Sharper uncertainty principles for the windowed Fourier transform

The windowed Fourier transform replaces the Fourier transform’s sinusoidal wave by the product of a sinusoid and a window which is localized in time. It has been shown to represent a powerful tool for non-stationary signals and time-varying systems. In the present paper, we investigate the uncertainty principles in the short-time spectral domain. Two sharper uncertainty principles for complex signals are proposed. The tighter lower bounds are related to the covariance of time and frequency, and can be achieved by complex chirp signals with Gaussian envelope. The results presented in this paper explain interesting phenomena in signal recovery problems where there is an interplay of missing data and is time-limiting.

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