Showing papers on "Filter design 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.

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.

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.

Analog sample-data filters

Abstract: An analogue sample-data filter exactly equivalent, in the sample- data limit, to a simple RC low pass filter is demonstrated. The implementation requires only capacitors, MOSFETS, and a pulse generator. The filter time constant can be adjusted by changing the generator's pulse rate. The basic concept is then extended to apply to high-pass and to very-high-Q bandpass filters.

Practical Least pth Optimization of Networks

Abstract: A new and practical approach to computer-aided design optimization is presented. Central to the process is the application of least pth approximation using extremely large values of p, typically 1000 to 1 000 000. It is shown how suitable and reasonably well conditioned objective functions can be formulated, giving particular emphasis to more general approximation problems as, for example, in filter design. It is demonstrated how easily and efficiently extremely near minimax results can be achieved on a discrete set of sample points. Highly efficient gradient methods can be employed and, in network design problems, the use of the adjoint network approach for evaluating gradients results in greater savings in computer effort. A comparison between the Fletcher-Powell method and the more recent Fletcher method is made on the application of least pth approximation, using a range of values of p up to 1 000 000 000 000 on transmission-line transformer problems for which optimal minimax solutions are known. This is followed by filter design examples subject to certain constraints.

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.

Equivalence of the Likelihood Ratio Processor, the Maximum Signal-to-Noise Ratio Filter, and the Wiener Filter

Abstract: It is shown that for the problem of detecting a nonfluctuating target in Gaussian noise, three common optimality criteria lead to identical multichannel filter designs.

Digital filters for sample-rate reduction

Abstract: The design of bandwidth-limiting filters for the purpose of sample-rate reduction is considered. Realization of linear-phase finite-duration impulse-response (FIR) filters for this application by direct convolution is shown to be more efficient than the recursive realization [1]. The degree to which the Nyquist rate (relative to the desired signal bandwidth) must be exceeded at the filter output in order to avoid aliasing is suggested as a measure of filter effectiveness. Direct convolution is faster than the fast convolution for FIR equiripple [2] filters designed to operate within 10 percent of the Nyquist rate with 60- to 70-dB stopband attenuation at a 2:1 sample-rate reduction. This advantage improves with the log of the sample-rate reduction ratio. Several comparisons made with recursive realizations of elliptic filters give the advantage to direct convolutional realization of FIR filters for sampling within about 20 percent of the Nyquist rate at 60- to 70-dB attenuation. Elliptic filters become more efficient at higher complexities (of about eight poles and eight zeros). Two design techniques that exploit the reduced output sample rate in the design of FIR filters by direct convolution are suggested. The effects of quantization of FIR filter coefficients on the frequency response are considered and several examples illustrated.

Driving-Point Synthesis of Resistor-Terminated Cascades Composed of Lumped Lossless Passive 2-ports and Commensurate TEM Lines

Abstract: It has long been appreciated that microwave filters incorporating cascades of lumped reactive 2-ports and equi-delay ideal TEM lines offer many practical advantages over those designed with lines alone. To develop an insertion-loss design theory for these fiters comparable in precision to the one now available in the lumped case, it is first necessary to solve the intermediate problem of discovering necessary and sufficient conditions for a driving-point function to represent the input impedance of a resistor-terminated cascade of generic type. A simple decisive solution with the aid of the 2-variable positive-real concept is offered by 1) introducing the 1-variable real polynomial "resistivity matrix" associated with the driving-point function and 2) demonstrating that it must satisfy a fundamental structure constraint. Lastly, in addition to elucidating several important corollaries, the class of characteristic polynomials of all such microwave filters is given a description which reveals the difficulties to be overcome before an exact filter design procedure can be achieved. We wish to emphasize that the necessary and sufficient conditions for realizability presented in this paper are not algorithmic in character but explicit. To make the results accessible to as wide an audience as possible we have adopted a leisurely tutorial style with considerable attention paid to some of the more relevant background material.

Video signal processing device for extracting the chrominance and luminance signals from a composite video signal in a color television receiver

Abstract: A video signal processing device for a color television receiver includes a low-pass filter for obtaining lower frequency components out of a composite video signal consisting of a luminance signal and a carrier chrominance signal, a band-pass filter for obtaining higher frequency components of the composite video signal, and a signal wave processing unit for delivering the second order differential of the composite video signal. There is provided in the device a first comb-shaped filter and a second comb-shaped filter for obtaining carrier chrominance signal components and luminance signal components from the outputs of the band-pass filter and the signal wave processing unit, respectively, and an adder for adding the luminance signal components extracted from the output of the signal wave processing unit by means of the second comb-shaped filter to the output obtained from the low-pass filter, whereby a low noise luminance signal added with a preshoot and an overshoot can be obtained from the adder, and a carrier chrominance signal also of low noise can be obtained from the first comb-shaped filter. Alternate embodiments are also simplified by the fact that only a single comb-shaped filter is required.

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.

Monte Carlo study of the optimal non-linear estimator: linear systems with non-gaussian initial states †

Abstract: The optimal, in the mean-square sense, estimate of state vector of a linear discrete system that is excited by white zero mean gaussian noise and that has non-gaussian initial state vector is presented. Both the optimal estimate and the corresponding error covariance matrix are given. It is shown that the optimal estimator consists of two parts : a linear estimator which is a Kalman filter and a non-linear part which is a parameter estimator. In addition, the a posteriori probability density function, p(x(k)λk), is also given. Finally, a suboptimal procedure that reduces the computational requirements is presented. The results of extensive digital computer simulations including Monte Carlo study have been presented to establish that the non-linear filter presented here is far superior to the best linear Kalman filter. A practical filter design criterion for utilizing this non-linear filter with reduced data processing requirements is also given.

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.

The prolate filter: An ideal lowpass filter with optimum step-response

Abstract: An ideal lowpass filter permits no signal transmission outside of a prescribed frequency band centered around the origin. In this paper, it is shown that the ideal lowpass filter which provides the fastest monotonic step-response for a prescribed bandwidth is the prolate filter. The system-function of this circuit is obtained from the autocorrelation of the zero-order, zero degree angular prolate spheroidal wave function. The bandwidth and risetimes of the filter are related through the largest eigenvalue of the same wave function. The computation and realization of the optimum frequency- and time-responses is discussed in detail and is illustrated by a numerical example. It is also shown how the asymptotic forms of the optimum system function degenerate, for very small or very large risetimes, into the well-known Hadamard and Gaussian filter functions, respectively.

Automatic electronic filter system

Abstract: A combination bandpass and rejection filter system having a null point at a center frequency, comprising:

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.

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...

The compensated Kalman filter.

Abstract: This paper introduces the compensated Kalman filter, a suboptimal state estimator which can be used to eliminate steady-state bias errors when it is used in conjunction with the mismatched steady-state (asymptotic) time-invariant Kalman-Bucy filter. The uncompensated mismatched steady state Kalman-Bucy filter exhibits bias errors whenever the nominal plant parameters used in the filter design are different from the actual plant parameters. The approach used relies on the utilization of the residual (innovations) process of the mismatched filter to estimate, via a Kalman-Bucy filter, the state estimation errors and subsequent improvements of the state estimate. The compensated Kalman filter augments the mismatched steady state Kalman-Bucy filrby the introduction of additional dynamics and feedforward integral compensation channels.

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.

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.

Pre-emphasis loop filter for improved fm demodulator noise threshold performance

Abstract: The performance of a noise threshold extension circuit for an FM demodulator is substantially improved by the incorporation of a pre-emphasis-type filter in the control loop of the circuit, which filter "matches" the frequency response characteristic of the loop to that of the modulating signal The threshold extension circuit preferably includes a steerable, narrowband tracking filter which tracks the FM signal so that extraneous noise is filtered out

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.

Some Matched Filter Configurations for Infrared Systems

Abstract: An analysis of the output of three alternative matched filter configurations in an infrared scanning system model is presented. The sensor is corrupted by thermal noise, generation-recombination noise, photon noise, and modulation noise, the latter providing an extreme discoloration in the signal passband. Expressions for the signal voltage density spectrum, signal pulse shape, noise power spectrum, and average noise power at the matched filter output are derived where the integral evaluations attendant to these derivations do not appear elsewhere in the literature. The paper also provides graphical displays of the signal-to-noise power ratio at the filter output versus various system parameters, noise power spectrum out of the matched filter versus ?, and the signal pulse shape out of the filter versus time. Also included are discussions of practically realizable approximations to the matched filters and curve fitting techniques for the signal pulse shape function.

Filter with periodic phase delay and insertion-loss ripple

Abstract: An analytical design procedure is presented for the lowpass prototype selective linear phase filter, from which bandpass-channel filters may be deduced, whose insertion-loss and phase-delay-error functions vanish at an optimum number of equidistant points in the passband. Synthesis is performed using an even-and-odd-mode decomposition for a symmetrical filter comprising capacitors and impedance invertors. Finally, explicit formulas are given for element values in the 2nd-, 4th- and 6th-degree networks from which a simple realisability condition is deduced for all positive coupling elements, and numerical results on a 12th-degree filter are presented to illustrate the typical response characteristics. The main application of the design technique is in the construction of channel filters in high-capacity communication systems which use frequency modulation, particularly at microwave frequencies where the compact physical devices are readily constructed

Die cast waveguide low pass filter

Abstract: A microwave low pass filter of the so-called "waffle iron" type is disclosed. The filter utilizes die cast construction techniques and cast-in dowel holes for dimensional fidelity, close tolerances and precise alignment. The filter uses fewer parts than previous devices and can be easily assembled without the use of jigs, fixtures or special bonding techniques. Die cast construction techniques are made possible in the filter design by departing from the optimum electrical design of such components.

Design of digital filters using state-space realization†

Abstract: A procedure for the design of a digital filter, based on state-space.realization, is presented. The digital filter obtained has low sensitivity to eigenvalue variations. Also particularly attractive features are stability and low coefficient spread. The design technique is well suited for computer-aided design, starting from a prototype analogue filter function and the desired critical frequencies. Simulation results for different computer word-length are presented, and comparison is made with an analogue filter for both frequency and transient response.

Digital filtering for radar signal processing applications

Abstract: A novel approach in synthesizing digital filters for signal processing applications is presented. This approach is an extension of the frequency sampling method of nonrecursive filter synthesis. Appropriate time delays are used in conjunction with a set of parallel complex exponential resonators whose outputs are summed to yield a desired filter impulse response. This synthesis method takes advantage of the known signal waveform structure and results in many fewer digital computations as compared to convolution processing. This approach is particularly suited to synthesis of matched filters for radar signal processing and yields matched or approximately matched filters which simultaneously have very low storage and very low computational requirements.