to-noise (S/N) ratio is low, the optimum filter is described by the product of the Fourier transform of the probability distribution describing the signal location and the conjugate of the signal spatial spectrum divided by the noise spectral density. The fabrication of such a filter is described. Other cases discussed are those of high S/N ratio and uniform probability distribution.

Computer Aids in Filter Design: A Review

Abstract: The role of the digital computer in various phases of electric filter design is summarized in this review paper. It is pointed out that as the computer made it possible to design more and more sophisticated and complicated filters, more numerical problems arose that necessitated new theoretical advances in the field. Brief descriptions of these new developments as well as assessments of the present situation are given for conventional passive, RC -active, and digital filters.

Nonlinear extensions of the fading memory filter

Abstract: The equations for a recursive extended Kalman filter with exponential age-weighting of data and dynamics are derived. A similar result is given for a second-order filter. It is seen that the filter equations are essentially of the same form as their unfaded counterparts. This technique offers promise in controlling the divergence problem that recursive filtering often encounters.