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This article describes a variety of digital signal processing algorithms in the basic principles, including the Z transform, DFT transform and its fast algorithm FFT and other signal transform algorithm and including IIR and FIR digital filter design and implementation, discussed in detail by using MATLAB software, the signal transformation The principle and design of digital filters ﹑ steps and implementations, and gives MATLAB-based simulation and emulation. Article Finally, the experimental results and the results made on the further explanation and clarification. Key words: Z transform, discrete Fourier transform DFT, digital filter, system architecture simulation