Variable parameter window families for digital spectral analysis
01 Jun 1989-IEEE Transactions on Acoustics, Speech, and Signal Processing (IEEE)-Vol. 37, Iss: 6, pp 946-949
TL;DR: Two different window function families, namely, the first-order Bessel (I/sub 1/-cosh) family and raised-cosine family, which have variable parameters and hence make them flexible in digital spectrum analysis applications, are considered and closed-form expressions are obtained which facilitate the tradeoffs between record length, spectral resolution, leakage suppression, bandwidth, etc.
Abstract: Two different window function families, namely, the first-order Bessel (I/sub 1/-cosh) family and raised-cosine family, which have variable parameters and hence make them flexible in digital spectrum analysis applications, are considered. Closed-form expressions are obtained which facilitate the tradeoffs between record length, spectral resolution, leakage suppression, bandwidth, etc. Simple expressions relating to mainlobe width and maximum sidelobe level are given for the two families considered. The results are compared to those obtained by J.F. Kaiser and R.W. Schafer (1980) in the case of zeroth-order Bessel (I/sub 0/-sinh) family. >
Citations
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TL;DR: These results suggest that discrimination performance is related to changes in higher-order image structure; a bandpass model observer based on third-moment statistics was applied to all stimulus images and was found to provide a good fit to the psychophysical data.
Abstract: Several studies of natural-image statistics have concluded that the majority of structural image information is represented in the Fourier domain not by the power spectrum, which can be modeled with a power function of spatial frequency, but by the phase spectrum. Psychophysical experiments are described in which human observers were required to discriminate between visual stimuli differing only in their global second-order statistics. The patterns of sensitivity recorded were found to depend on whether these stimuli were natural images or images with random-phase spectra. These results suggest that discrimination performance is related to changes in higher-order image structure; a bandpass model observer based on third-moment statistics was applied to all stimulus images and was found to provide a good fit to the psychophysical data.
58 citations
14 Apr 1991
TL;DR: The idea of asymmetric windowing as a way of reducing time delay in spectral analysis is explored and it is shown that it is possible to reduce the time delay up to about 25% of the analysis window size.
Abstract: The idea of asymmetric windowing as a way of reducing time delay in spectral analysis is explored. Traditional windows are analyzed in relation to time delay. Some asymmetric windows are introduced and a comparative analysis with traditional windows is made. It is shown that it is possible to reduce the time delay up to about 25% of the analysis window size. Application to linear predictive speech coding is analyzed, and the experimental results of using an asymmetric window on a standard LPC vocoder are presented. >
20 citations
TL;DR: The results show that the window functions generated using the cyclic algorithm (CA) yield better performance overall than the windows of conventional methods, achieving a narrower MW, a lower PSL, and a controllable SLFOR.
Abstract: In the field of sensor signal processing, windows are time-/frequency-domain weighting functions that are widely applied to reduce the well-known Gibbs oscillations Conventional methods generally control the spectral characteristics of windows by adjusting several of the parameters of closed-form expressions Designers must make trade-offs among the mainlobe width (MW), the peak sidelobe level (PSL), and sometimes the sidelobe fall-off rate (SLFOR) of windows by carefully adjusting these parameters Generally, not all sidelobes need to be suppressed in specified applications In this paper, a novel method, ie, the inverse of the shaped output using the cyclic algorithm (ISO-CA), for designing window functions with flexible spectral characteristics is proposed Simulations are conducted to test the effectiveness, flexibility and versatility of the method Some experiments based on real measured data are also presented to demonstrate the practicability The results show that the window functions generated using the cyclic algorithm (CA) yield better performance overall than the windows of conventional methods, achieving a narrower MW, a lower PSL, and a controllable SLFOR In addition, steerable sidelobes over specified regions can be acquired both easily and flexibly while maintaining the original properties of the initial window as much as possible
8 citations
TL;DR: In this paper, a complete spectrum analysis for discrete signals is proposed, which is based on the concept to establish a complete solution, divided into three steps: first, this paper analyzes the signal characteristics to be the basis of spectrum adjustment, and then finds optimum spectrum parameters to make the new spectrum match with signal characteristics.
Abstract: This paper provides a complete method to solve the defects of spectrum analysis for discrete signals. Many researches had issued to deal with the defects of fast Fourier transform (FFT). Those methods may cause the characteristics of original signal altered, or solve this problem in part only. The defects of spectrum analysis cannot be solved efficiently and completely by those methods. These defects result from that those frequency scales cannot match with signal characteristics. This paper is based on the concept to establish a complete solution, divided into three steps: First, this paper analyzes the signal characteristics to be the basis of spectrum adjustment. A simple and accurate algorithm is used to find the frequency and amplitude of each component. Next, this paper finds optimum spectrum parameters to make the new spectrum match with signal characteristics. Finally, this paper takes the parameters to reanalyze the original signal. The method will make spectrum analysis reach optimization. Every procedure in this paper compares with traditional ones to prove its benefits. Moreover, the authors verify the theory feasible by analyzing actual signals.
7 citations
Cites methods from "Variable parameter window families ..."
...For example, the window method ameliorates the leakage effect, the zero padding method solved the picket-fence effect, and the IPE method improved the leakage effect [ 10 ]....
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25 May 1992
TL;DR: This paper shows a fast implementation method of a two dimensional (2D) filter based on fast convolution related to the fast Fourier transform (FFT) look up table that gives a good accurate selection of the desired frequency.
Abstract: This paper shows a fast implementation method of a two dimensional (2D) filter. The filter design is based on fast convolution related to the fast Fourier transform (FFT) look up table. This is then extended to the 2D FFT. The design and implementation of the system gives a good accurate selection of the desired frequency. The system has a step advantage of a reduction in the operation time. >
6 citations
References
More filters
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Abstract: An efficient method for the calculation of the interactions of a 2' factorial ex- periment was introduced by Yates and is widely known by his name. The generaliza- tion to 3' was given by Box et al. (1). Good (2) generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series. In their full generality, Good's methods are applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices, where m is proportional to log N. This results inma procedure requiring a number of operations proportional to N log N rather than N2. These methods are applied here to the calculation of complex Fourier series. They are useful in situations where the number of data points is, or can be chosen to be, a highly composite number. The algorithm is here derived and presented in a rather different form. Attention is given to the choice of N. It is also shown how special advantage can be obtained in the use of a binary computer with N = 2' and how the entire calculation can be performed within the array of N data storage locations used for the given Fourier coefficients. Consider the problem of calculating the complex Fourier series N-1 (1) X(j) = EA(k)-Wjk, j = 0 1, * ,N- 1, k=0
11,795 citations
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.
7,130 citations
"Variable parameter window families ..." refers background in this paper
...Therefore, the selection of good data windows in spectral estimation of stationary random processes is an important consideration and has received much attention [I], [2], [ 6 ]-[8]....
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...It is well known that the application of fast Fourier transform (FFT) to a finite length data gives rise to leakage [ 6 ]....
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TL;DR: In this paper, the authors apply the theory developed in the preceding paper to a number of questions about timelimited and bandlimited signals, and find the signals which do the best job of simultaneous time and frequency concentration.
Abstract: The theory developed in the preceding paper1 is applied to a number of questions about timelimited and bandlimited signals. In particular, if a finite-energy signal is given, the possible proportions of its energy in a finite time interval and a finite frequency band are found, as well as the signals which do the best job of simultaneous time and frequency concentration.
2,498 citations
TL;DR: In this paper, Measurement and Analysis of Random Data (MADR) is used for the analysis of random data in the context of measurement and analysis of statistical data sets.
Abstract: (1968). Measurement and Analysis of Random Data. Technometrics: Vol. 10, No. 4, pp. 869-871.
1,041 citations
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.
1,024 citations