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Showing papers on "Filter design published in 1974"


Journal ArticleDOI
TL;DR: A new tracking filter is developed that incorporates, in an a posteriori statistical fashion, all data available from sensor reports located in the vicinity of the track, and that provides both optimal performance and reliable estimates of this performance when operating in dense environments.
Abstract: When tracking targets in dense environments, sensor reports originating from sources other than the target being tracked (i.e., from clutter, thermal false alarms, other targets) are occasionally incorrectly used in track updating. As a result tracking performance degrades, and the error covariance matrix calculated on-line by the usual types of tracking filters becomes extremely unreliable for estimating actual accuracies. This paper makes three contributions in this area. First, a new tracking filter is developed that incorporates, in an a posteriori statistical fashion, all data available from sensor reports located in the vicinity of the track, and that provides both optimal performance and reliable estimates of this performance when operating in dense environments. The optimality of and the performance equations for this filter are verified by analytical and simulation results. Second, several computationally efficient classes of suboptimal tracking filters based on the optimal filter developed in this paper and on an optimal filter of another class that appeared previously in the literature are developed. Third, using an extensive Monte Carlo simulation, the various optimal and suboptimal filters as well as the Kalman filter are compared, with regard to the differences between the on-line calculated and experimental covariances of each filter, and with regard to relative accuracies, computational requirements, and numbers of divergences or lost tracks each produces.

282 citations


Journal ArticleDOI
Dominique Godard1
TL;DR: This paper shows how a Kalman filter may be applied to the problem of setting the tap gains of transversal equalizers to minimize mean-square distortion, and its speed of convergence depending only on the number of taps.
Abstract: This paper shows how a Kalman filter may be applied to the problem of setting the tap gains of transversal equalizers to minimize mean-square distortion. In the presence of noise and without prior knowledge about the channel, the filter algorithm leads to faster convergence than other methods, its speed of convergence depending only on the number of taps. Theoretical results are given and computer simulation is used to corroborate the theory and to compare the algorithm with the classical steepest descent method.

271 citations


Journal ArticleDOI
TL;DR: The method is extended to recursive filters and a comparison is made with existing techniques of implementing digital filters for the needs in computation and storage hardware: a specific example of design underlines the reduction in computation speed achieved in practice through this method.
Abstract: Any digital filter can be decomposed into two basic subsets, an extrapolator the output of which is sampled at a frequency depending only on the filter bandwidth and an interpolator delivering the filtered signal at the imposed output sampling rate. Redundancy in extrapolator and interpolator is removed by introducing half-band nonrecursive filtering elements for which definition, performance figures and efficient implementation are supplied. They reduce significantly the necessary computation and storage at the cost of a slight group delay increase. A formula is given for the amount of multiplications to be carried out every second in a filter; it depends on the filter bandwidth, signal to distortion ratio, and input-output sampling rate. The method is extended to recursive filters and a comparison is made with existing techniques of implementing digital filters for the needs in computation and storage hardware: a specific example of design underlines the reduction in computation speed achieved in practice through this method, which brings digital filters in a most favorable position for their competition against analog filters in many application fields.

133 citations


Journal ArticleDOI
G. Maria1, M. Fahmy
TL;DR: An optimization algorithm is developed to minimize the p-error criterion under the constraint that the resulting filter be stable, and several examples are solved to illustrate the technique.
Abstract: In this paper a design technique for the two-dimensional filters is proposed. An optimization algorithm is developed to minimize the p-error criterion under the constraint that the resulting filter be stable. Design of one-dimensional filter may be considered as a special case to which the proposed algorithm is applicable. Several examples are solved to illustrate the technique.

108 citations


Journal ArticleDOI
TL;DR: The philosophy adopted is that for a given FIR filter structure, the filter coefficients can be designed to provide a minimum mean-squared error (MMSE) estimate of a random signal sequence imbedded in a random noise sequence.
Abstract: The problem of designing a finite duration impulse response (FIR) digital filter to approximate a desired spectral response is treated in this paper. The philosophy adopted is that for a given FIR filter structure, the filter coefficients can be designed to provide a minimum mean-squared error (MMSE) estimate of a random signal sequence (the design-signal) imbedded in a random noise sequence. By treating the signal and noise covariance functions as design parameters, one can design FIR filters with spectral responses that approximate the power spectral density of the design-signal. For signal processing applications that require some attention to signal fidelity, as well as noise rejection, the MMSE philosophy seems appropriate (as opposed to a maximum signal-to-noise ratio philosophy, for example). Several practical designs are presented that emphasize the simplicity of the design technique and illustrate the selection of design parameters. The designs show quite dramatically that the MMSE design technique can be competitive with existing low-pass and bandpass design techniques. Finally, considerable attention is given to an efficient Toeplitz matrix inversion algorithm that permits rapid inversion of the covariance matrices that arise in the MMSE design. The resulting computation times for the design of high-order filters (N = 128, e.g.) appear to be shorter than computation times for competing algorithms.

62 citations


Journal ArticleDOI
TL;DR: It is shown that a second-order digital notch filter is uniquely characterized by two distinct parameters, the notch frequency and the 3-dB rejection bandwidth, as a result, such a filter can be realized using only two multipliers.
Abstract: It is shown that a second-order digital notch filter is uniquely characterized by two distinct parameters, the notch frequency and the 3-dB rejection bandwidth. As a result, such a filter can be realized using only two multipliers. Methods are outlined to design a notch filter for a prescribed notch frequency and a prescribed 3-dB rejection bandwidth, along with procedures for postdesign adjustment of these parameters. All two-multiplier, canonic and noncanonic, notch filter configurations are developed using the multiplier extraction approach. These networks are then compared with regard to the effect of internal multiplication roundoff errors. Results of computer simulation of the notch filter configurations are also included.

50 citations


Patent
08 Mar 1974
TL;DR: In this paper, the transversal filter coefficients are adjusted in accordance with a criterion for minimizing the mean square error, and the sampling phase is adjusted by adjusting the same criterion.
Abstract: An automatic adaptive equalizing arrangement for data transmission channels, including a non-recursive section in the form of an adjustable transversal filter arranged between output of the transmission channel and input of the decision circuit and also a recursive section, if any, in the form of an adjustable transversal filter arranged between output and input of the decision circuit. The transversal filter coefficients are adjusted in accordance with a criterion for minimizing the meansquare error. By also adjusting the sampling phase in accordance with the same criterion a considerable improvement in the equalization quality is achieved, while generally the transmission of a training sequence for starting the equalization prior to the actual data transmission is not necessary.

40 citations


Journal ArticleDOI
TL;DR: Filters of the type exp(in theta)sgn J(n)(z(o)r) with theta the azimuthal angle and r the radial coordinate in the filter plane, are shown to maximize the energy content in a narrow annular image of radius z(o), with respect to incident energy.
Abstract: Filters of the type exp(inθ)sgn Jn(zor) with θ the azimuthal angle and r the radial coordinate in the filter plane, are shown to maximize the energy content in a narrow annular image of radius zo with respect to incident energy. The simplest optimal filter, sgnJo(zor), is well approximated by the binary circular phase grating sgn cos(zor − π/4). The single lobe of the first order image of this filter contains 46% of the incident energy within the half-width 0.4λf/a, centered around the image radius Nλf/(2a), where N ≃ zo/π is the number of filter sections.

37 citations


Journal ArticleDOI
TL;DR: In this article, the authors developed a solution for the resulting complex Wiener filter in terms of complex autocorrelation and cross-correlation functions, and an algorithm for the efficient evaluation of the complex filter weights is also available.
Abstract: The ordinary time or space domain Wiener filter is conventionally obtained for real-valued inputs and real-valued desired outputs. Situations exist for which these variables are complex-valued.It is possible to develop a solution for the resulting complex Wiener filter in terms of complex autocorrelation and crosscorrelation functions. An algorithm for the efficient evaluation of the complex filter weights is also available.

35 citations


Journal ArticleDOI
TL;DR: In this article, the authors examine the theoretical and practical issues of designing multiband filters and present several strategies for choosing the input parameters for the McClellan et al. filter-design algorithm to yield reasonable filters which meet arbitrary specifications.
Abstract: Although much has been learned about the relationships between design parameters for finite impulse-response (FIR) low-pass digital filters, very little is known about the relationships between the parameters of multiband filters. Thus given a set of design specifications for a multiband FIR filter (e.g., filter band edge frequencies and desired ripples in each of the bands) it is difficult to choose a set of modified parameters which will yield an acceptable filter using a standard FIR design algorithm. By an acceptable filter we mean one with monotonic behavior of the frequency response in the DON'T-CARE or transition regions between bands and one providing at least the desired attenuation (or ripple) in each of the bands. In this paper, we examine the theoretical and practical issues of designing multiband filters and present several strategies for choosing the input parameters for the McClellan et al. filter-design algorithm to yield reasonable filters which meet arbitrary specifications.

34 citations


Journal ArticleDOI
TL;DR: In this article, a quasi-optical bandpass filter for millimeter and submilliieter wavelengths and in the far infrared region is described, which consists of three or more wire-grid polarizers with quarter-wave spacings.
Abstract: A quasi-optical bandpass filter suitable for millimeter and submilliieter wavelengths and in the far infrared region is described. It consists of three or more wire-grid polarizers with quarter-wave spacings. The filter has the advantage over conventional quasi-optical filters, e.g., Fabry-Perot filters, that its bandwidth and the shape of its frequency response are adjustable. This is achieved by changing the angular orientations of the wires of the different polarizers. The filter requires the input electric field to be linearly polarized in a direction perpendicular to the wires of the first grid. The theory of operation is presented and design formulas for the filter are given, under the assumption that ideal wire-grid polarizers are employed. The effects of using realistic grids on the performance of the filter are dealt within another paper.

Journal ArticleDOI
TL;DR: In this article, the linear digital filtering technique developed for the computation of standard curves for conventional resistivity and electromagnetic depth soundings is applied to the determination of filter coefficients for the computations of dipole curves from the resistivity transform function by convolution.
Abstract: The technique of linear digital filtering developed for the computation of standard curves for conventional resistivity and electromagnetic depth soundings is applied to the determination of filter coefficients for the computation of dipole curves from the resistivity transform function by convolution. In designing the filter function from which the coefficients are derived, a sampling interval shorter than the one used in the earlier work on resistivity sounding is found to be necessary. The performance of the filter sets is tested and found to be highly accurate. The method is also simple and very fast in application.

Journal ArticleDOI
TL;DR: In this article, the problem of minimizing the roundoff noise in digital filters using fixed-point arithmetic under sinusoidal input is treated, and the minimax noise principle is introduced to serve as a guide in the filter design.
Abstract: This paper treats the problem of minimizing the roundoff noise in digital filters using fixed-point arithmetic under sinusoidal input. A basic assumption made is that of representing the roundoff error as white noise that is independent from sample to sample and from source to source. The minimax noise principle is introduced to serve as a guide in the filter design to optimize the structure for minimum noise. One application is illustrated through the design of low-noise cascade digital filters under dynamic range constraints. Numerical examples demonstrate the lower noise possible in comparison to other known designs and serve to verify the effectiveness of a design procedure based on the minimax concept.

Patent
Dennis D. Buss1
13 Nov 1974
TL;DR: In this paper, a handpass filter for detecting a chirp signal is provided, which includes the step of selectively varying the clock rate applied to a charge-transfer shift register responsive to the frequency variations of a selected chircp signal.
Abstract: A charge-transfer transversal filter and method of use is provided. In one aspect of the invention a handpass filter is provided where the center frequency of the bandpass is variable responsive to the clock rate applied to the charge-transfer devices. In a different aspect of the invention a matched filter for a chirp signal is provided. The filter requires a minimum number of Nyquist samples by including the provision of a clock rate which varies responsive to the frequency sweep of the input chirp signal. A method for detecting a chirp signal is provided which includes the step of selectively varying the clock rate applied to a charge-transfer shift register responsive to the frequency variations of a selected chirp signal.

Journal ArticleDOI
TL;DR: In this article, an algorithm for the design of optimal detection filters in radar and communications systems, subject to inequality constraints on the maximum output sidelobe levels, is presented, and numerical results are presented.
Abstract: An algorithm is presented for the design of optimal detection filters in radar and communications systems, subject to inequality constraints on the maximum output sidelobe levels. This problem was reduced in an earlier paper (Ref. 1) to an unconstrained one in the dual space of regular Borel measures, with a nondifferentiable cost functional. Here, the dual problem is solved via steepest descent, using the directional Gateaux differential. The algorithm is shown to be convergent, and numerical results are presented.

Journal ArticleDOI
TL;DR: Algorithms for moving average, recursive and “Fourier transform” low-pass linear digital filters are described, with reference being made to the methods of design.
Abstract: Algorithms for moving average, recursive and “Fourier transform” low-pass linear digital filters are described, with reference being made to the methods of design. The characteristics, including frequency, phase and impulse responses, of four specific filters are discussed in detail. In addition, some of the practical problems of programming these filters are considered. Factors such as execution times are evaluated in concluding which designs are most appropriate for filtering electrocardiograms.

Journal ArticleDOI
TL;DR: In this article, an extension of the Bessel filter is given for which the transfer function is a rational function with finite zeros, and a design example for a second-order all-pass constant time delay filter with linear phase response is given.
Abstract: An extension of the Bessel filter is given for which the transfer function is a rational function with finite zeros A special case is shown to combine the constant magnitude response of the all-pass filter with the linear phase response of the Bessel filter A design example for a second-order all-pass constant time delay filter is given; there is good agreement with theory

Journal ArticleDOI
TL;DR: This paper describes an algorithm that is suitable for fast implementations of nonrecursive and recursive digital filters and the memory-speed tradeoff is flexible so that many hardware and software implementations are practical.
Abstract: This paper describes an algorithm that is suitable for fast implementations of nonrecursive and recursive digital filters. High speed is realized at the expense of memory; however, the memory-speed tradeoff is flexible so that many hardware and software implementations are practical. When memory is not limited, the time required to compute a filter output value is independent of the order of the filter.

Journal ArticleDOI
TL;DR: Bucket-brigade devices have been used to build a new type of active filter that is equivalent to a second-order digital filter without the need for complex analog-to-digital conversion.
Abstract: Bucket-brigade devices have been used to build a new type of active filter that is equivalent to a second-order digital filter without the need for complex analog-to-digital conversion. The filter response characteristics, i.e., center frequency and bandwidth, depend on the circuit parameters of gain and clock frequency, both of which may be electronically controlled. By using a variable clock signal, 1023 frequencies can be accurately selected by the proper setting of ten switches. The selected clock frequency uniquely determines the center frequency of the bucket-brigade filter. The programmable feature of the clock circuit, therefore, allows the convenient selection of the center frequency of the bandpass filter. A slight modification to the programmable bandpass filter converts it into a programmable oscillator. Thus, any one of 1023 tones can be generated by the proper setting of the switches. A device that exhibits both filter and oscillator functions has been demonstrated in the laboratory.

Journal ArticleDOI
Abstract: Various methods based on optimization have been used to design linear phase filters. One such method has been to use a general-purpose optimization program to minimize some error criterion, a function of the filter coefficients and of the error between the specified and achieved gain responses. However, if this were to be used with arbitrary phase designs, the error criterion would have to be formulated as a function that combines the gain and phase errors in a meaningful way. It is shaown here that this particular difficulty can be avoided by regarding the phase specification as a deviation from the linear phase and splitting the characteristic into real and imaginary components, rather than gain and phase, and optimizing separately.

Journal ArticleDOI
TL;DR: The use of time-domain specifications is demonstrated for designing frequency-sampling digital filters that generate data pulses for transmission over an ideal band-limited channel to protect against intersymbol interference (ISI) and timing error.
Abstract: The use of time-domain specifications is demonstrated for designing frequency-sampling digital filters that generate data pulses for transmission over an ideal band-limited channel. Desired characteristics of the transmitted pulse are used to formulate the set of constraint equations and objective function used in linear programming to obtain an optimum set of filter coefficients, i.e., frequency samples {| H(k) |} - The constraints are the amplitudes assigned to the set of regularily spaced samples taken from the pulse. The objective function is either to minimize the maximum absolute error between desired and generated pulse samples over the specified pulse duration or to provide zero crossings in the transmitted pulse with near-zero slope in order to protect against intersymbol interference (ISI) due to timing error (jitter).

Journal ArticleDOI
TL;DR: In this paper, an analytical solution for the transfer function of a digital filter which exhibits an optimum maximally flat amplitude characteristic and a maximumally flat delay characteristic simultaneously was obtained for the direct realization in terms of the degree of the network and an arbitrary bandwidth scaling factor.
Abstract: An analytical solution is obtained for the transfer function of a digital filter which exhibits an optimum maximally flat amplitude characteristic and a maximally flat delay characteristic simultaneously. Explicit values for the multipliers are given for the direct realization in terms of the degree of the network and an arbitrary bandwidth scaling factor. Finally, it is concluded that this type of filter is useful in the area where the degree of a non-recursive filter becomes excessive to fulfil an amplitude requirement (e.g. narrow bandwidth) and where recursive filters designed solely on an amplitude basis are too dispersive.

Journal ArticleDOI
TL;DR: In this paper, the design of filters for detection and estimation in radar and communications systems with inequality constraints on the maximum output sidelobe levels is considered, and a constrained optimization problem is formulated, incorporating the sidelobe constraints via a partial ordering of continuous functions.
Abstract: The design of filters for detection and estimation in radar and communications systems is considered, with inequality constraints on the maximum output sidelobe levels. A constrained optimization problem in Hilbert space is formulated, incorporating the sidelobe constraints via a partial ordering of continuous functions. Generalized versions (in Hilbert space) of the Kuhn-Tucker and duality theorems allow the reduction of this problem to an unconstrained one in the dual space of regular Borel measures.

Proceedings ArticleDOI
01 Jan 1974
TL;DR: A basic building block constructed with CCD and MNOS technologies will be described, where the tap weights are analog and electrically reprogrammable to realize Fourier transformers, matched filters and correlators, and adaptive filters.
Abstract: A basic building block constructed with CCD and MNOS technologies will be described. The tap weights are analog and electrically reprogrammable to realize Fourier transformers, matched filters and correlators, and adaptive filters.

Patent
29 Nov 1974
TL;DR: In this article, a recursive digital filter and delay circuits are arranged in cascade there with a discrete Fourier transformer connected to the signal paths, such that the difference between such a phasefrequency characteristic and the phase-frequency characteristic of a reference digital filter has a sawtooth-shaped variation.
Abstract: An arrangement for digitally processing a given number of analog channel signals, more particularly a digital multiplexer and demultiplexer provided with a number of signal paths each comprising a recursive digital filter and delay circuits arranged in cascade therewith, said filter circuits having an amplitude-frequency characteristic of a lowpass filter having a cut-off frequency which is equal to half the bandwidth of a channel signal and a phase-frequency characteristic which is such that the difference between such a phase-frequency characteristic and the phase-frequency characteristic of a reference digital filter has a sawtooth-shaped variation, the slope of the sawtooth being opposite to the slope of the cooperating delay circuit. The arrangement furthermore comprises in cascade a discrete Fourier transformer connected to the signal paths.

Journal ArticleDOI
TL;DR: In this article, the equivalent index of a symmetrical nonabsorbing three-layer stack is plotted vs the thickness ratio and index ratio of the high-index and low-index layers.
Abstract: The equivalent index of a symmetrical nonabsorbing three-layer stack is plotted vs the thickness ratio and index ratio of the high-index and low-index layers. This furnishes some useful insight into the behavior of the equivalent index and is useful in the design of antireflection coatings and edge filters.

Patent
24 Jan 1974
TL;DR: A digital filter with a cut-off frequency of fc to which code words of a frequency fs are applied and which supplies code words at a frequency f's is described in this paper.
Abstract: A digital filter having a cut-off frequency of fc to which code words of a frequency fs are applied and which supplies code words at a frequency of f's The filter comprises a first digital filter section supplying numbers having a reduced frequency fm and whose output is directly coupled to an interpolating digital filter supplying the outgoing numbers of the filter at the frequency f's The first filter section and the interpolating digital filter are each built up as a digital filter having a cut-off frequency of fm/2

Patent
11 Nov 1974
TL;DR: In this article, a recursive (zeros and poles) filter having input and output signals y and yo and having impulse response hr apparatus and method for obtaining the convolution yo = y * hr using either the CNN integral or using the discrete Fourier transform (DFT).
Abstract: In a recursive (zeros and poles) filter having input and output signals y and yo and having impulse response hr apparatus and method for obtaining the convolution yo = y * hr using either the convolution integral or using the discrete Fourier transform (DFT). When using the convolution integral the apparatus first computes the impulse response hr then obtains the response yo in a convolver while when using the DFT the apparatus first computes the transfer function Hr then obtains the frequency spectrum Syo of response yo. By implementing the recursive filter as a matched clutter filter, the error normally associated with this type filter is minimized.

PatentDOI
TL;DR: In this article, a voltage controlled filter for an electronic synthesizer incorporates a plurality of individual voltage-controlled filter stages connected in cascade with a variable feedback interconnecting the input and output stages.
Abstract: A voltage controlled filter for an electronic synthesizer incorporates a plurality of individual voltage controlled filter stages connected in cascade with a variable feedback interconnecting the input and output stages. Each of the stages is controlled by application of a series of pulses, with the period between successive pulses determining the cutoff frequency of the filter. Application of pulses to the filter stages at different pulse repetition rates changes the cutoff frequency of the filter and modifies the relative amplitudes of different frequency components of an audio signal to be passed by the filter. The filter is suited for use with high level signals and provides an extremely wide dynamic range through a very high signal-to-noise ratio.

Patent
Yoichi Sato1
18 Mar 1974
TL;DR: In this paper, a self-adaptive equalizer comprises a transversal filter wherein the attenuators are adjusted with reference to the output signals of the filter, and means are provided for producing binary signals representative of the signs of the first filter outputs.
Abstract: A self-adaptive equalizer comprises a transversal filter wherein the attenuators are adjusted with reference to the output signals of the filter. For use in a multilevel data transmission system according to correlative encoding, a first filter removes the correlation encoding from the transversal filter outputs. Means is provided for producing binary signals representative of the signs of the first filter outputs. A second filter encodes the binary signals in accordance with the correlative encoding. The attenuators are adjusted in compliance with the respective products of the difference between one each of the second and transversal filter outputs and the signals derived from those taps of the delay line of the transversal filter to which the relevant attenuators are connected.