The Fourier transform and spectral analysis

Abstract

This chapter develops the mathematical relationship behind the discrete Fourier transform (DFT) operation and highlights the limitations of the finite data record on the DFT performance analysis. This is then developed into the classical and modern techniques which are widely used for estimation of the power spectrum from signal sample data records. The power spectral density of a signal was defined previously in section 7.3 via the autocorrelation sequence. Here we extend this to the case of a discretely sampled sequence, x(n) which, in most practical situations, is restricted to a finite and limited number of signal samples.