外文翻譯---fir濾波器設(shè)計(jì)技術(shù)

1、外文原文 外文原文FIR Filter Design TechniquesAbstractThis 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 wit

2、h their merits and demerits. Different optimization 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 fr

3、equency sampling technique at the non-sampled 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 f

4、unction of a polynomial in z and 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(1)FIR filte

5、rs 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 essentially co

6、nsists 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 or ideal response

7、 is chosen, usually in the frequency domain. (ii) An allowed class of filters is chosen (e.g.the length N for a FIR filters). (6)Thus the convolution of Hd(w) with W(w) yields the frequency response of the truncated FIR

8、filter (7)The frequency response can also be obtained using the following relation (8)But direct truncation of hd(n) to M terms to obtain h(n) leads to the Gibbs phenomenon effect which manifests itself as a fixed percen

9、tage overshoot and ripple before and after an approximated discontinuity in the frequency response due to the non-uniform convergence of the fourier series at a discontinuity.Thus the frequency response obtained by using

10、 (8) contains ripples in the frequency domain. 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 towa

11、rd zero gradually, instead of abruptly as it 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

12、 effect of smoothing Hd(w). The several 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)

13、 become transition bands between 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).

14、(iii) Since the 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 mainl