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# WAVELET TRANSFORM OF A VECTOR

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.

Next: The recursion step Up: Schwab: Daubechies Wavelets Previous: INTRODUCTION
Stanford Exploration Project
11/18/1997