# Optimum binary windows for discrete Fourier transforms

01 Feb 1986-IEEE Transactions on Acoustics, Speech, and Signal Processing (IEEE)-Vol. 34, Iss: 1, pp 216-220

TL;DR: A class of windows, called binary windows, for the frequency-domain implementation of the discrete Fourier transform is proposed, which do not require multiplications or stored constants; rather, they are replaced by shift and add operations.

Abstract: A class of windows, called binary windows, for the frequency-domain implementation of the discrete Fourier transform is proposed. While the conventional time-domain windowing requires N/2 stored values of the data window and N multiplications, the binary windows do not require multiplications or stored constants; rather, they are replaced by shift and add operations. Typical hardware structures are presented for efficient implementation of the binary windows.

Topics: Discrete Fourier transform (56%), Fourier transform (52%), Binary number (51%)

##### Citations

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TL;DR: A real-time IIR filter structure is presented that possesses exact phase linearity with 10 approximately 1000 times fewer general multiplies than conventional FIR filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay IIR filters.

Abstract: A real-time IIR filter structure is presented that possesses exact phase linearity with 10 approximately 1000 times fewer general multiplies than conventional FIR filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay IIR filters. This structure is based on a technique using local time reversal and single pass sectioned convolution methods to realized a real-time recursive implementation of the noncausal transfer function H(z/sup -1/). The time reversed section technique used to realize exactly linear phase IIR filters is described. The effects of finite section length on the sectional convolution are analyzed. A simulation methodology is developed to address the special requirements of simulating a time reversed section filter. A design example is presented, with computer simulation to illustrate performance, in terms of overall magnitude response and phase linearity, as a function of finite section length. Nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct FIR implementation. >

99 citations

### Cites background from "Optimum binary windows for discrete..."

...-0.006 -70 shorter section lengths than L‘. However, windows with coefficients other than 2” require additional multipliers [ 24 ]....

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TL;DR: The simulation demonstrates that the improved estimation method, in which the symmetric windows are replaced by the asymmetric windows, shows a stronger capability of additive noise resistance than the traditional method.

Abstract: Classic windows have constant time delay and linear phase because of the symmetry and the time shift causality-imposed in the time domain. And thus, all such windows have the same spectral phase response. Removal of the symmetry constraint on a classic window can result in a variable phase response and in an alterable time delay. In essence the time delay becomes shorter will bring about a lot of benefits in speech coding. Some asymmetric windows with better magnitude response also can lead to a better recognition performance if the result is relatively insensitive to phase distortion. However, it is surprising that so little attention has been paid to the asymmetric windows in past literature; and never in past history has this issue been systematically or comprehensively studied. As a result, several methods to obtain the asymmetric windows are being presented in this paper. The asymmetric windows are displayed and compared with the classic windows, concerning both in time and frequency domains. Some ne...

7 citations

##### References

More filters

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01 Jan 1978-

TL;DR: A comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared is included, and an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.

Abstract: This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared. Finally, an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.

6,731 citations

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TL;DR: Correct plots of Harris' windows are presented and additional windows with very good sidelobes and optimal behavior under several different constraints are derived.

Abstract: Some of the windows presented by Harris [1] are not correct in terms of their reported peak sidelobes and optimal behavior. We present corrected plots of Harris' windows and also derive additional windows with very good sidelobes and optimal behavior under several different constraints. The temporal weightings are characterized as a sum of weighted cosines over a finite duration. The plots enable the reader to select a window to suit his requirements, in terms of bias due to nearby sidelobes and bias due to distant sidelobes.

946 citations

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Abstract: FIR digital filters with discrete coefficient values selected from the powers-of-two coefficient space are designed using the methods of integer programming. The frequency responses obtained are shown to be superior to those obtained by simply rounding the coefficients. Both the weighted minimax and the weighted least square error criteria are considered. Using a weighted least square error criterion, it is shown that it is possible to predict the improvement that can be expected when integer quadratic programming is used instead of simple coefficient rounding.

443 citations