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Discrete Time-Frequency Projection Filtering Based on an Alias-Free Discrete Time-Frequency Analysis
Hiroshi HASEGAWA Isao YAMADA Kohichi SAKANIWA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2004/06/01
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
time-frequency analysis, Cohen's class, discrete time and frequency, linear time-varying filtering,
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In this paper, we propose a method of linear time-varying filtering of discrete time signals. The objective of this method is to derive a component, of an input signal, whose alias-free generalized discrete time-frequency distribution [Jeong & Williams 1992] concentrates on a specific region of a time-frequency plane. The method is essentially realized by computing an orthogonal projection of an input onto a subspace that is spanned by orthonormal signals, whose distributions concentrate on the region. We show that such orthonormal signals can be derived as eigenvectors of a matrix whose components are explicitly expressed by using the kernel of the distribution and the regions. This result shows that we can design such a filter prior to processing of the input if the specific region is given as a priori. This result is a generalization of [Hlawatsch & Kozek 1994], that is originally derived for the continuous Wigner distributions, to the discrete distributions.