A Wavelet Tour of Signal Processing
after the book by Stéphane Mallat.

The tutorial starts with some background of the frequency representations of signals, and proceed then to their analysis in a time/frequency representation. The performance of the windowed Fourier transform is compared to that of the wavelet transform when tracking a time varying frequency.

Multiresolution approximations are then introduced, leading to the definition of dyadic wavelet transforms. Wavelets are used to represent the amount of detail that is gained by switching from one resolution to the next finer resolution.

The dyadic wavelet transform is implemented by cascade of perfect reconstruction filter banks.

An important feature of the various wavelet transforms is their ability to analyze and manipulate the pointwise regularity of a signal.

Fourier and wavelet frames are redundant representations of signals. Their properties are similar to their non redundant counterparts, except that not all functions of two variables may be a signal transform. To recover a signal from such a function that lies outside of the image of the transform, one generally uses a least squares procedure.

The tutorial is here.