Cross-Correlation-Based Method vs. Classical Fft for Spectral Analysis of Impulse Response

Abstract

The paper presents comparison of results of impulse response spectral analysis that has been obtained using a method based on cross-correlation with results obtained using classical FFT. The presented non-Fourier method is achieved by correlating the analyzed signal and reference single-harmonic signals and using Hilbert transform to obtain an envelope of cross-correlation. The envelope of crosscorrelation makes it possible to calculate appropriate indicator and make its plot in frequency domain as a spectrum. The spectrum obtained this way has its advantage over the FFT that the spectral resolution does not depend on duration of signal. At the same time, the spectral resolution can be much greater than spectral resolution resultant from FFT. Obtained results show that presented non-Fourier method gives frequency readout more accurate in comparison to FFT when the impulse response is a short-time signal e.g. few dozen of miliseconds lasting.