Research On The Application Of Novel Numerical Representation Method In Modern Digital Signal Processing

With the continuous in-depth research and development of communication and information technology,cryptography,and computer architecture,VLSI has brought new demands and challenges in the area,speed,and power consumption.As one of the important research contents in the digital system,numerical representation method involves the algorithm,architecture,implementation and optimization of the digital system,which greatly affects the hardware performance in the digital system.In the traditional binary system,the long chain of carry propagation and the finite word length effect greatly limit the performance of the VLSI.In order to solve this problem,this paper makes deep research on the applications and the basic arithmetic unit design of algebraic integer quantification and residue number system in the modern digital signal processor.The purpose is to optimize the digital signal processor in the traditional binary system and improve the performance of digital systems with the novel numerical representation method.In this dissertation,algebraic integer quantization method is adopted to design the key elements of modern digital signals such as FIR(Finite Impulse Response)filter,IIR(Infinite Impulse Response)notch filter and 2-dimensional FFT(Fast Fourier Transformation).Firstly,in the design of FIR filter,algebraic integer quantization method is mainly applied to sparse the coefficients of FIR filter to reduce the number of adders in the filter.The synthesis results show that the area-delay product of the filter structure designed with the algebraic integer quantization method decreased by about 10%-20%.Secondly,based on the algebraic integer quantization method,we propose an optimal design of IIR notch filter.Under this design,the multiplier and adder in the IIR notch iteration loop are replaced by an adder to optimize the iterative boundary.The synthesis results show that its hardware performance increased by about27%.Finally,the algebraic integer quantization method is utilized to solve the problems of hardware complexity and finite word length effect in the 2-D FFT.Compared to the traditional way,the SNR of the 2-D FFT studied in this paper increased by about 3dB and the hardware performance increased by about 40%.Besides,in order to solve the overflow problem in digital signal processing,we mainly researched the scaler and multiplier design based on the Chinese remainder theorem with the modulo set{2”-1,2”,2”+1}.This paper proposes the hardware architecture design and implementation of the scalers with different scaling factors,which has optimized the calculation error in the existing scaler.The scaler architecture design and synthesis results have an important significance for the research and design of the residue number system.Based on the scaler,this paper proposes a multiplier structure under the residue number system.This structure can solve the overflow problem of the multiplier calculation,and be cut down to save the power and area of the digital system with the requirement.