Time-varying filter interpretation of Fourier transform and its variants

Authors:
Prasanta Kumar Ghosh;T. V. Sreenivas
Affiliations:
Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, India;Department of Electrical Communication Engineering, Indian Institute of Science, Bangalore, India
Venue:
Signal Processing - Special section: Distributed source coding
Year:
2006

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Abstract

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.