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Showing papers in "IEEE Transactions on Audio and Electroacoustics in 1972"


Journal ArticleDOI
TL;DR: It is demonstrated that the simplified inverse filter tracking algorithm (hereafter referred to as the SIFT algorithm) encompasses the desirable properties of both autocorrelation and cepstral pitch analysis techniques.
Abstract: In this paper a new method for estimating F 0 , the fundamental frequency of voiced speech versus time, is presented. The algorithm is based upon a simplified version of a general technique for fundamental frequency extraction using digital inverse filtering. It is demonstrated that the simplified inverse filter tracking algorithm (hereafter referred to as the SIFT algorithm) encompasses the desirable properties of both autocorrelation and cepstral pitch analysis techniques. In addition, the SIFT algorithm is composed of only a relatively small number of elementary arithmetic operations. In machine language, SIFT should run in several times real time while with special-purpose hardware it could easily be realized in real time.

398 citations


Journal ArticleDOI
TL;DR: In this article, a simplified version of a stability theorem due to Shanks is presented and shown to be equivalent to some results of Ansell, and several examples of stability tests are discussed.
Abstract: We discuss some aspects of the stability problem in two-dimensional recursive filtering. In particular, we derive a simplified version of a stability theorem due to Shanks and show that it is equivalent to some results of Ansell. We also give several examples of stability tests and pose a few unsolved problems.

359 citations


Journal ArticleDOI
TL;DR: Two-dimensional recursive bandpass filters as mentioned in this paper can be synthesized to approximate large varieties of desired two-dimensional pulse responses by a conformal transformation of the one-dimensional filters.
Abstract: Two-dimensional recursive filters are conveniently described in terms of two-dimensional z transforms. The designer of these filters faces two fundamental problems, their stability and their synthesis. Stability is determined by the location of the zero-valued region of the filter's denominator polynomial. A conjecture based on a one-dimensional stability theorem leads to a useful empirical stabilization procedure. Two-dimensional recursive filters can be synthesized to approximate large varieties of desired two-dimensional pulse responses. A conformal transformation yields two-dimensional recursive bandpass filters from appropriately specified one-dimensional filters.

340 citations


Journal ArticleDOI
A. Deczky1
TL;DR: In this article, the problem of designing a stable recursive digital filter to have an arbitrarily prescribed frequency response may be considered as an approximation problem using the minimum p -error criterion, which is successfully solved using the Fletcher-Powell algorithm.
Abstract: The problem of designing a stable recursive digital filter to have an arbitrarily prescribed frequency response may be considered as an approximation problem. Using the minimum p - error criterion, a new problem of minimizing a function of n variables results, which is successfully solved using the Fletcher-Powell algorithm. An important theorem guaranteeing the existence of a stable optimum for a large class of synthesis problems is stated, and necessary modifications to the Fletcher-Powell algorithm to assure stability are considered. Finally a number of results of the application of this method are given.

265 citations


Journal ArticleDOI
J. McClellan1, T. Parks1
TL;DR: The eigenvalues of a suitably normalized version of the discrete Fourier transform (DFT) are {1, -1,j, -j} and an eigenvector basis is constructed for the DFT.
Abstract: 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.

232 citations


Journal ArticleDOI
TL;DR: In this article, a digital inverse filter formulation is used to estimate the resonance or formant structure of voiced speech and the output of the algorithm is a set of raw data corresponding to peak frequencies versus time, which is then used for estimating the first three and sometimes four continuously varying formant trajectories.
Abstract: A new algorithm, based upon a digital inverse filter formulation, is presented and shown to be quite useful for estimating resonance or formant structure of voiced speech. The output of the algorithm is a set of raw data corresponding to peak frequencies versus time which is then used to estimate the first three and sometimes four continuously varying formant trajectories. Although an algorithm for automatically extracting the formants from the raw data is not presented here, for nearly 90 percent of the time an automatic decision algorithm is trivial, namely, the first three peaks of the reciprocal of the inverse filter spectrum define the first three formants.

180 citations


Journal ArticleDOI
Lawrence R. Rabiner1
TL;DR: The use of linear programming techniques for designing digital filters has become widespread in recent years as discussed by the authors, among the techniques that have been used include steepest descent methods, conjugate gradient techniques, penalty function techniques and polynomial interpolation procedures.
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.

175 citations


Journal ArticleDOI
TL;DR: An algorithm that can be used to design finite impulse response (FIR) digital filters with linear phase with Fortran IV listing of the program is presented.
Abstract: 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.

169 citations


Journal ArticleDOI
TL;DR: It is shown that good two-dimensional windows can be obtained by rotating good one- dimensional windows, that is, if w(x) is a good symmetrical one-dimensional window, then w sub 2(x,y) = w(square root of (x squared + y squared)) is aGood circularly symmetrical two- dimensional window.
Abstract: : Two-dimensional windows find applications in many diverse fields, such as the spectral estimation of random fields, the design of two-dimensional digital filters, optical apodization, and antenna array design. Many good one- dimensional windows have been devised, but relatively few two-dimensional windows have been investigated. In this paper we show that good two-dimensional windows can be obtained by rotating good one-dimensional windows. That is, if w(x) is a good symmetrical one-dimensional window, then w sub 2(x,y) = w(square root of (x squared + y squared)) is a good circularly symmetrical two- dimensional window.

118 citations


Journal ArticleDOI
J. Hu1, Lawrence R. Rabiner1
TL;DR: The theory for designing finite-duration impulse response (FIR) digital filters can readily be extended to two or more dimensions using linear programming techniques, and several of the issues involved in designing two-dimensional digital filters are discussed in this article.
Abstract: The theory for designing finite-duration impulse response (FIR) digital filters can readily be extended to two or more dimensions. Using linear programming techniques, both frequency sampling and optimal (in the sense of Chebyshev approximation over closed compact sets) two-dimensional filters have been successfully designed. Computational considerations have limited the filter impulse response durations (in samples) to 25 by 25 in the frequency sampling case, and to 9 by 9 in the optimal design case. However, within these restrictions, a large number of filters have been investigated. Several of the issues involved in designing two-dimensional digital filters are discussed.

116 citations


Journal ArticleDOI
C. Burrus1
TL;DR: In this article, different forms of block recursive digital filters are formulated using a matrix representation of convolution, and the multiplication efficiencies are calculated and compared, showing that the block realization can become more efficient for filters with orders exceeding approximately 25.
Abstract: Different forms of block recursive digital filters are formulated using a matrix representation of convolution. These approaches have the same relation to recursive filters that fast convolution does to nonrecursive filters. The multiplication efficiencies are calculated and compared, showing that the block realization can become more efficient for filters with orders exceeding approximately 25. The general improvements on stability and sensitivity to roundoff error and coefficient accuracy are discussed.

Journal ArticleDOI
TL;DR: Two methods for reducing the necessary word length of a digital filter by choosing a suitable structure for the filter and taking selective filters as a model will be presented.
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.

Journal ArticleDOI
TL;DR: In this article, the authors investigate the effect of digital ladder structures on the performance of low-coefficient word length and conclude that the digital ladder structure in many cases can be implemented with lower coefficient word lengths than conventional structures.
Abstract: Recently, there has been a great deal of interest in the implementation of digital filter structures with low-coefficient word length. A conjecture has been made by Fettweis that if digital filter structures are modeled after analog ladder structures, which are known to have desirable coefficient sensitivity properties, then the digital ladder structures will also have these properties and could be implemented with low-coefficient word lengths. To investigate this conjecture, a seventh-order Chebyshev low-pass filter was realized as a digital ladder structure and the coefficient sensitivity was analyzed experimentally under coefficient rounding in floating-point representation. To serve as a comparison similar examples of cascade structures of direct and coupled form sections were also analyzed in the same manner. The conclusions drawn are that, indeed, the digital ladder structures in many cases can be implemented with lower coefficient word lengths than the conventional structures.

Journal ArticleDOI
TL;DR: A method is described that yields the fast Walsh transform (FWT) in sequency order based on the Cooley-Tukey-type fast Hadamard transform (FHT) algorithm, whose computational effort is identical to the conventional FHT.
Abstract: A method is described that yields the fast Walsh transform (FWT) in sequency order. The advantages of this method over others are: 1) it is based on the Cooley-Tukey-type fast Hadamard transform (FHT) algorithm, 2) the computational effort is identical to the conventional FHT, and 3) the transform remains its own inverse.

Journal ArticleDOI
TL;DR: This paper proposes terminology for use in papers and texts on digital signal processing which it is felt is self-consistent, and which is in reasonably good agreement with current practices.
Abstract: The committee on Digital Signal Processing of the IEEE Group on Audio and Electroacoustics has undertaken the project of recommending terminology for use in papers and texts on digital signal processing. The reasons for this project are twofold. First, the meanings of many terms that are commonly used differ from one author to another. Second, there are many terms that one would like to have defined for which no standard term currently exists. It is the purpose of this paper to propose terminology which we feel is self-consistent, and which is in reasonably good agreement with current practices. An alphabetic index of terms is included at the end of the paper.

Journal ArticleDOI
TL;DR: The Walsh power spectrum of a sequence of random samples is defined as the Walsh transform of the logical autocorrelation function of the random sequence and the Fourier power spectrum can be obtained from the Walsh power Spectrum by a linear transformation.
Abstract: The Walsh power spectrum of a sequence of random samples is defined as the Walsh transform of the logical autocorrelation function of the random sequence. The "logical" autocorrelation function is defined in a similar form as the "arithmetic" autocorrelation function. The Fourier power spectrum, which is defined as the Fourier transform of the arithmetic autocorrelation function, can be obtained from the Walsh power spectrum by a linear transformation. The recursive relations between the logical and arithmetic auto-correlation functions are derived in this paper. For a given process with computed or modeled autocorrelation function the Fourier and Walsh power spectra are computed by using the fast Fourier and Walsh transforms, respectively. Examples are given from the speech and imagery data.

Journal ArticleDOI
I. Sandberg1, J. Kaiser
TL;DR: In this article, an upper bound on the rms value of self-sustained limit cycles in fixed-point implementations of digital filters is presented, which can be easily evaluated for the important special case of sections of order two.
Abstract: We present an upper bound on the rms value of self-sustained limit cycles in fixed-point implementations of digital filters. The bound can be easily evaluated for the important special case of sections of order two, and simulation results for this case show that the bound is a useful tool.

Journal ArticleDOI
TL;DR: In this article, the problem of maximally flat delay design of recursive digital filters has been solved by Thiran, using a direct z-domain approach, and the solution is obtained in a much simpler way by making use of the familiar bilinear transform s of the variable z.
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.

Journal ArticleDOI
TL;DR: In this paper, it was shown that any row of the matrix is approximately a linear combination of other rows, and the difficulty of numerical deconvolution is explained by examining the matrix of the linear equations generated by approximating the linear system superposition integral.
Abstract: The difficulty of numerical deconvolution is explained by examining the matrix of the linear equations generated by approximating the linear system superposition integral. It is shown that any row of the matrix is approximately a linear combination of other rows.

Journal ArticleDOI
TL;DR: Canonic realizations of a digital transfer function using the continued fraction expansion techniques are derived in this article, where realizability conditions of each realization are provided along with illustrative examples of realizations.
Abstract: Canonic realizations of a digital transfer function using the continued fraction expansion techniques are derived. Realizability conditions of each realization are provided along with illustrative examples.

Journal ArticleDOI
A. Crooke1, J. Craig
TL;DR: In this article, the authors considered the effect of quantization of FIR filter coefficients on the frequency response and showed that quantization can improve the performance of FIR filters with respect to the log of the sample rate reduction ratio.
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.

Journal ArticleDOI
TL;DR: A random search optimization algorithm for integer-valued functions and the application of the algorithm to the design of digital filters with finite word length is presented.
Abstract: A random search optimization algorithm for integer-valued functions is proposed. The application of the algorithm to the design of digital filters with finite word length is presented.

Journal ArticleDOI
TL;DR: The algorithm discussed can achieve the decomposition of a certain class of noisy composite signals composed of nonidentical unknown multiple wavelets overlapping in time, namely those signals with reasonably well-defined independent resonances in the spectrum.
Abstract: Research in fields such as communication, speech, oceanography, seismic exploration, economics, and biomedical data processing is often directed toward the analysis of nonstationary or transient data. Complex demodulation is shown to be a valuable method that can be used to decompose a composite signal composed of differing transient wavelets and to estimate spectra. For the latter application it is shown that several other techniques recently advanced in the literature are special cases of complex demodulation. The algorithm discussed can achieve the decomposition of a certain class of noisy composite signals composed of nonidentical unknown multiple wavelets overlapping in time, namely those signals with reasonably well-defined independent resonances in the spectrum. The decomposition estimates the arrival time, peak, envelope, and frequency of the damped oscillatory transient wavelet. The procedure has been tested extensively and several selected experimental results are tendered. It has been found that for wavelets of the type t^{k}e^{-at} \sin (\omegat) , k =0, 1 , that an uncertainty relationship for the product of the 3-dB bandwidth and the time duration of the wavelet must be satisfied. An error analysis has established a relationship between envelope-and phase-estimation errors to wavelet and filter parameters. The results obtained via complex demodulation are discussed relative to those obtained via inverse filtering, the complex cepstrum, and the chirp z transform.

Journal ArticleDOI
D. Kalikow1, J. Swets1
TL;DR: Three displays were evaluated for their effectiveness in overcoming pronunciation problems that typically confront Spanish speakers attempting to learn English.
Abstract: Three displays were evaluated for their effectiveness in overcoming pronunciation problems that typically confront Spanish speakers attempting to learn English. One display shows tongue location and trajectory during vowels; another similar display isolates the vowels in multisyllabic words that should be reduced; the third display shows the amount of aspiration of initial consonants and the time lapse before voicing of the succeeding vowel. Other displays are being developed for teaching a tone language to English speakers.

Journal ArticleDOI
TL;DR: In this paper, a time-domain method is presented for designing nonrecursive digital filters that are optimum in the sense that the output samples are least mean-square estimates of the samples of some desired signal.
Abstract: A time-domain method is presented for designing nonrecursive digital filters that are optimum in the sense that the output samples are least mean-square estimates of the samples of some desired signal. The method requires that one know the input autocorrelation function and the cross-correlation function between the input and the desired output. Several examples are given of filters designed by the method. The optimum filters can be obtained by sampling the impulse responses of optimum filters for continuous reconstruction of the waveforms from their samples.

Journal ArticleDOI
TL;DR: By eliminating all unnecessary steps and storage locations, and by rearranging the intermediate results and the operation sequence, it is possible to reduce the computation time and the required core storage by a factor of 2 as compared to the case of arbitrary real input.
Abstract: A new algorithm is presented for calculating the real discrete Fourier transform of a real-valued input series with even symmetry. The algorithm is based on the fast Fourier transform algorithm for arbitrary real-valued input series (FTRVI) [1], [2]. By eliminating all unnecessary steps and storage locations, and by rearranging the intermediate results and the operation sequence, it is possible to reduce the computation time and the required core storage by a factor of 2 as compared to the case of arbitrary real input or by a factor of 4 as compared to the general fast Fourier transform for complex inputs.

Journal ArticleDOI
TL;DR: In this article, the general Remes exchange algorithm and its implementation are discussed briefly and an analog of the exchange algorithm is applied to the problem in which upper and lower constraints are imposed on the frequency response of a non-recursive digital filter with linear phase.
Abstract: The general Remes exchange algorithm and its implementation are discussed briefly An analog of the exchange algorithm is applied to the problem in which upper and lower constraints are imposed on the frequency response of a nonrecursive digital filter with linear phase. A typical design example is presented with rather tight constraints in the passband

Journal ArticleDOI
R. W. Schafer1
TL;DR: Some recent work in speech processing including design of digital filter bank spectrum analyzers, homorphic analyzers of speech, predictive coding, and hardware realization of a digital formant synthesizer are discussed.
Abstract: Digital signal processing techniques are becoming increasingly important in speech analysis and synthesis. These techniques can be implemented using a general purpose computer facility (often not in real time), or special purpose hardware realizations can be constructed. This paper discusses some recent work in speech processing including design of digital filter bank spectrum analyzers, homorphic analyzers of speech, predictive coding, and hardware realization of a digital formant synthesizer. The survey concentrates on those speech processing techniques relevant to the development of sensory aids for the deaf.

Journal ArticleDOI
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.

Journal ArticleDOI
TL;DR: The Fourier filter and detector is examined and shown to be an optimum receiver for a very generalized signal model that covers a single sinusoidal pulse, pulse trains, and continuous signals.
Abstract: FFT processing systems have become important and extremely useful implementations of narrow-band signal detectors for signals with unknown phase and frequency This paper examines the Fourier filter and detector and shows it to be an optimum receiver for a very generalized signal model The general signal model covers a single sinusoidal pulse, pulse trains, and continuous signals The model provides for the finite bandwidth encountered in real signals and includes the affect of redundant processing which can be employed with high-speed FFT processors The paper provides a method for evaluating detection sensitivity for this class of signal detectors and gives experimental results from an FFT processor implementation