STFT-like time frequency representations of nonstationary signal with arbitrary sampling schemes

Spectrograms provide an effective way of time–frequency representation (TFR). Among these, short-time Fourier transform (STFT) based spectrograms are widely used for various applications. However, STFT spectrogram and its revised versions suffer from two main issues: (1) there is a trade-off between time resolution and frequency resolution and (2) almost all the existing TFR methods, including STFT spectrogram, are not designed to handle arbitrary nonuniformly sampled data. To address these two issues, short-time iterative adaptive approach (ST-IAA) was recently proposed as a data-dependent adaptive spectral estimation method that can provide much enhanced TFR performance. In this paper, inspired by the ST-IAA method, we present an alternative approach, namely short-time sparse learning via iterative minimization (ST-SLIM), which can provide sparser and slightly better TFR performance than its ST-IAA counterpart. Moreover, in order to extend the applicability of ST-IAA to signals in the missing data case, we also propose a short-time missing-data iterative adaptive approach (ST-MIAA) which can retrieve the missing data effectively and outperform ST-IAA and ST-SLIM in the missing data case. We will demonstrate via simulation results the superiority of our proposed algorithms in terms of resolution, sidelobe suppression and applicability to signals with arbitrary sampling patterns.