Time-varying filter interpretation of Fourier transform and its variants

We show that a stationary signal concept such as the Fourier transform (FT) can be linked to a time-varying (TV) concept such as linear TV filtering. In particular, we give a continuous-time and discrete-time linear TV filter interpretation to continuous-time FT and discrete Fourier transform (DFT),...

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Bibliographic Details
Published in:Signal processing 2006-11, Vol.86 (11), p.3258-3263
Main Authors: Ghosh, Prasanta Kumar, Sreenivas, T.V.
Format: Article
Language:English
Subjects:
Applied sciences
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Fourier transform
Information, signal and communications theory
Miscellaneous
Short-time Fourier transform
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Time-varying filter
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Summary:We show that a stationary signal concept such as the Fourier transform (FT) can be linked to a time-varying (TV) concept such as linear TV filtering. In particular, we give a continuous-time and discrete-time linear TV filter interpretation to continuous-time FT and discrete Fourier transform (DFT), respectively. As a consequence, important variants such as warped DFT, DCT, DST also can be viewed as linear TV filtering operations. Extending these results, we show that short-time Fourier transform (STFT) can be viewed as a linear TV filterbank operation, thereby interpreting time-varying spectrum of a signal as the output of a linear TV filterbank.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2006.01.005