An adaptive technique for high resolution time-varying spectral estimation

An adaptive technique which determines the spectral coefficients of a time-varying signal is presented. The algorithm performs a least-squares decomposition of the signal onto a high-resolution nonharmonic Fourier basis. The spectral estimate is updated sample by sample and produces a decomposition with very good localization in both the time and frequency domains. This yields a distribution of signal intensities in the time-frequency plane which tracks the instantaneous frequency and local bandwidth of the signal. The detection of tones spaced closer than expected by the uncertainty distance (super-resolution) is shown by computer simulation. Numerical results demonstrate the super-resolving capability and fast tracking rate as well as the stability in the presence of additive noise. Potential applications of this method include tracking of frequency hopping communications, FM demodulation, and formant tracking in speech signals