Estimation of FM modulation of multi-component signals from the Fourier phase

The spectral phase is a quantity which is normally discarded in analyzing signals. The concept of a complex time-frequency representation is presented in which the rows are narrow bandpass filters and the columns are broadband Fourier spectra. Methods are developed which exploit the spectral phase of the surface to recover the FM modulating function of an FM modulated tone and an FM modulated multi-component harmonic signal.