I am new to wavelets. I was reading about wavelets and Fourier transforms. So the main disadvantage of Fourier Transform is that you cannot use it on a non-uniform signal. Even though you use it you have to use a window and select your region of interest. If the window is small enough you can see the high frequency components, but not the low frequency components. But if the window is large, then you see the LF components but not the HF components. [Small window:good time resolution, bad freq res. Large window: bad time resolution, good freq resolution.] So why not use both windows on the same signal. Maybe even use a lot of windows from narrow to wide. Wouldn't this give us all the LF,HF information about the signal? In wavelets, how do you decide on a mother wavelet? If I have understood correctly, wavelet transform is similar to sampling a signal. In sampling you multiply the signal with a delta function. In WT, you multiply the signal with a mother wavelet. Instead of doing it once, you change the frequency of(expand/compress) the mother wavelet and multiply it with the signal each time. correct? This will give us several results with HF only, LF only components of the original signal. So what after this? Isn't this similar to sampling a signal(say well beyond Nyquist rate) and then decimating it in steps to get different frequency components?