|Institution:||University of Canterbury|
|Full text PDF:||http://hdl.handle.net/10092/12503|
Number representation can be used for representing the coeﬃcients of the digital ﬁlter as a means of reducing the multiplication size and improved the computation speed. However, when each coeﬃcient is rounded to the diﬀerent number representations, their quantization diﬀerent error is caused. This quantization round-oﬀ error of coeﬃcients can inﬂuence the magnitude of the stopband attenuation when implementing the ﬁnite impulse response(FIR) low pass ﬁlter(LPF). The number representation systems here include two’s complement number representation sys tem, canonical signed digit(CSD) number representation system and sum of power-of-two(SPT) number representation system. In this work, we analyze the round-oﬀ error of coeﬃcient of digital ﬁlter using diﬀerent number representation systems and give the probability density distribution of round-oﬀ error at various word-lengths. As the SPT number representation is also related to the Hamming weight K, the probability density distribution changes with varies the value of the K. Then implementing the FIR LPF ﬁlter with the diﬀerent number system to ﬁnd out the inﬂuence of coeﬃcients quantization on the stopband attenuation. Furthermore, a cost function is used to connect the computation size and ﬁlter performance together to ﬁnd a FIR LPF which has acceptable performance and quicker computation. This cost function is used to indicate the proper word-length and ﬁlter length for approximate FIR LPF which achieved by diﬀerent number representations systems. After comparison of 1159 of approximate FIR LPF used diﬀerent number representation, we try to ﬁnd out the suitable number representation which can make the approximate ﬁlter has better ﬁlter performance and lowest computation size.