Showing papers on "Impulse response published in 1972"
TL;DR: In this paper, the problem of the derivation of simple transfer function models from high-order state variable models is reviewed, and methods of reduction are classified according to whether they involve 1) the computation of the time or frequency responses, 2) the derivations, as an intermediate step, of a transfer function which is the ratio of two polynomials, the denominator being of the same order as the state variable model, or 3) a set of characterising functions.
127 citations
TL;DR: In this article, a method for estimation of the parameters in a linear flow model with time invariant parameters based on a least-squares error analysis in the time domain is described, and numerical examples for two commonly used models containing two and four parameters, respectively, are given.
51 citations
TL;DR: In this paper, the authors considered the coupled line equations for two-mode random media in which both modes travel in the same (forward) direction as a model for multimode millimeter waveguides and optical fibers, in which mode conversion at imperfections occurs primarily in the forward direction.
Abstract: We consider the coupled line equations for two-mode random media in which both modes travel in the same (forward) direction as a model for multimode millimeter waveguides and optical fibers, in which mode conversion at imperfections occurs primarily in the forward direction. Some exact general properties satisfied by the transfer function and the impulse response of such a system are given for an arbitrary coupling coefficient. A random stationary coupling coefficient with statistically independent successive values, and consequently a white spectrum (e.g., a white Gaussian or a Poisson noise), permits exact determination of transmission statistics; we obtain first- and second-order statistics in the time and frequency domains. No perturbation or other approximations are made in any of the above results, which are obtained directly from the coupled line equations. These results are used to study signal distortion in long guides. By straightforward extension of this work more complicated calculations can treat more forward modes, but not backward modes or nonwhite coupling coefficient spectra. In this paper the coupling coefficient is assumed frequency independent, and under certain conditions the signal distortion decreases as the mode conversion increases. In practical cases the coupling coefficients are frequency dependent and the above behavior is modified; the present work is extended to this important case in a companion paper.
40 citations
Patent•
19 Jan 1972
TL;DR: In this paper, an improved method for making real-time system IMPULSE respond to MEASUREMENTS, which involved the use of BINARY PSEUDO-RANDOM NOISE SEQUENCES as test signals.
Abstract: IMPROVED METHOD FOR MAKING REAL TIME SYSTEM IMPULSE RESPONSE MEASUREMENTS WHICH INVOLVES THE USE OF BINARY PSEUDO-RANDOM NOISE SEQUENCES AS TEST SIGNALS.
28 citations
TL;DR: In this paper, it was shown that there is no square integrable impulse response that is optimum in Chebyshev's sense since the van der Maas function can be regarded as the limit of a sequence of square integral functions.
Abstract: The optimum impulse response of a band-limited system, viz., the van der Maas function, is derived from considerations based on the theory of entire functions. The ^{2} version of the optimization problem is also discussed. In particular, it is shown that there is no square integrable impulse response that is optimum in Chebyshev's sense since the van der Maas function, which is not square integrable, can be regarded as the limit of a sequence of square integrable functions. Some modified L^{2} versions of the optimization problem, in which weighted square integral measures of the sidelobes are prescribed, are also described.
28 citations
TL;DR: In this paper, it is shown that no loss of generality takes place considering the feedback to be unity, and necessary and sufficient conditions are derived for the closed-loop impulse response to be stable in a prescribed sense.
Abstract: Linear time-invariant feedback systems with multiple inputs and multiple outputs are examined. It is demonstrated that no loss of generality takes place considering the feedback to be unity. Necessary and sufficient conditions are derived for the closed-loop impulse response to be stable in a prescribed sense.
23 citations
TL;DR: In this paper, a method for very fast non-recursive digital filtering is presented in which over three fourths of the coefficients of the filter impulse response are forced to be zero by the judicious choice of filter center frequency, bandwidth, and window.
Abstract: A method for very fast nonrecursive digital filtering is presented in which over three fourths of the coefficients of the filter impulse response are forced to be zero by the judicious choice of filter center frequency, bandwidth, and window. Nearly half of the remaining coefficients can be discarded by taking advantage of the symmetry of the impulse response, A technique is described for separating a signal into octave bands using the same set of coefficients for each filter operation provided that either the data is "decimated" or the impulse response is "stretched" prior to each pass. Timing comparisons show that this method is faster than Radix 2 FFT convolution using filters with up to 300 coefficients. For many applications, real-time filtering can be achieved by using fixed-point arithmetic and an impulse response having as few as seven nonzero values.
18 citations
TL;DR: In this paper, it is shown that very much faster rise times can be obtained by pole-zero configurations which ensure a non-negative impulse response, which differs from traditional methods and also shows that intuitive notions of the response for given pole zero distributions can be misleading.
Abstract: In the design of filters for which it is required that there should be little or no overshoot of the transient response for a step input, it is common practice to adjust parameters so that the binomial filters are realized. This results in relatively slow rise times, but ensures zero overshoot. It is shown in this article that very much faster rise times can be obtained by pole-zero configurations which ensure a non-negative impulse response. The concept differs from traditional methods and also shows that intuitive notions of the response for given pole-zero distributions can be misleading.
16 citations
TL;DR: In this article, an approximate Z-transform approach is presented to compute at discrete time intervals the time responses of lumped or distributed parameter systems which exhibit wave propagation or time delay effects, which is an extension of the more familiar Laplace transform technique which is used for the analysis of continuous linear systems.
Abstract: An approximate Z‐transform approach is presented to compute at discrete time intervals the time responses of lumped or distributed parameter systems which exhibit wave propagation or time delay effects. The approach was previously developed by Boxer and Thaler [R. Boxer and S. Thaler, Proc. IRE 44, 89–101 (1956)] as a numerical method of solving linear and nonlinear equations and is an extension of the more familiar Laplace transform technique which is used for the analysis of continuous linear systems. Rather than directly utilizing the inverse Laplace transformation to obtain the time function, a mapping of the Laplace transform of the function from the s domain to the z domain is performed via the transformation z = esT, where T is the desired sampling interval of the time function. Unlike the inverse Laplace transformation, which requires the pole‐zero structure of the transform to obtain the continuous time function, the sampled time function is then obtained from its z domain representation without ...
11 citations
TL;DR: In this article, the mean-square response of linear systems to nonstationary random excitation of the form given by y (t) = f(t) x(t), in which x( t) = a stationary process and f(T) is deterministic.
Abstract: Development of a method for computing the mean-square response of linear systems to nonstationary random excitation of the form given by y(t) = f(t) x(t), in which x(t) = a stationary process and f(t) is deterministic. The method is suitable for application to multidegree-of-freedom systems when the mean-square response at a point due to excitation applied at another point is desired. Both the stationary process, x(t), and the modulating function, f(t), may be arbitrary. The method utilizes a fundamental component of transient response dependent only on x(t) and the system, and independent of f(t) to synthesize the total response. The role played by this component is analogous to that played by the Green's function or impulse response function in the convolution integral.
9 citations
Patent•
05 Sep 1972TL;DR: In this article, an echo canceller with compandors is used to improve echo return loss enhancement, where the echo signal is also syllabically compressed and applied to an adaptive control loop where the approximation is subtracted from the echo and the replica of the impulse response is varied in accordance with the difference obtained.
Abstract: An echo canceller with compandors results in improved echo return loss enhancement. The incoming signal is compressed prior to its application to a digital transversal filter. The filter produces an approximation of the integral of the syllabically compressed incoming signal times a replica of the impulse response of an echo return path including a compressor. The echo signal is also syllabically compressed and applied to an adaptive control loop wherein the approximation is subtracted from the echo and the replica of the impulse response is varied in accordance with the difference obtained.
TL;DR: In this paper, a hierarchy of functional descriptors called power-moments spectra is presented for the mathematical characterization of stochastic transmission media and transients, which may serve as inputs to either deterministic or non-deterministic media.
TL;DR: In this article, an underwater acoustic surface-reflection channel is treated as a linear random time-varying filter, and complete characterization of the channel reduces to a statistical description of its stochastic system functions.
Abstract: An underwater acoustic surface‐reflection channel is treated as a linear random time‐varying filter. Thus complete characterization of the channel reduces to a statistical description of its stochastic system functions. This paper presents the results of measurements made in a model tank with a wind‐driven surface in terms of the channel impulse response, transfer function, bifrequency function, and their ensemble averages. The impulse response is taken as the primitive because it permits evaluation of the transfer and bifrequency functions without need to resort to multiple measurements at different frequencies. Both the time‐ and frequency‐spreading characteristics of the channel are clearly evident in the system function data. It is shown that, given a single set of impulse response measurements for each geometrical configuration of interest, it is an easy matter to study the frequency response and frequency‐spreading behavior of the channel over the bandwidth of the acoustic pulse. The impulse response itself, of course, yields the time‐spreading behavior of the channel directly. Furthermore, favorable comparisons are made between impulse response derived data, and data obtained by single‐frequency measurement techniques.
TL;DR: This report describes a method by which the effect of feeding on drinking behaviour is assessed in terms of an impulse response, and it is hoped that it will prove to be useful in a wide variety of behavioural situations.
Abstract: TRANSFER functions and impulse responses are used by engineers as a means of describing, in a single equation, the relationship between input and output of a system. Frequency analysis, which uses sinusoidal input functions, is a classic method of determining transfer functions in physical systems, and has also been used for behavioural systems1. In the behavioural context, sinusoidal input functions are not always convenient, and the determination of the impulse response by application of a binary stimulus offers an alternative method of obtaining the same information as that gained by frequency analysis. In this report we describe a method by which the effect of feeding on drinking behaviour is assessed in terms of an impulse response. The method involves minimal interference with the natural course of behaviour, and we therefore hope that it will prove to be useful in a wide variety of behavioural situations.
TL;DR: In this paper, the authors considered a subclass of time-variable linear networks, which contains time-invariant components as well as ideal modulators one of whose inputs is a fixed periodic or almost periodic signal (the control signal).
Abstract: The subclass of time-variable linear networks is considered which contains time-invariant components as well as ideal modulators one of whose inputs is a fixed periodic or almost periodic signal (the control signal). Using the state-variable description of such systems, necessary and sufficient conditions are given for a time-variable impulse response to be realizable by this class of networks. Two realizations are given and shown to be equivalent, although the second one, called the general N - path filter, has certain practical advantages due to the greater degree of freedom in selecting the natural modes of the time-invariant part of the realization.
TL;DR: The problem of equalizing a discrete signal that has been transmitted through a channel selected at random from an ensemble of channels is considered and the minimum number of adjustable parameters required to achieve a given level of performance is sought.
Abstract: The problem of equalizing a discrete signal that has been transmitted through a channel selected at random from an ensemble of channels is considered. Using mean-square error as the performance index, the minimum number of adjustable parameters required to achieve a given level of performance is sought. For certain special cases, it is shown that, using nonrecursive sampled data filters, the optimum tap weights are given by the eigenvectors of the matrix formed from the covariances of the channel's impulse response. A numerical algorithm is developed to find the optimum equalizer structure for a wide class of channels with the restriction that the number of channels in the given ensemble is finite. Results worked out for several examples show that the optimum equalizer structure requires significantly fewer adjustable parameters than the standard transversal equalizer in order to obtain the same level of performance.
TL;DR: In this article, the three-dimensional intensity impulse responses of rectangular and circular apertures are calculated, taking into account the variation of magnification with the amount of defocusing, and the results may be applied to images of thin clouds of particles with arbitrary depth.
Abstract: The three-dimensional intensity impulse responses of rectangular and circular apertures are calculated. The calculations take into account the variation of magnification with the amount of defocusing. The results may be applied to images of thin clouds of particles with arbitrary depth.
Patent•
14 Nov 1972
TL;DR: In this paper, an adaptive equalized data modem is employed to adaptively learn the impulse response of the transmission channel, through cross-correlation of previously received data bits with the signal currently received.
Abstract: An adaptively equalized data modem affords cancellation of both lead-in and trailing transients, affording optimum correction of distortion in, and resulting intersymbol interference of, digital data received over a transmission channel. Adaptive feedback equalization is employed, as known heretofor, for adaptively learning the impulse response of the transmission channel, through cross-correlation of previously received data bits with the signal currently received. A correction signal is derived by multiplying the learned impulse response values by the stored data bits and summing the products. The correction signal is utilized in a feedback path to cancel trailing transients. Preliminary data decisions are produced in an input delay line system for multiplying with corresponding ones of the learned impulse response values, to produce cancellation terms corresponding generally to lead-in transients. A succession of preliminary data decisions of any desired number may be produced for developing a desired number of lead-in terms, and thereby to afford a desired degree of accuracy in the cancellation of the lead-in transients. Whereas the preliminary data decisions are discarded, the lead-in transient cancellation terms developed in accordance therewith, and the trailing transient cancellation terms developed through adaptive feedback equalization, provide for cancellation of both lead-in and trailing transients and a high degree of accuracy in recovery of the transmitted digital data.
TL;DR: In this paper, the feasibility of performing transmission loss and diffraction measurements using correlation techniques is demonstrated, which consists of first cross-correlating noise signals, then finding the Fourier transform of the resulting impulse response, and finally correcting for source imperfections in the frequency domain.
Abstract: The feasibility of performing transmission loss and diffraction measurements using correlation techniques is demonstrated. In contrast to standard measurements which make use of reverberant sound fields, the correlation techniques developed herein directly yield the responses due to signals transmitted through and around the acoustic barriers. The technique consists of first cross‐correlating noise signals, then finding the Fourier transform of the resulting impulse response, and finally correcting for source imperfections in the frequency domain. Comparative measurements of the transmission loss of some common materials are presented along with transmission loss measurements made as functions of angle and distance, and also presented are measurements of sound diffraction around panels. The results of these measurements (where comparison is possible) are shown to be as good or better than measurements resulting from standard techniques, and these results are shown to be in excellent agreement with existin...
TL;DR: In this paper, a simple and efficient method to approximate a given pulse shape by the impulse response of a two-port with rational transfer function is described, where the criterion of approximation is least mean-square error.
Abstract: A simple and efficient method to approximate a given pulse shape by the impulse response of a two-port with rational transfer function is described The criterion of approximation is least mean-square error The approximation can be performed very simply by using poles from atable and by determining the numerator of the transfer function, from which the zeros can be determined by solving a linear set of equations The obtained result may be improved by optimizing poles and zeros simultaneously This can be carried out by means of the same procedure used for finding the zeros
TL;DR: The statistical properties of a random variable E that denotes either the time‐averaged power in a received band of noise or the total energy in areceived transient waveform are studied for situations where the variablity in E is due to uncertainty in the detailed structure of the multipath transmission channel.
Abstract: The statistical properties of a random variable E that denotes either the time‐averaged power in a received band of noise or the total energy in a received transient waveform are studied for situations where the variablity in E is due to uncertainty in the detailed structure of the multipath transmission channel. The transmission channel impulse response function is modeled by a nonstationary Gaussian random process—a model that predicts the Rayleigh probability density for received amplitudes of transmitted pure tones. General expressions are derived for the mean and variance of E. These expressions are reduced to the practically important case of impulse response functions that are δ‐correlated in time. Approximate expressions and bounds are derived for the relative variance of E. Special cases of the results are shown to be in essential agreement with results previously obtained in studies of the responses of rooms to bands of noise.
TL;DR: In this paper, the authors considered correspondence time-varying linear operators in a distributional setting and provided necessary and sufficient conditions for the operators to be representable in terms of a generalized impulse response.
Abstract: In this correspondence time-varying linear operators in a distributional setting are considered. Necessary and sufficient conditions for the operators to be representable in terms of a generalized impulse response are described. The result is given without proof and is part of a study on translation-varying linear operators.
TL;DR: In this article, a brief survey is given for the method of impulse analysis of scalar systems to show the distinct advantages of time-domain infinite matrices (t.i.m.) methods.
Abstract: A brief survey is given for the method of impulse analysis of scalar systems to show the distinct advantages of time-domain infinite matrices (t.d.i.m.) methods. To tackle the problem of describing and manipulating multivariable systems by these techniques. an extension of the algebra of lower semi-infinite matrices to the multivariable case is developed. Of special importance in this respect are now recursion formulae for inverting stationary and non-stationary impulse response matrices of any dimensions. It is shown that for stationary matrices of dimensions n× n × ∞. the adjoint matrix has to be evaluated at the first sampling instant only. In terms of this evaluation the inverse matrix is generated at any sampling instant by carrying out simple algebraic operations (i.e. addition and multiplication). For non-stationary matrices similar conditions arc derived. The formulae of this paper are useful for the solution of a variety of problems in functional analysis. A numerical example is given to illustra...
TL;DR: In this paper, the form of the fundamental wavelet in the model itself, as modified by the linear filtering effects of the remainder of the system, can be found, and a technique is developed for calibration and verified by comparing Lamb's theoretical and experimental seismograms for elastic wave propagation over the edge of a half plate.
Abstract: Simple electronic circuitry and axially polarized ceramic transducers are employed to generate and detect elastic waves in a two‐dimensional analog model. The absence of reverberation and the basic simplicity. of construction underlie the advantages of this system. If the form of the fundamental wavelet in the model itself, as modified by the linear filtering effects of the remainder of the system, can be found, then calibration is achieved. This permits direct comparison of theoretical and experimental seismograms for a given model if its impulse response is known. A technique is developed for calibration and verified by comparing Lamb’s theoretical and experimental seismograms for elastic wave propagation over the edge of a half plate. This comparison also allows a critical examination of the basic assumptions inherent in a model seismic system.
TL;DR: A method of using the one-sided Laplace transform to produce N-dimensional, approximately spherically symmetric filters, which are derived in numerical form and can be produced just as readily by means of actual hardware provided the appropriate data scanning is carried out.
Abstract: The processing of naturally occurring information (eg the examination of the visual field by a pattern recogniser) can be significantly simplified if the raw information is initially processed in such a way as to enhance those features that are important with respect to the given task whilst attenuating the spurious or undesired information A convenient method of specifying what information is to be removed and what preserved in, for example, the class of one-dimensional signals typified by the output from a microphone is to use the Laplace transform to generate a suitable realisable filter whose frequency characteristics can be easily and accurately specified A severe drawback associated with using these filters however is that, unavoidably with the class of signals mentioned above, the impulse response function is asymmetric This asymmetry is responsible for the well-known phase shift effect produced by electrical filters Such filters can be derived and analysed by means of the one-sided Laplace transform, the one-sidedness resulting from the limitations imposed by physical realisability This note describes a method of using the one-sided Laplace transform to produce N-dimensional, approximately spherically symmetric filters Although these are derived in numerical form they can be produced just as readily by means of actual hardware provided the appropriate data scanning is carried out The method is compared with the mesh operator approach and its relative merits are enumerated The effect of these filters, which operate recursively, is demonstrated by their application to the enhancement of fingerprint images—a notoriously difficult cleaning-up problem Fingerprints, by virtue of their almost constant width line structure have a very narrow two-dimensional band-width Thus it is possible, by centring a band pass filter on the dominant frequency for a given fingerprint, to remove a great deal of the spurious data that is inevitably included by the data-capturing process (Received July 1970)
01 Jan 1972
TL;DR: In this paper, the authors present specific results and also develop guidelines for use in stability analysis and design of block and inverse digital filters with poles in the geometry of partial sums, which is the theory that describes the behavior of the zeros of these polynomials.
Abstract: The z transform of the truncated impulse response of a digital filter with poles is a polynomial that is important in the stability analysis of certain types of block and inverse digital filters. The geometry of partial sums is the theory that describes the behavior of the zeros of these polynomials. This paper presents specific results and also develops guidelines for use in stability analysis and design of block and inverse digital filters.
TL;DR: A compact form of P_e that depends only on the overall system impulse response taken over N time instants is obtained by first performing statistical averaging and then using the variational method.
Abstract: Results useful in the calculation of the exact closed-form expression for the minimum average probability of error P_e of a binary pulse linear communication system with 2N intersymbol interferences and additive colored Gaussian noise are given. By first performing statistical averaging and then using the variational method, a compact form of P_e that depends only on the overall system impulse response taken over N time instants is obtained. These N unknowns are given as the solution of N simultaneous nonlinear equations. Specific examples illustrating this approach are considered.
Patent•
IBM1
TL;DR: In this paper, a comb type impulse response spectrum of the form In a digital filter to which is applied a succession of binary coded input signals X(NT), X (NT-T), -X(NT-iT) -XNT-IT, -NT (N-1)T) at a frequency F 1/T, the filter output in the time domain at time NT being related to the input by the approximation
Abstract: WHERE R BEING THE NUMBER OF INPUT DIGITS THAT CAN BE SIMULTANEOUSLY WEIGHTED, H(IT) being the filter impulse response or coefficient at frequency F. Usually, such filters exhibit a comb type impulse response spectrum of the form In a digital filter to which is applied a succession of binary coded input signals X(NT), X(NT-T), -X(NT-iT) -X(NT (N-1)T) at a frequency F 1/T, the filter output in the time domain at time NT being related to the input by the approximation
19 May 1972
TL;DR: Examples designs are presented which illustrate that excellent waveforms can be generated with frequency-sampling filters and the ease with which digital transversal filters can be designed for preset equalization.
Abstract: A time domain technique is developed to design finite-duration impulse response digital filters using linear programming. Two related applications of this technique in data transmission systems are considered. The first is the design of pulse shaping digital filters to generate or detect signaling waveforms transmitted over bandlimited channels that are assumed to have ideal low pass or bandpass characteristics. The second is the design of digital filters to be used as preset equalizers in cascade with channels that have known impulse response characteristics. Example designs are presented which illustrate that excellent waveforms can be generated with frequency-sampling filters and the ease with which digital transversal filters can be designed for preset equalization.
TL;DR: The relationship between the impulse response function approach and the replica pulse approach is clarified in this article, and the relationship between impulse response functions and replica pulse approaches is discussed in Section 2.
Abstract: The relationship between the impulse response function approach and the replica pulse approach is clarified.