Time-frequency representations based on compressive samples

A recent rise of compressive sensing (CS) algorithms has prompted many questions about the analysis of such sensed signals. Specifically, calculating a time-frequency representation (TFR) of these signals is an open question. In this paper, we propose an approach for calculating TFRs of compressed sensed signals based on recently proposed CS algorithm using modulated discrete prolate spheroidal sequences (MDPSS). The results of our numerical analysis show that a visually reliable TFR of compressed sensed signals can be obtained using the proposed approach. Furthermore, these compressed sensed signals can also be used for accurate estimation of signal parameters such as the instantaneous frequency.