Sparse frequency extrapolation of spectrograms

Abstract

Abstract-The short-time Fourier transform is a prevalent method used to analyze the frequency composition of a signal as a function of time. In order to achieve high resolution in frequency a large sliding window needs to be applied which degrades the time resolution. This paper proposes the adoption of sparse reconstruction as a mean to extrapolate supplementary values in time domain for each segment. Over short durations a signal's frequency content is likely to contain a limited number of effective frequencies and a sparse regeneration approach can be advantageous as an extrapolating mechanism. An enlarged number of samples can thus yield spectrograms with high frequency resolution. The capabilities of the proposed techniques are demonstrated on several synthetic and real data signals.