A multistage DFT-FFT-CZT approach for accurate efficient analysis of sparsely distributed spectra

The FFT is a classical approach to fast spectral analysis and measurement. However, it is not the best choice when high accuracy is desired for signals with a very sparse, unpredictable, wide spectral distribution. This paper describes a multistage algorithm designed for more efficient and very accurate calculation of the spectral components in such cases. The approach taken is to combine the advantages of three algorithms FFT CZT and DFT. The FFT is used for a coarse resolution scan of the entire frequency range. The chirp z transform (CZT) is used with an interpolation technique to find a more precise location of the frequency components. The DFT is used along with a windowing technique to ensure a very accurate computation of magnitude and phase. Accurate phase is very difficult to obtain with traditional approaches. This approach shows that depending on the number and distribution of components, and desired accuracy, the combined algorithm can reduce the computational burden by as much as a factor of ten.