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

              j=1,2,¡­¡­.,N (6)

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 wavelet transform.
(Not aviable here, it is a part of the web course "Wavelet Tutorial" )
Discrete Wavelet Transform By Mallat. Algorithm