Wavelet Transform

Abstract

In Chap. 3, we discussed the Fourier transform , which converts the stationary signal x(t) from the time domain to the frequency domain $X(\omega )$ and thus allows us to perform a frequency analysis. Thanks to this transform, we can determine the amplitudes and frequencies of the sine and cosine making up the signal x(t), but we cannot determine at what time the corresponding amplitude occurs. The STF transform used in the analysis of non-stationary signals allows us to obtain the distribution of frequency components in time, but we are faced with the problem of selecting the appropriate window width. Selection of the wrong width blurs the time –frequency data obtained as a result of applying the transform. In the wavelet transform, the problem of time–frequency resolution is solved by replacing the time window with a wavelet function.