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With the rapid development of VLSI, it is essential and possible to use special chips designed for signal processing to make the mathematical transforms faster. Hardware realization structure can provide a way of realizing Mallat's algorithm. In this paper, the author employed digital filter design techniques in wavelet representation of discrete signals. The finite impulse response (FIR) and infinite impulse response (IIR) filters were used as mirror filters based on convolutions with quadrature mirror filtering. Digital filter for down-sampling is proposed and described mainly. This paper showed that the structures of FIR and IIR filters can accomplish the decomposing of a discrete approximation A2 i+1 d f into approximation at a coarser resolution A2 j d f and the detail signal D2 j f . The realization structure of hardware chips can be used to signal processing, analysis and pattern recognition.