Thomas W. Parks

A computer program for designing optimum FIR linear phase digital filters

This paper presents a general-purpose computer program which is capable of designing a large Class of optimum (in the minimax sense) FIR linear phase digital filters. The program has options for designing such standard filters as low-pass, high-pass, bandpass, and bandstop filters, as well as multipassband-stopband filters, differentiators, and Hilbert transformers. The program can also be used to design filters which approximate arbitrary frequency specifications which are provided by the user. The program is written in Fortran, and is carefully documented both by comments and by detailed flowcharts. The filter design algorithm is shown to be exceedingly efficient, e.g., it is capable of designing a filter with a 100-point impulse response in about 20 s.

Eigenvalue and eigenvector decomposition of the discrete Fourier transform

The principal results of this paper are listed as follows. 1) The eigenvalues of a suitably normalized version of the discrete Fourier transform (DFT) are {1, -1,j, -j} . 2) An eigenvector basis is constructed for the DFT. 3) The multiplicities of the eigenvalues are summarized for an N×N transform as follows.

A program for the design of linear phase finite impulse response digital filters

This paper presents an algorithm that can be used to design finite impulse response (FIR) digital filters with linear phase. The presentation is in the form of a block diagram together with the Fortran IV listing of the program.

Time domain design of recursive digital filters

The problem of synthesis of recursive digital filters to give a desired pulse response over a specified interval is studied. Realizability conditions are stated and a linear design method is developed. Several design procedures that require only linear calculations are given for approximate realization of recursive filters. Finally, an error analysis of the techniques is made.

Estimating slowness dispersion from arrays of sonic logging waveforms

Acoustic wave propagation in a fluid‐filled borehole is affected by the type of rock which surrounds the hole. More specifically, the slowness dispersion of the various body‐wave and borehole modes depends to some extent on the properties of the rock. We have developed a technique for estimating the dispersion relations from data acquired by full‐waveform digital sonic array well‐logging tools. The technique is an extension of earlier work and is based on a variation of the well‐known Prony method of exponential modeling to estimate the spatial wavenumbers at each temporal frequency. This variation, known as the forward‐backward method of linear prediction, models the spatial propagation by purely real‐valued wavenumbers. The Prony exponential model is derived from the physics of borehole acoustics under the assumption that the formation does not vary in the axial or azimuthal dimensions across the aperture of the receiver array, but can vary arbitrarily in the radial dimension. The exponential model fits...

Extrapolation and spectral estimation with iterative weighted norm modification

An algorithm is developed to define, from the data samples themselves, a frequency-weighted norm to use in minimum-weighted-norm extrapolation. The iterative procedure developed consists of using a periodogram spectrum estimate obtained from some samples of the signal estimate/extrapolation found at one iteration to define the weight that is used to estimate at the next iteration. This algorithm usually converges in less than 10 iterations to an extrapolation which is characterized as a nonparametric frequency-stationary extension of the data. The frequency resolution and extrapolation length are controlled by the length of a time-domain window used to obtain smooth spectral estimates between iterations. Examples are provided to illustrate the use of the algorithm for interpolation/extrapolation. The examples give comparable results to nonadaptive extrapolation methods without the need for a priori knowledge. For a certain spectral estimation example, the algorithm provides comparable resolution to the parametric methods with more accurate values of the relative strengths of the narrowband components. >

A personal history of the Parks-McClellan algorithm

This article describes the work that led to what is now known as the Parks-McClellan algorithm. Within the bigger picture of filter design methods, this paper recount events that had an impact on the inspiration to develop the Parks-McClellan algorithm, i.e., the Remez exchange algorithm with optimal Chebyshev approximation for FIR filter design.

A high resolution data-adaptive time-frequency representation

We present a data-adaptive time-frequency representation that obtains high resolution of signal components in time-frequency. This representation 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 adaptive Gaussian windows, with the window 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 parameter estimation approach, and a method that maximizes a measure of local signal concentration.

Generation and Combination of Grains for Music Synthesis

Granular synthesis has been used for a number of years as a sound synthesis technique. This method constructs an acoustic signal from a number of short-duration acoustic elements, called grains. These grains are produced either by extracting short segments of natural sounds such as speech, or by synthesis according to a mathematical description of the grains. Efficient methods of producing and combining these grains are currently especially interesting, because the recent development of special-purpose digital signal processing (DSP) microprocessors has made real-time granular synthesis possible at a reasonable hardware cost. This paper discusses the computational aspects of granular synthesis. Methods of extracting grains from natural signals and recombining them with phase alignment are described. Fast methods for digital generation of synthetic signals with linear frequency modulation (FM) are also presented.

On the transition width of finite impulse-response digital filters

Several properties of finite-duration impulse-response (FIR) digital filters designed to have the maximum possible number of ripples are discussed and illustrated with examples. Such filters have been called extraripple filters. Among the properties of such filters are as follows. 1) Extraripple low-pass filters with fixed passband ripple δ 1 and stopband ripple δ 2 achieve the local minimum of transition width in the class of linear phase filters with fixed impulse-response duration of N samples. 2) For the case δ 1 = δ 2 the minimum transition width is roughly independent of F p , the passband cutoff frequency. 3) For the case δ 2 1 , the minimum transition width decreases with increasing bandwidth. Several figures are included to show the relation between the transition width and bandwidth for low-pass filters.