Study of statistical properties of random signals in multirate filter banks

Leu-Shing Lan

doi:10.1117/12.206644

21 April 1995 Study of statistical properties of random signals in multirate filter banks

Leu-Shing Lan

Proceedings Volume 2501, Visual Communications and Image Processing '95; (1995) https://doi.org/10.1117/12.206644
Event: Visual Communications and Image Processing '95, 1995, Taipei, Taiwan

Abstract

Previous works on subband-related signal processing were mainly dedicated to the applications of subband systems and to the formulation of multirate filter banks. Only very limited results can be found that treat statistical properties of random signals inside a multirate filter bank. In this paper, such a theoretical study is performed from the statistical viewpoint. Our main interest lies in how a multirate structure interacts with a random signal. The key statistical properties examined are stationarity, autocorrelation, cross-correlation, power spectral density, and spectral flatness measure. Exact explicit expressions are obtained. These results have their counterparts in a fullband system; however, inside a multirate structure or a subband system, the aliasing effect caused by decimation should be taken into account. In a multirate system, stationarity is not preserved when an upsampling (or expanding) operation is encountered. Furthermore the equivalent filtering operation is nonlinear. A test example of an AR-1 process is included for demonstration. From this example, an interesting phenomenon is observed. When the correlation coefficient of the AR-1 process is close to 1, the lowpassed signal is not, in any sense, a rough replica of the source. This example justifies the significance and necessity of a theoretical analysis of subband systems from a statistical viewpoint. We believe that stochastic signal processing applications of a subband structure such as estimation, detection, recognition, etc. will benefit from study of this nature.

Citation Download Citation

Leu-Shing Lan "Study of statistical properties of random signals in multirate filter banks", Proc. SPIE 2501, Visual Communications and Image Processing '95, (21 April 1995); https://doi.org/10.1117/12.206644

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KEYWORDS

Signal processing

Electronic filtering

Filtering (signal processing)

Optical filters

Stochastic processes

Statistical analysis

Fourier transforms

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