Spectrum enhancement using linear programming

In this paper a new approach to spectral analysis is presented. The method consists of two stages of processing. The first stage is used to reduce the variance of the noise. This stage of processing corresponds to many standard spectral estimation processes which involve averaging of one kind or another. This averaging stage is realized in this paper by using an adaptive line enhancer (ALE). The output of the ALE is a spectral estimate with reduced noise variance but a coarse frequency resolution. The second stage of processing is used to improve the frequency resolution of this coarse spectral estimate. The frequency resolution enhancement process is accomplished by a template matching method. The method uses Linear Programming to search for the best fit of functions to the coarse spectral estimate. The position and scale factors of the functions then yield the frequencies and amplitudes of the underlying sinusoids. The numerical results indicate that this second stage of processing gives a significantly better spectral estimate in terms of frequency accuracy (one tone) and resolution (two tone).