Continuous wavelet transform is powerful, but the computation amount
of the continuous wavelet transform is very large. It is like to use the
continuous Fourier transform to compute the spectrum of a signal. And a
mathematical formula of wavelet is need, this is very difficult in some
conditions. For practical computing and application, the wavelet transform
can be discretized by sampling both the scale parameter s and the translation
parameter t. The discrete wavelet transform takes the form
From the viewpoint of signal processing, a wavelet
is a band-pass filter and the wavelet family
is composed of a filter bank, which separates the signal x(m) into different
frequency bands. Below is the model of the multi-frequency channel separation
of the wavelet transform in the recursive filter bank.
where the wavelet is defined and generated by a pair of digital filter
. is the low-pass filter
and is the high-pass filter.
They work together to synthesize a wavelet and to realize one scale of
wavelet transform. .
To help users to understand basic concepts and theories of discrete
wavelet transform, we design a Java program to show the procedure of discrete
(Not aviable here, it is a part of the web course "Wavelet Tutorial"