Polynomial approximation: An alternative to windowing in Fourier analysis

This paper presents polynomial approximation as an alternative to classical windowing in Fourier Analysis. It is demonstrated the new method is superior for a certain class of signals and in particular when using the FFT to perform normalized phase correlation. An algebraic analysis of the new process is presented: the positional dependence of the Gibbs error associated with polynomial approximation is analyzed and demonstrated; and the covariance propagation, i.e. noise behaviour of the new method, is computed. The new method is best suited in applications where intermediate frequencies are to be estimated and it is important not to have spectral spreading of the signal.