The kepstrum method for spectral analysis

The Fourier transform of the logarithm of spectral density is a useful tool for spectral analysis of random signals which are highly resonant. This is because the logarithm compresses the large peaks of the spectrum and a resulting power series expansion (kepstrum) can be truncated at a suitable length to suppress the higher frequencies. This paper utilizes the FFT in a similar form in order to obtain spectral smoothing. Several examples show the advantages of the method including an analysis on the pitch and roll data of a container ship. It is also shown how a smooth frequency response (Bode plot) can be found to identify the signal generating process. This technique is extended to systems with signal plus noise and the identification then becomes equivalent to spectral factorization, a technique particularly useful in the determi nation of Kalman filters.