A method for instantaneous frequency tracking of multiple narrowband signals

An adaptive technique to compute the Fourier coefficients of time-varying signals is presented. The algorithm is based on a decomposition of the signal onto a set of sinusoids which are not constrained to be linearly independent. The Kaczmarz Row Action Projection algorithm is used to solve the decomposition as a constrained least squares problem. An adaptive strategy is used to partition the frequency spectrum into isolated narrowband regions. The algorithm updates the spectral estimates of the resulting frequency bands on a sample by sample basis in the time domain. The new technique produces a signal decomposition with very good localization in both time and frequency domains. The detection of tones spaced closer than that expected by the uncertainty principle is demonstrated. The performance of the method for fast frequency tracking of multiple tones is also presented. The instantaneous frequency tracking capability of the new algorithm is shown by computer simulation to offer certain advantages over that of the analytic signal and the Wigner distribution methods. Computational complexity issues of the new method are also discussed.