Interpolation Algorithms of DFT for Parameters Estimation of Sinusoidal and Damped Sinusoidal Signals

Abstract

Discrete Fourier Transform (DFT) is probably the most popular signal processing tool. Wide DFT use is partly dedicated to fast Fourier Transform (FFT) algorithms (Cooley & Tukey, 1965, Oppenheim et al., 1999, Lyons, 2004). DFT may also be efficiently computed by recursive algorithms in the window sliding by one sample (Jacobsen & Lyons, 2003, Duda, 2010). Unfortunately, DFT has two main drawbacks that deteriorate signal analysis which are (Harris, 1978, Oppenheim et al., 1999): 1) spectral leakage, and 2) sampling of the continuous spectrum of the discrete signal. Spectral leakage is reduced by proper time windows, and the frequency bins between DFT bins are computed by interpolated DFT (IpDFT) algorithms, thoroughly presented in this chapter.