Showing papers on "Impulse response published in 1976"

Image method for efficiently simulating small‐room acoustics

Abstract: Image methods are commonly used for the analysis of the acoustic properties of enclosures. In this paper we discuss the theoretical and practical use of image techniques for simulating, on a digital computer, the impulse response between two points in a small rectangular room. The resulting impulse response, when convolved with any desired input signal, such as speech, simulates room reverberation of the input signal. This technique is useful in signal processing or psychoacoustic studies. The entire process is carried out on a digital computer so that a wide range of room parameters can be studied with accurate control over the experimental conditions. A fortran implementation of this model has been included.

Stationary and nonstationary learning characteristics of the LMS adaptive filter

Abstract: This paper describes the performance characteristics of the LMS adaptive filter, a digital filter composed of a tapped delay line and adjustable weights, whose impulse response is controlled by an adaptive algorithm. For stationary stochastic inputs, the mean-square error, the difference between the filter output and an externally supplied input called the "desired response," is a quadratic function of the weights, a paraboloid with a single fixed minimum point that can be sought by gradient techniques. The gradient estimation process is shown to introduce noise into the weight vector that is proportional to the speed of adaptation and number of weights. The effect of this noise is expressed in terms of a dimensionless quantity "misadjustment" that is a measure of the deviation from optimal Wiener performance. Analysis of a simple nonstationary case, in which the minimum point of the error surface is moving according to an assumed first-order Markov process, shows that an additional contribution to misadjustment arises from "lag" of the adaptive process in tracking the moving minimum point. This contribution, which is additive, is proportional to the number of weights but inversely proportional to the speed of adaptation. The sum of the misadjustments can be minimized by choosing the speed of adaptation to make equal the two contributions. It is further shown, in Appendix A, that for stationary inputs the LMS adaptive algorithm, based on the method of steepest descent, approaches the theoretical limit of efficiency in terms of misadjustment and speed of adaptation when the eigenvalues of the input correlation matrix are equal or close in value. When the eigenvalues are highly disparate (λ max /λ min > 10), an algorithm similar to LMS but based on Newton's method would approach this theoretical limit very closely.

Source shape estimation and deconvolution of teleseismic bodywaves

Abstract: We consider the deconvolution of a suite of teleseismic recordings of the same event in order to separate source and transmission path phenomena. The assumption of source uniformity may restrict the range of muths and distances of the seismograms included in the suite. The source shape is estimated by separately averaging the log amplitude spectra and the phase spectra of the recordings. This method of source estimation uses the redundant source information contained in secondary arrivals. The necessary condition for this estimator to resolve the source wavelet is that the travel times of the various secondary arrivals be evenly distributed with respect to the initial arrivals. The subsequent deconvolution of the seismograms is carried out by spectral division with two modifications. The first is the introduction of a minimum allowable source spectral amplitude termed the waterlevel. This parameter constrains the gain of the deconvolution filter in regions where the seismogram has little or no information, and also trades-off arrival time resolution with arrival amplitude resolution. The second modification, designed to increase the time domain resolution of the deconvolution, is the extension of the frequency range of the transmission path impulse response spectrum beyond the optimal passband (the passband of the seismograms). The justification for the extension lies in the fact that the impulse response of the transmission path is itself a series of impulses which means its spectrum is not band-limited. Thus, the impulse response is best represented by a continuous spectrum rather than one which is set to zero outside the optimal passband. This continuity is achieved by a recursive application of a unit-step prediction operator determined by Burg's maximum entropy algorithm. The envelopes of the deconvolution are used to detect the presence of phase shifted arrivals.

The use of second-order information in the approximation of discreate-time linear systems

Abstract: It is common practice to partially characterize a filter with a finite portion of its impulse response, with the objective of generating a recursive approximation. This paper discusses the use of mixed first and second information, in the form of a finite portion of the impulse response and autocorrelation sequences. The discussion encompasses a number of techniques and algorithms for this purpose. Two approximation problems are studied: an interpolation problem and a least squares problem. These are shown to be closely related. The linear systems which form the solutions to these problems are shown to be stable. An efficient algorithm for obtaining solutions is given and shown to be closely related to a well-known algorithm of Levinson and the Jury stability test. The close connection between these algorithms suggests that they are fundamental in the numerical analysis of stable discrete-time linear systems.

The impulse response and pressure nearfield of a curved ultrasonic radiator

Abstract: A method of calculating sound pressure with the aid of the impulse response is applied to a circular concave ultrasonic radiator. First the impulse response of a curved radiator is derived and found to be expressible in closed form; then the impulse response function is used to give a closed-form formula for the pressure at the axis of symmetry. An approximate formula is shown to give satisfactory results in the region near the centre of curvature in the focal plane. Finally a complete pressure amplitude pattern of a curved radiator based on numerical computations is given.

Stochastic theory of minimal realization

Abstract: This paper exploits the concept of a predictor space in the minimal realization problem for systems generating an analytic impulse response matrix. The predictor space constructed, by stochastic input and output processes forms the state space for the stochastic system representation, where a system is represented by the basis of the predictor space and the innovation process of input. The minimal realization problem is then solved for a given analytic impulse response matrix by defining a stochastic system driven by white noise whose input-output covariance equals the given impulse response matrix. It is shown that the coefficient matrices of the stochastic system representation constitute a solution to the minimal realization problem for the deterministic system with given impulse response matrix. The paper provides a unifying overview to many aspects of the realization problem and its algorithms.

Improvements in and relating to active sound attenuation

Abstract: A primary sound wave in a confined space is attenuated by a secondary sound wave generated to null with the primary wave. The secondary wave is produced by a first electrical signal representing the primary wave as sensed by a microphone, which is convolved with a second signal derived from the system impulse response as a program of operational steps. A second convolution process can cancel feedback of the secondary sound wave. Downstream residual noise is sensed by a second microphone which feeds a microprocessor which adjusts the convolution processes.

Design and implementation of multirate digital filters

Abstract: Two new design methods for infinite-duration impulse-response (IIR) multirate digital filters are introduced, and a state-variable implementation is given. One method is an extension of the impulse-invariant method and results in the direct synthesis of a multi-rate filter which realizes in discrete time the response of a continuous time circuit. The second method employs linear programming (LP) to optimize the frequency domain response. For finite-length impulse response (FIR) multirate filters an efficient fast Fourier transform (FFT) implementation is presented.

Identification of linear systems response by parametric programing

Abstract: Experience indicates that in the identification of the impulse response function of a linear hydrologic system the results are extremely sensitive to minor errors in the input-output data. In particular, low-amplitude random errors in these data tend to cause severe oscillations in the response function, thereby making it often impossible to obtain a physically realizable solution by conventional methods. Artificial filtering of the input-output records may help, but since the extent of noise is seldom known a priori, one cannot be sure about the proper choice of a cutoff frequency. Such filtering also causes a loss of data at the end points of the record and is therefore undesirable when the number of data points is small. Filtering the response function itself is only effective in eliminating high-frequency oscillations, and it is far less effective when the frequency of the oscillations is relatively low. Clearly, the ultimate goal of identification is to determine a solution which optimizes the predictive capabilities of the linear model. To achieve this goal, it is not sufficient that an observed output be correctly reproduced from a given input; an equally important criterion of optimality is that the shape of the response function be physically plausible. It is shown that one way to obtain a stable and physically realizable response function from a relatively short input-output record is to use parametric linear programing. According to this approach, the problem is formulated as a multicriterion decision process under uncertainty in a manner analogous to that previously described by one of the authors in connection with the inverse problem of groundwater hydrology. Parametric programing serves as a means of generating a continuous set of alternative solutions to the identification problem together with a bicriterion function representing these alternatives. The shape of this bicriterion curve is then used as a guide by the hydrologist in selecting a particular solution when he is relying on his own value judgment. If none of the alternative solutions appears to be physically plausible at this stage, the hydrologist has a further option of imposing modality constraints to eliminate undesirable low-frequency oscillations from the response function. The method is illustrated by two examples, and the results are compared with those obtained by another approach developed previously by one of the authors.

Dynamic properties of the responses of single neurones in the cochlear nucleus of the rat.

Abstract: 1. The dynamic properties of unit responses to amplitude-modulated tones were studied using modulation with pseudorandom noise and described by cross-covariance and integrated cross-covariance functions between the discharge rate and the modulation. Under the experimental conditions used, these two functions are valid approximations of the system's impulse and step response functions respectively. 2. On the basis of their impulse response functions units could be classified into two groups, Type I with a low adaptation and Type II with a large degree of adaptation as well as a damped oscillation in their impulse response functions. 3. The response pattern of the Type II units is most likely the result of a negative feed-back striving to keep the discharge rate at a nearly constant level. 4. The cross-covariance functions are shown to remain unchanged during long duration recordings from the same unit.

Convergence of the van Cittert iterative method of deconvolution

Abstract: Conditions necessary for the convergence of the van Cittert iterative method of deconvolution are studied. Conditions that can be expressed in the function domain are derived, some of which are readily apparent restrictions on the shape of the impulse response. The position of the response function along the abscissa is considered, since the shifting of the function can influence convergence. Only real, piecewise-analytic responses with pointwise Fourier transforms and pointwise Fourier inversion are considered.

Effective Antenna Pattern of Scanning Radars

Abstract: It is shown that weather radar signal averaging causes a broadened apparent pattern of the scanning radar antenna The apparent pattern is obtained by convolving the original pattern with the averaging circuit impulse response Echo displacement and pattern broadness are examined for square law, linear, and logarithmic detectors having exponential and finite time integrators

Analysis of neuronal networks in the visual system of the cat using statistical signals. Part I.

Abstract: If the input signals of the visual system in the cat are statistical patterns in space and time, a complete system analysis can be carried out. What counts here as a system are the neuronal networks between retina and recording site. In the case of linearity, one obtains the temporal impulse response functions at every point in the receptive field with the aid of correlation methods. The measuring time is about one minute. Some aspects of the procedure are explained in terms of examples. The method of measurement also makes it possible to determine the characteristic function of the system in time and space between different recording sites within the cortex. It is possible to specialize the procedure for analysing the stationary space dependent behaviour of neuronal networks. The extension of the analysis procedure allows a concise, relatively simple description for nonlinear systems in which linear and nonlinear subsystems can be separated. Besides this, there are no restrictions concerning the kind of nonlinearity. A second paper will present the detailed experimental application of these methods.

Dynamic properties of excitation and two-tone inhibition in the cochlear nucleus studied using amplitude-modulated tones.

Abstract: The dynamic properties of excitation and two-tone inhibition in the cochlear nucleus were studied from extracellularly recorded unit responses to two simultaneously presented tones. One tone was presented at the unit's characteristic frequency, CF, the other at the unit's best inhibitory frequency, BIF. One or both of the tones were amplitude-modulated with pseudorandom noise. The system under study is in general nonlinear, but can be considered to function as a linear system for small changes in sound intensity around a certain operating point. The dynamic properties are likely to be different at different operating points. A suitable method for the study of dynamic properties of such a system employs tones that are amplitude-modulated with pseudorandom noise. In the present study, the dynamic properties were assessed by cross-correlating the unit discharge rate with the modulation. This was accomplished by computing the crosscovariance function between a period of noise and a period histogram of the discharges, the histogram being locked to the periodicity of the pseudorandom noise. In this way, it has been shown in previous works (Moller, 1973, 1974b), that the cross-covariance function is a valid approximation of the system's impulse response function at a certain sound intensity, provided the modulation is kept at a low value. In the present study the computed cross-covariance function is thus an approximation of the change in discharge rate of the cochlear nucleus units in response to a brief increase in stimulus intensity. As the response of the system under the given circumstances is approximately that of a linear system, the integrated cross-covariance is an approximation of the system's step response function, i.e the change in discharge rate that results from a hypothetical step increase in stimulus intensity. The results of the present study can be summarized as follows: 1. The impulse and step response functions computed from the responses to the modulated inhibitory tone of the great majority of units from which recording was made were found to be virtual mirror images of those obtained when the excitatory tone was modulated, the inhibitory response being somewhat smaller in amplitude than the excitatory. 2. When both tones were modulated simultaneously, the step response function was approximately the algebraic sum of the two responses obtained when the tones were modulated singly, further indicating that the system functions as a linear system when the stimulus amplitude is varied slightly around a certain operating point. 3. The shape of the cross-covariance functions is similar for all three stimulus situations, but varies with stimulus intensity and is different in different units. 4. The implication of the results is that the inhibition studied may either originate from the inhibition (suppression) seen in primary fibers or it may be the result of a true neural inhibition in the cochlear nucleus that occurs without any interneurons.

Optical-fiber impulse-response measurement system

Abstract: This paper describes time-domain instrumentation that was designed to measure impulse response and delay of multimode optical fibers that are being used in an experimental optical communications system at Bell Laboratories. Time-domain data is transformed to frequency-domain by a minicomputer, and the result is displayed as the fiber's baseband frequency response.

Model following using partial state feedback

Abstract: This short paper considers the problem of designing a compensating control scheme for an observable linear multivariable plant using partial state feedback so that the impulse response matrix of the resulting system exactly corresponds to the impulse response matrix of a prespecified linear model. A procedure is given for the synthesis of the compensator that does not require a separate realization for the plant observer. A sufficient condition is given for the internal stability of the model following system.

Transmission Channel Characterization by Impulse Response Measurements

Abstract: Some basic concepts. design criteria and hardware implementations are reviewed for measuring the impulse responses which characterize radio transmission channels. A channel sounder which is presently being used by the Institute for Telecommunication sciences (ITS) is described. The sounder was implemented for easy transport and operational convenience in collecting response data on a variety of transmission paths and over a wide frequency range. Some applications and measurement results are presented to illustrate the capabilities.

Echo cancelling system for multiplex telephone circuits

Abstract: An echo cancelling system for multiplex circuits, in which an impulse response of an echo-path is obtained from signals at respective ends of the transmission path and the receiving path connected to the echo-path to produce an echo-path model, and in which a pseudo echo signal is then provided to subtract it from an echo signal of the echo-path thereby to cancel the echo signal. In accordance with this invention, adaptive echo-path models each for corresponding channel of the multiplex circuits are provided for storing impulse response signals within a holding time of an impulse response in the long distance multiplex telephone circuits, and an adaptive echo-path model for the common use of multiplex circuits is provided for storing, in a time-divisional manner according to the known queue control, (a) information within a flat delay time of the impulse response, (b) impulse response signals within the holding time of the impulse response and (c) information within a certain constant time after the impulse response. The adaptive echo-path model for the common use is activated if the level of a residual echo signal is higher than a predetermined value, and the adaptive echo-path model for each channel is activated if the level of a residual echo signal is smaller than the predetermined value.

Linear systems identification by Mellin deconvolution

Abstract: This proposed method of identification is particularly well, adapted to the study of linear systems whose transfer function has real simple poles. It also permits the identification of systems with real multiple poles as well as complex conjugate poles. No prior knowledge of the number of poles and of zeros is necessary. The identification is accomplished by means of a digital process of the impulse response of the system. This process corresponds to the resolution of a Mellin convolution equation.

Asymptotic behavior of the acoustic nearfield of a circular piston

Abstract: The acoustic nearfield of a circular piston is investigated using the impulse response technique. Although the harmonic field can be expressed as either a convolution integral or Fourier transform, the integrals cannot be simply evaluated. An asymptotic evaluation of the Fourier transform of the spatially dependent impulse response for the circular piston is, however, readily performed. The resulting expressions very simply illustrate the nearfield behavior of the piston. Furthermore, the expressions are shown to be in agreement with the asymptotic properties of known nearfield results and are consistent with the usual farfield expressions.Subject Classification: [43]20.55, [43]20.15.

Exact realisation of 2-dimensional digital filters by separable filters

Abstract: A scheme for the exact realisation of 2-dimensional digital filters by using separable filters is proposed. The desired impulse response is obtained by a process of successive corrections. The performance criterion in terms of computing speed is compared with that of another existing technique.

On the design of all-pass signals with peak amplitude constraints

Abstract: In this paper, the problem is discussed of designing a signal other than the standard impulse function to be used to test a digital system of limited dynamic range. The constraints on such a signal are that it must be all-pass, of limited duration (approximately), and peak-amplitude-limited so as to utilize the limited dynamic range of the system as far as possible. Stated another way, the goal is to spread out the energy in the signal as much as possible to reduce its peak amplitude and therefore to be able to pass higher energy signals through the system without clipping them. The class of all-pass signals (obtained as the impulse response of a variable order all-pass filter) was investigated for use as the test signal. The parameters of the all-pass filter of a given order were optimized to give an all-pass signal whose peak amplitude was the smallest possible. Filter orders from first to eighth order were designed and investigated. It was found that reductions in the peak signal level of up to 11.2 dB (relative to the signal level of an equivalent energy impulse) could be obtained for an eighth-order all-pass signal. Interpolated versions of these all-pass signals showed that the peak value of the interpolated waveform was only on the order of 6 dB. Thus, the use of an all-pass signal, rather than the standard impulse, for testing a digital system can result in about 1 bit extra dynamic range.

Precise Impulse Response Measurement of SAW Filters

Abstract: A technique for measuring the effective tap weights and delays of a surface acoustic wave transducer is presented. Data taken in the frequency domain are fast Fourier transformed and processed to give the discrete impulse response. This technique provides a means of accurately determining the center frequency of a SAW bandpass filter. Additive errors are analyzed by comparing this discrete impulse response with the theoretical impulse response on a tap by tap basis. The effect of individual propagation modes is presented along with an analysis of effective tap position with respect to tap weight.

Vocal tract area function measurements: Two time-domain methods

Abstract: Two methods are described for determining the vocal tract area function from measurements at the lips of the response to an impulsive acoustic pressure wave: - In one case, the impulse response at the lips obtained by deconvolution is used to compute the area function at all points; - Alternatively, the vocal tract is modeled by successive approximation, a search is made for the constrictions by decreasing order of importance rather than sequentially from the lips. Results obtained with both methods are good, the area functions are measured in absolute values rather than in arbitrary units. Advantages, difficulties and limitations of both methods are discussed.

Laplace transform system

Abstract: A system for determining the location of poles in the complex s-plane and their residues from empirical data is disclosed. The system utilizes the impulse response or similar data of a specimen and through repeated differentiations of a frequency domain representation of this response locates the frequency of the poles. The results of any two consecutive differentiations are used to determine the location of the poles in the s-plane and their residues.

An integral equation for the transient response of a stratified magnetoplasma

Abstract: The problem of finding the transient response of a cold plasma half space to an impulsive plane wave at vertical incidence is considered. The electron density of the plasma is allowed to vary arbitrarily with the vertical coordinate; and the effects of a vertical magnetic field and losses are included in the analysis. The impulse response is formulated in terms of a time-dependent integral equation by extending previous results obtained via a multiple-scattering technique. As an example of this method numerical results are presented for the special case of reflection from a linear plasma half space.