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), 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 shorttime 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. r 2006 Elsevier B.V. All rights reserved.