Extended Fourier for multi‐component chirp analysis: Application to bat signals.

Much progress has been made recently for improving the time‐frequency analysis. Typically, signals have frequencies that change with time. Even, in bio‐acoustic, creatures such as bats and dolphins rely on time varying signals for echolocation and target detection. With the advent of pulse compression techniques in radar and sonar technologies, the need for time‐frequency representations has become more important. The underlying basis of many of the techniques is the Fourier transform. In this paper, we present a technique, which relies on Fourier transform, exhibiting both greater resolution and conceptual simplicity. We have termed the technique Fourier extension analysis since it extends the use of Fourier analysis to signals with time varying components. Furthermore, we demonstrate how the analysis extends naturally to a time‐frequency representation using the image processing Hough transform tool without the need for windowing, as it is the case for short time Fourier transform, for example, and we a...