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.
1. Ahn S. J., Jeong W. B., Yoo W. S. (2005), Improvement of impulse response spectrum and its application, Journal of Sound and Vibration, 288, 1223-1239.
2. Bendat J. S., Piersol A. G. (1980), Engineering applications of correlation and spectral analysis, Wiley-Interscience, New York.
3. Cawley P., Adams R. D. (1979), Improved frequency resolution from transient tests with short record lengths, Journal of Sound and Vibration, Vol. 64, 123-132.
4. Dunne J. F. (2002), A fast time-domain integration method for computing non-stationary response histories of linear oscillators with discrete-time random forcing, Journal of Sound and Vibration, Vol. 254, 635-676.
5. Feldman M. (2011), Hilbert transform in vibration analysis, Mechanical Systems and Signal Processing, 25, 735-802.
6. Gasior M. (2006), Improving frequency resolution of discrete spectra, Ph.D. thesis, AGH University of Science and Technology, Krakow, Poland.
7. Gasior M. (2010), Improving frequency resolution of discrete spectra - Algorithms of three-node interpolation, ISBN 978-3-8383-5943-4, LAP LAMBERT Academic Publishing.
8. Gasior M., Gonzalez J. L. (2004), Improving FFT frequency measurement resolution by parabolic and gaussian interpolation, AB-Note-2004-021 BDI, CERN, Geneva, Switzerland.
9. Kotowski A. (2010), Reading the frequency of harmonics by crosscorrelation function and its envelope, Proc. 6th Int. Conf. Mechatronic Systems and Materials, 108-109.
10. Kotowski A. (2014), A new method for spectral analysis of nonstationary signals from impact tests, Journal of Vibroengineering, 16, 2171-2177.
11. Quinn B. G. (2009), Recent advances in rapid frequency estimation, Digital Signal Processing, 19, 942-948.
12. Thrane N. (1984), The Hilbert Transform, Technical Review, No. 3, Brüel&Kjær, BV 0015.
13. Thrane N., Wismer J., Konstantin-Hansen H., Gade S. (1999), Practical use of the “Hilbert transform”, Application Note, Brüel&Kjær, BO 0437.