DWT is a time-frequency analysis tool for which the wavelets are discretely sampled. DWT is different from the Fourier transform, which provides frequency information on the whole time domain. A key advantage of DWT is that it provides frequency information at different time points.
Mallat's algorithm can be described as a series of iterative steps. For example, for a 3-level wavelet transform:
- Use S(n) as the original time domain sequence as the input of level 1.
- Convolve the input sequence with high-pass filter h(n) and low-pass filter g(n).
The two generated sequences are the detail coefficients D k and the approximation coefficients A k in level k.
- If current level k is the maximum transform level n, stop; otherwise, use A k as the input sequence for the next level (that is, increment k by 1 and go to step 2.)