This Paper Is a Postprint of a Paper Submitted to and Accepted for Publication in Iet Signal Processing and Is Subject to Institution of Engineering and Technology Copyright. the Copy of Record Is Available at Iet Digital Library

1 AbstractThe estimation of time-varying instantaneous frequency for monocomponent signals with incomplete set of samples is considered. A suitable time-frequency distribution reduces the nonstationary signal into a local sinusoid over the lag variable prior to Fourier transform. Accordingly, the observed spectral content becomes sparse and suitable for compressive sensing reconstruction in the case of missing samples. Although the local bilinear or higher order autocorrelation functions will increase the number of missing samples, the analysis shows that accurate instantaneous frequency estimation can be achieved even if we deal with only few samples, as long as the auto-correlation function is properly chosen to coincide with signal’s phase non-linearity. Additionally, by employing the sparse signal reconstruction algorithms, the ideal time-frequency representations are obtained. The presented theory is illustrated on several examples dealing with different auto-correlation functions and corresponding time-frequency distributions.