Vlsi Based On The Rns Fft And Matrix Inversion

Nowadays, with the development of the modern communications, signal processing, multimedia, and internet technologies, the requirements for the Very Large Scale Integrated (VLSI) circuits'implementation of Digital Signal Processing (DSP) devices, like FFT, DCT, Matrix Inversion (MI), and so forth, are increasing. However, over the last few decades, the high performance of VLSI circuits is mainly achieved by high integratioin. Attributing to the advanced process technologies, such as shrinking of feature sizes, increasing die sizes and interconnect density, scaling of supply voltage, faster clock rates, there are two issues, high-speed and low power dissipation, to be addressed for the VLSI design in the future. While large scale parallel processing technology is one of the most effective methods.Residue Number System (RNS) is a non-weighted number system with the parallelism and independency properties. In RNS, several parallel and independent operations with small wordlength are used to replace one single operation with large wordlength in Two's Complementary System (TCS). Thus, high-speed and low power comsumption could be achieved, making a better performance for each processing element. Hence, the huge potential applications for RNS based DSP systems are worth of exploring in this realm. However, the issues, such as scaling, sign detection, and so on, are not well solved yet, which restrict the applications of RNS.In order to explore the merits and defects of RNS, we take the RNS based VLSI implementations for FFT and MI as examples. Firstly, we give out some background metarials for RNS, and then describe the algorithms and structures for FFT and MI implementations. And this may provide some novel methods and technology preparations for VLSI design of DSP chips. Next, we describe the implementation methods and procedures for RNS based FFT and MI in detail, respectively. Moreover, combined with the existing researches, we summarize the problems which may be encountered, and analyze the possible reasons. Eventually, we make a futher classification for these problems, the math issue and engineering issue.