A traditional frequency analysis is not appropriate for observation of properties of non-stationary signals. This stems from the fact that the time resolution is not defined in the Fourier spectrum. Thus, there is a need for methods implementing joint time-frequency analysis (t/f) algorithms. Practical aspects of some representative methods of time-frequency analysis, including Short Time Fourier Transform, Gabor Transform, Wigner-Ville Transform and Cone-Shaped Transform are described in this paper. Unfortunately, there is no correlation between the width of the time-frequency window and its frequency content in the t/f analysis. This property is not valid in the case of a wavelet transform. A wavelet is a wave-like oscillation, which forms its own “wavelet window”. Compression of the wavelet narrows the window, and vice versa. Individual wavelet functions are well localized in time and simultaneously in scale (the equivalent of frequency). The wavelet analysis owes its effectiveness to the pyramid algorithm described by Mallat, which enables fast decomposition of a signal into wavelet components.

JO - Metrology and Measurement Systems L1 - http://rhis.czasopisma.pan.pl/Content/90293/PDF/Journal10178-VolumeXXI+Issue4_12.pdf L2 - http://rhis.czasopisma.pan.pl/Content/90293 PY - 2014 IS - No 4 EP - 758 KW - frequency analysis KW - time-frequency analysis KW - Short-Time Fourier Transform KW - Gabor Transform KW - Wigner-Ville Transform KW - Cone-Shaped Transform KW - wavelet analysis KW - time-scale analysis KW - wavelet decomposition KW - filter banks KW - wavelet packets A1 - Majkowski, Andrzej A1 - KoĆodziej, Marcin A1 - Rak, Remigiusz J. PB - Polish Academy of Sciences Committee on Metrology and Scientific Instrumentation JF - Metrology and Measurement Systems DA - 2014 T1 - Joint Time-Frequency And Wavelet Analysis - An Introduction SP - 741 UR - http://rhis.czasopisma.pan.pl/dlibra/docmetadata?id=90293 DOI - 10.2478/mms-2014-0054 ER -