Browsing by Author "Parks, Thomas"

Now showing 1 - 6 of 6
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    A comparative study of some recursive digital filter design techniques
    (1968) Warmack, Ralph E; Parks, Thomas
    This study explores four techniques for simulating analog filters by recursive digital filters. A uniform basis for comparing these methods is provided by requiring each digital filter to maintain the D.C. gain and order of the given analog filter. Three of these techniques are modified versions of existing methods found in the literature. The fourth is a proposed compensation scheme for the bilinear transformation which preserves the finite critical frequency locations of the original analog filter. For band-limited filters and for sampling intervals approaching zero, it is demonstrated that the D.C. gain requirement with the standard Z-transformation of the analog filter transfer function results in the so-called impulse-invariant method. The nature of the mappings induced by the bilinear transformation is investigated and some contours generated by this mapping are given. While under the most general conditions, none of these methods minimizes the mean-squared error at the sampling instants, it is shown that the frequency responses of these digital filters (in the Nyquist interval) and their unit-step responses are often acceptable approximations to those of the given analog filter and warrant their use as simulators. Some numerical examples are given which illustrate implementation of these filters. Roundoff accumulation errors are encountered and bounds which show the effect of filter order and sampling rate are discussed.
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    A HIGH RESOLUTION DATA-ADAPTIVE TIME-FREQUENCY REPRESENTATION
    (1987) JONES, DOUGLAS LLEWELLYN; Parks, Thomas
    The short-time Fourier transform and the Wigner distribution are the time-frequency representations that have received the most attention. The Wigner distribution has a number of desirable properties, but it introduces nonlinearities called cross-terms that make it difficult to interpret when applied to real multi-component signals. The short-time Fourier transform has achieved widespread use in applications, but it often has poor resolution of signal components and can bias the estimate of signal parameters. A need exists for a time-frequency representation without the shortcomings of the current techniques. This dissertation develops a data-adaptive time-frequency representation that overcomes the often poor resolution of the traditional short-time Fourier transform, while avoiding the nonlinearities that make the Wigner distribution and other bilinear representations difficult to interpret and use. The new method uses an adaptive Gaussian basis, with the basis parameters varying at different time-frequency locations to maximize the local signal concentration in time-frequency. Two methods for selecting the Gaussian parameters are presented: a method that maximizes a measure of local signal concentration, and a parameter estimation approach. The new representation provides much better performance than any of the currently known techniques in the analysis of multi-modal dispersive waveforms.
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    A procedure for calculating the best exponents for signal representation
    (1970) Jan, Yih-Guang John; Parks, Thomas
    The approximation of a given signal over (0,^ ) by a linear combination of a given number n of exponentials in such a sense that the integrated squared error is minimized over both the coefficients of the linear combination and the exponents used is discussed. The necessary conditions for the minimizations lead to nonlinear equations. Analog and digital computer implementations have been developed that are capable of adjusting the exponents of the basis functions and the coefficients of the linear combinations to minimize the integrated squared error between a signal and its representation. The influence of each parameter of the orthonormal filters on the performance criterion is determined using an iterative convergent process. These parameter changes are introduced into the analog and digital systems to form a closed loop system.
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    A Prony speech processing technique
    (1972) Scanio, Thomas Joseph; Parks, Thomas
    A method for speech processing is presented. The method does not require voiced/unvoiced or pitch determination. It models the sampled speech wave as a concatenation of initial segments of unit pulse responses of linear, time-invariant, recursive discrete time systems. The poles of the systems are calculated by Prony's method applied to blocks of speech samples. The zeroes are chosen to zero the error between the speech wave and the first output samples of each system. The analysis phase proceeds as follows. After an initial block of unit pulse response, the system output samples are compared with the speech samples and the system continues to function until the error between the two grows too large. At this time the next block of samples is used to calculate a new system and the process continues. The parameters describing the speech are thus the system parameters (poles and zeroes, for example) and the number of output samples taken from each system. This information is quantized to produce a bit rate for the process of 20 kilobits/second. The approximate speech is synthesized by implementing each system sequentially, applying a pulse to the input and concatenating the required number of output samples to the samples from previous systems. The speech obtained is very noisy, but it is intelligible and speakers can be recognized. A demonstration tape is available from Dr. T. W. Parks of the Electrical Engineering Department. The entire analysis and synthesis procedure for 8 kHz sampling runs in 145 times real time on a Burroughs B-5500 computer with an ALGOL program. It is estimated that this is fast enough to be done in real time by a special purpose processor.
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    Chebyshev approximation for non-recursive digital filters
    (1972) McClellan, James Harold; Parks, Thomas
    An efficient procedure for the design of finite length impulse response filters with linear phase is presented. The algorithm obtains the optimum Chebyshev approximation on separate intervals corresponding to pass and/or stop bands, and is capable of designing very long filters. This approach allows the exact specification of arbitrary band-edge frequencies as opposed to previous algorithms which could not directly control pass and stop band locations and could only obtain N-1 / 2 different band edge locations for a length N low-pass filter, for fixed phi1 and phi2. As an aid in practical application of the algorithm, several graphs are included to show relations among the parameters of filter length, transition width, band-edge frequencies, passband ripple, and stopband attenuation.
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    Reconstruction of signals of a known class from a given set of linear measurements
    (1970) Meier, Russell Gilbert; Parks, Thomas
    This paper investigates the error in reconstructions of a signal based on a given, finite set of linear measurements, and presents two schemes that, if there is available a prior knowledge of the class of signals of which the measured signal is a member, can achieve a reduction of this error beyond the best that could be done without such knowledge. The error measure used is the supremum over the class of the distance between a signal and its reconstruction. The essence of the proposed reconstruction techniques is a coordinate transformation from the sampling subspace to a new reconstruction subspace known to be efficient for representation of signals of the given class. This study makes application of the theory of extremal subspaces and n-widths of signal classes originated by Kolmogorov. Results are applied to the much-studied class of time-concentrated, band-limited signals. The measurement process is here assumed to be the convenient one of Nyquist rate time sampling. For this problem, plots of the error bounds and of several test functions and their reconstructions are presented, both for the proposed reconstructions, and for conventional cardinal sampling theorem reconstructions.