Wavelet

Context

Intuitive explanation of wavelet transform

Before trying to understand wavelets, let's see what a Fourier transform does. It decomposes a signal into it's frequency components. However, one downside of this is that the temporal information of the time-domain signal is encoded indirectly in the phase of the frequency- domain signal. It is well known that phase information in this form is difficult to interpret. Imagine that I have with me an audio signal of a song, and I want to find out what note is being played at what instant. If I use a Fourier transform, I get frequency characteristics for the entire signal. There's nothing I can directly say about any time instant. How do I get out of this problem? One solution is to break my signal into windows of fixed-sized duration, and then apply my Fourier transform there. This is called Short-time Fourier transform (STFT). I will now essentially get frequency characteristics for time intervals (rather than instants).