Journal•ISSN: 0018-9278

# IEEE Transactions on Audio and Electroacoustics

Institute of Electrical and Electronics Engineers

About: IEEE Transactions on Audio and Electroacoustics is an academic journal. The journal publishes majorly in the area(s): Digital filter & Discrete-time Fourier transform. It has an ISSN identifier of 0018-9278. Over the lifetime, 427 publications have been published receiving 28264 citations.

Topics: Digital filter, Discrete-time Fourier transform, Adaptive filter, Network synthesis filters, Speech processing

##### Papers

More filters

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IBM

^{1}TL;DR: In this article, the use of the fast Fourier transform in power spectrum analysis is described, and the method involves sectioning the record and averaging modified periodograms of the sections.

Abstract: The use of the fast Fourier transform in power spectrum analysis is described. Principal advantages of this method are a reduction in the number of computations and in required core storage, and convenient application in nonstationarity tests. The method involves sectioning the record and averaging modified periodograms of the sections.

9,705 citations

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TL;DR: A general-purpose computer program which is capable of designing a large Class of optimum (in the minimax sense) FIR linear phase digital filters and is shown to be exceedingly efficient.

Abstract: 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.

1,160 citations

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TL;DR: The digital technique lends itself to the production of phase coherent or phase controlled sinusoids because of the indexing arrangement used and finer frequency steps than the READ-ONLY memory allows are available by expanding theindexing register at no increase in inaccuracy.

Abstract: A digital frequency synthesizer has been designed and constructed based on generating digital samples of \exp [j(2^{\pi}nk/N)] at time nT . The real and imaginary parts of this exponential form samples of quadrature sinusoids where the frequency index k is allowed to vary (-N/4) \leq K . The digital samples drive digital to analog converters followed by low-pass interpolating filters to produce analog sinusoids. The method is superior to digital difference equations with poles on the unit circle since the noise or numerical inaccuracy remains bounded. The digital technique used consists of factoring the exponential into two table look-ups from an efficiently organized small READ-ONLY memory table and performing a complex multiply to produce the real and imaginary components. A small array multiplier efficiently organized performs the multiplications. The technique lends itself to the production of phase coherent or phase controlled sinusoids because of the indexing arrangement used. In addition finer frequency steps than the READ-ONLY memory allows are available by expanding the indexing register at no increase in inaccuracy.

698 citations

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TL;DR: A computational algorithm for numerically evaluating the z -transform of a sequence of N samples is discussed, based on the fact that the values of the z-transform on a circular or spiral contour can be expressed as a discrete convolution.

Abstract: A computational algorithm for numerically evaluating the z -transform of a sequence of N samples is discussed. This algorithm has been named the chirp z -transform (CZT) algorithm. Using the CZT algorithm one can efficiently evaluate the z -transform at M points in the z -plane which lie on circular or spiral contours beginning at any arbitrary point in the z -plane. The angular spacing of the points is an arbitrary constant, and M and N are arbitrary integers. The algorithm is based on the fact that the values of the z -transform on a circular or spiral contour can be expressed as a discrete convolution. Thus one can use well-known high-speed convolution techniques to evaluate the transform efficiently. For M and N moderately large, the computation time is roughly proportional to (N+M) \log_{2}(N+M) as opposed to being proportional to N . M for direct evaluation of the z -transform at M points.

608 citations

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TL;DR: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey, and includes an efficient method for permuting the results in place.

Abstract: This paper presents an algorithm for computing the fast Fourier transform, based on a method proposed by Cooley and Tukey. As in their algorithm, the dimension n of the transform is factored (if possible), and n/p elementary transforms of dimension p are computed for each factor p of n . An improved method of computing a transform step corresponding to an odd factor of n is given; with this method, the number of complex multiplications for an elementary transform of dimension p is reduced from (p-1)^{2} to (p-1)^{2}/4 for odd p . The fast Fourier transform, when computed in place, requires a final permutation step to arrange the results in normal order. This algorithm includes an efficient method for permuting the results in place. The algorithm is described mathematically and illustrated by a FORTRAN subroutine.

534 citations