Wavelet

Context

Intuitive explanation of wavelet transform

Before trying to understand wavelets, consider what a Fourier transform does. It decomposes a signal into its frequency components. A big downside 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 to 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). With this you essentially get frequency characteristics for time intervals (rather than instants).