【正文】 nsfer function is a polynomial in 1?z : ???? NnnznhzH0 ][)( For reduced putational plexity, the degree N of H(z) must be as small as possible. In addition, if a linear phase is desired, then the FIR filter coefficients must satisfy the constraint: ][][ Nnhnh ??? T here are several advantages in using an FIR filter, since it can be designed with exact linear phase and the filter structure is always stable with quantized filter coefficients. However, in most cases, the order NFIR of an FIR filter is considerably higher than the order NIIR of an equivalent IIR filter meeting the same magnitude specifications. In general, the implementation of the FIR filter requires approximately NFIR multiplications per output sample, whereas the IIR filter requires 2NIIR +1 multiplications per output sample. In the former case, if the FIR filter is designed with a linear phase, then the number of multiplications per output sample reduces to approximately (NFIR+1)/2. Likewise, most IIR filter designs result in transfer functions with zeros on the unit circle, and the cascade realization of an IIR filter of order IIRN with all of the zeros on the unit circle requires [(3 IIRN +3)/2] multiplications per output sample. It has been shown that for most practical filter specifications, the ratio NFIR/NIIR is typically of the order of tens or more and, as a result, the IIR filter usually is putationally more efficient[Rab75]. However ,if the group delay of the IIR filter is equalized by cascading it with an allpass equalizer, then the savings in putation may no longer be that significant [Rab75]. In many applications, the linearity of the phase response of the digital filter is not an issue,making the IIR filter preferable because of the lower putational requirements. Basic Approaches to Digital Filter Design In the case of IIR filter design, the most mon practice is to convert the digital filter specifications into analog lowpass prototype filter specifications, and then to transform it into the desired digital filter transfer function G(z). This approach has been widely used for many reasons: (a) Analog approximation techniques are highly advanced. (b) They usually yield closedform solutions. (c) Extensive tables are available for analog filter design. (d) Many applications require the digital simulation of analog filters. In the sequel, we denote an analog transfer function as )( )()( sD sPsH aaa ?, Where the subscript a specifically indicates the analog domain. The digital transfer function derived form Ha(s) is denoted by )( )()( zD zPzG ? The basic idea behind the conversion of an analog prototype transfer function Ha(s) into a digital IIR transfer function G(z) is to apply a mapping from the sdomain to the zdomain so that the essential properties of the analog frequency response are preserved. The implies that the mapping function should be such that (a) The imaginary(j? ) axis in the splane be mapped onto the circle of the zplane. (b) A stable analog transfer function