# How do I get started with Wavelets

Our current project requires us to do some analysis using Wavelet Transform. Can anybody suggest me a practical book, preferably with MATLAB or C examples. I am currently reading some tutorials, but it is not giving me a feeling as I have for Fourier transform. I need a book having many practical examples with source code.

• Related DSP question Commented May 29, 2013 at 19:30
• This one, as the title suggests, is really friendly. Commented Jun 6, 2013 at 16:29

If you're familiar with Fourier transforms, I think the bridge between the Fourier worlds and the wavelet worlds is the Gabor transform (a Gaussian-windowed STFT) and the complex Morlet wavelet transform. This is historically how they developed, too. They are basically the same thing, breaking down a signal into "blips" of complex sinusoids:

But the time-frequency space occupied by the blips are spaced differently:

The wavelet version has more frequency resolution at low frequencies and more time resolution at high frequencies, which is usually a good tradeoff (similar to the way the human ear works).

The Morlet is a continuous wavelet, though, so there is overlap/redundancy in the representation, a discrete version is not a minimal representation of the signal, and does not meet the "admissibility condition", which apparently means it cannot be inverted perfectly back into a signal(?), and Parseval's theorem can't be used on it. Modifying the wavelet so these things are possible results in other types of wavelets, and you can eventually work back to things like the Haar wavelet (I think).

I think "Introduction to Wavelets and Wavelet Transforms: A Primer" by Sidney Burrus (et al.) is a very good and practical book. It is very clear, has exercises, and contains some Matlab programs.

EDIT: I forgot to mention that this paper is also a very nice introduction to wavelets.

I would recommend the book "Wavelet Methods for Time Series Analysis" by Donald Percival and Andrew Walden. All concepts are clearly explained in text and with examples.

It doesn't have any source code but this can be found elsewhere i.e. the Matlab wavelet toolbox or PyWavelets.