It has been by far the most important signal processing tool for many (and I mean many many) years.It is a necessary background to understand how WT works.However, I would like to mention a couple important points again for two reasons: It is too wide of a subject to discuss in this tutorial.I will not go into the details of FT for two reasons: This, obviously tells us that we can not use the FT for non-stationary signals.īut why does this happen? In other words, how come both of the signals have the same FT? HOW DOES FOURIER TRANSFORM WORK ANYWAY?Īn Important Milestone in Signal Processing: Although the two signals are completely different, their (magnitude of) FT are the SAME !. The FT of both of the signals would be the same, as shown in the example in part 1 of this tutorial. Say one of the signals have four frequency components at all times, and the other have the same four frequency components at different times. Also suppose that they both have the same spectral components, with one major difference. For a quick recall, let me give the following example. I have written that Fourier Transform (FT) is not suitable for non-stationary signals, and I have shown examples of it to make it more clear.
We basically need Wavelet Transform (WT) to analyze non-stationary signals, i.e., whose frequency response varies in time. Let's have a short review of the first part. Fundamentals: the fourier Transform and The Short Term Fourier Transform
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