外文翻譯---fir濾波器設(shè)計技術(shù)（英文）

1、 1M.Tech. credit seminar report,Electronic Systems Group, EE Dept, IIT Bombay, submitted November2002 FIR Filter Design Techniques Arojit Roychowdhury (Roll No: 02307424) Supervisor: Prof P.C. Pandey Abstract Thi

2、s report deals with some of the techniques used to design FIR filters. In the beginning, the windowing method and the frequency sampling methods are discussed in detail with their merits and demerits. Different optimiz

3、ation techniques involved in FIR filter design are also covered, including Rabiner’s method for FIR filter design. These optimization techniques reduce the error caused by frequency sampling technique at the non-sample

4、d frequency points. A brief discussion of some techniques used by filter design packages like Matlab are also included. Introduction FIR filters are filters having a transfer function of a polynomial in z- and

5、is an all-zero filter in the sense that the zeroes in the z-plane determine the frequency response magnitude characteristic. The z transform of a N-point FIR filter is given by H(z) = n Nn z n h 10 ) ((1) FIR fil

6、ters are particularly useful for applications where exact linear phase response is required. The FIR filter is generally implemented in a non-recursive way which guarantees a stable filter. FIR filter design essential

7、ly consists of two parts (i) approximation problem (ii) realization problem The approximation stage takes the specification and gives a transfer function through four steps. They are as follows: (i) A desired

8、or ideal response is chosen, usually in the frequency domain. (ii) An allowed class of filters is chosen (e.g. the length N for a FIR filters). (iii) A measure of the quality of approximation is chosen. (iv) A method

9、or algorithm is selected to find the best filter transfer function. The realization part deals with choosing the structure to implement the transfer function which may be in the form of circuit diagram or in the form o

10、f a program. There are essentially three well-known methods for FIR filter design namely: (1) The window method (2) The frequency sampling technique (3) Optimal filter design methods 3ripples in the frequency domain.

11、 In order to reduce the ripples, instead of multiplying hd(n) with a rectangular window w(n), hd(n) is multiplied with a window function that contains a taper and decays toward zero gradually, instead of abruptly as i

12、t occurs in a rectangular window. As multiplication of sequences hd(n) and w(n) in time domain is equivalent to convolution of Hd(w) and W(w) in the frequency domain, it has the effect of smoothing Hd(w). The se

13、veral effects of windowing the Fourier coefficients of the filter on the result of the frequency response of the filter are as follows: (i) A major effect is that discontinuities in H(w) become transition bands be

14、tween values on either side of the discontinuity. (ii) The width of the transition bands depends on the width of the main lobe of the frequency response of the window function, w(n) i.e. W(w). (iii) Since t

15、he filter frequency response is obtained via a convolution relation , it is clear that the resulting filters are never optimal in any sense. (iv) As M (the length of the window function) increases, the mainlobe width of

16、 W(w) is reduced which reduces the width of the transition band, but this also introduces more ripple in the frequency response. (v) The window function eliminates the ringing effects at the bandedge and does result in

17、 lower sidelobes at the expense of an increase in the width of the transition band of the filter. Some of the windows [Park87] commonly used are as follows: 1. Bartlett triangular window: W(n) = 1) 1 ( 2Nnn = 0,1,2,…

18、….,(N-1)/2 (9) = 2 - 1) 1 ( 2Nnn = (N-1)/2,……,N-1 = 0 , otherwise - 2-5. Generalized cosine windows (Rectangular, Hanning, Hamming and

19、 Blackman) W(n) = a – bcos(2p(n+1)/(N+1)) + c cos(4p(n+1)/(N+1)) n= 0,1….N-1 (10) = 0 otherwise 6. Kaiser window

20、 with parameter ß :) () )) 1 /( ) 1 ( 2 ( 1 ( 2 ) (oo IN n I n Wn= 0,1,….,N-1 (11) = 0 otherwise The general cosine