The fast fourier transform for experimentalists part III: Classical spectral analysis

The concepts with a general approach to computing spectrum estimation problems, by the use of fast Fourier transform (FFT), are discussed. FFt is used in almost all the spectrum estimator programs in their calculations, but these programs can differ in their assumption about the missing data outside the observation window. These assumptions show profound effects on the spectral estimates. The Continuous Fourier transform (CFT) and the frequency spectrum on a danser frequency mesh can be approximated by appending zeros to the time series. Frequecncy spectrum estimation is a classical undetermined problem because it requires the estimation of spectrum at an infinite number of frequencies using only a finite amount of data. That is why, many researchers have concentrated on autoregressive spectral estimates, which give better resolution because they make better assumptions about the window of observation.