In many respects, the discrete wavelet transform
(DWT) is analogous to the fast Fourier transformation (FFT).
It is a fast linear operation which transforms
a one-dimensional input vector *B* of lenght *N* into a one-dimensional
output vector of the same length.
As with FFT, each of the *N* elements of the output vector
represents the scale of a certain base function.
In the case of FFT, these base functions are sine and cosine functions
of various frequencies. The base functions of the wavelet transform are
wavelets of different scale and location as seen in Figure 3.

The DWT is conveniently formulated as a recursion. Each recursion comprises
a filtering by matrix multiplication and a vector permutation.
The next section describes
this recursion by examining the case of the
4-point Daubechies wavelet exemplarily.

- The recursion step
- The butterfly
- The lowpass filter coefficients
- Wavelets of different orders
- READING VECTORS OF WAVELET COEFFICIENTS
- Reading vectors of wavelet coefficients

11/18/1997