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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,284,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,284,*,1,Introduction,FIR filter:direct design of DT filter with the often added linear-phase requirement,(1)Windowed Fourier series approach(,10.2),(2)Frequency sampling approach(,Problem 10.31,10.32),(3)Computer-based optimization method(,10.3),Chap.10 FIR Digital Filter Design,1Introduction Chap.10 FIR Di,2,10.1 Preliminary Considerations,For FIR system:,real polynomial approximation,if a linear phase is desired,10.1.1 Basic Approaches to FIR Digital Filter Design,2 10.1 Preliminary Considerati,3,10.1.2 Estimation of the Filter Order,Kaisers Formula,For lowpass FIR filter design:P397-398,Bellangers Formula,Hermanns Formula,Parameters see P398.,310.1.2 Estimation of the Fil,4,10.2,Design of FIR Filters by Windowing(P400),10.2.1 Least Integral-Squared Error Design of FIR Filters,410.2 Design of FIR Filters b,5,10.2.2 Impulse Responses of Ideal Filters,Ideal linear phase lowpass filter,Ideal linear phase,highpass filter,510.2.2 Impulse Responses of,6,Impulse Responses of Ideal Filters(II),Ideal linear phase bandpass filter,Ideal linear phase bandstop filter,6Impulse Responses of Ideal Fi,7,Impulse Responses of Ideal Filters(III),Ideal multiband filter,Ideal discrete-time Hilbert transformer,Ideal discrete-time differentiator,7Impulse Responses of Ideal Fi,8,Gibbs phenomenon:,Oscillatory behavior,in the magnitude response of causal FIR filters designed utilizing,truncation,10.2.3 Gibbs Phenomenon,8Gibbs phenomenon:,9,mainlobe,sidelobe,Mainlobe width-,truncation,periodic continuous convolution,=N/2,10.2.3 Gibbs Phenomenon(II),9mainlobesidelobeMainlobe widt,10,-2,/(N+1),10-2/(N+1),11,10.2.3 Gibbs Phenomenon(III),1110.2.3 Gibbs Phenomenon(II,12,N,oscillate more rapidly,but the amplitudes of the largest ripples=constant,For,N,m,sidelobe,10.2.3 Gibbs Phenomenon(IV),(2)For the integral,oscillation will,occur at each sidelobe of moves past the discontinuity,(3),The methods to reduce Gibbs phenomenon:,-tapering the window smoothly to zero at each end,but,m,-a smooth transition in magnitude specifications,12 N oscillate more rapi,13,10.2.4 Fixed Window Functions,(1)Hanning window:,A,=,B,=1/2,C,=0,;,Hamming window:,A,=0.54,B,=,0.46,C,=0,Blackman window:,A,=0.42,B,=,0.5,C,=0.08,.,Rectangular window:,w,n,=,u,n,u,n,N,1,Hanning,Hamming,Blackman:,Bartlett window:triangular,1310.2.4 Fixed Window Functio,14,P406 Fig.10.6 Commonly used fixed windows,10.2.4 Fixed Window Functions(II),N/2,N,Rectangular,Hamming,Hanning,Bartlett,Blackman,n,w,n,1,14P406 Fig.10.6 Commonly u,15,10.2.4 Fixed Window Functions(III),P407 Fig.10.7,50,N,1510.2.4 Fixed Window Functio,16,10.2.4 Fixed Window Functions(IV),Parameters predicting the performance of a window,main lobe width,relative sidelobe level,(dB),Same ripples in passband,and stopband,width of transition band,1610.2.4 Fixed Window Functio,Type of window,Relative Sidelobe,Level,(dB),Main-lobe width,Minimum Stopband Attenuation,(dB),Transition,Bandwidth,Rect.,13.3,4,/(N+1),20.9,1.84,/N,Bartlett,26.5,8,/N,Hanning,31.5,8,/N,43.9,6.22,/N,Hamming,42.7,8,/N,54.5,6.64,/N,Blackman,58.1,12,/N,75.3,11.12,/N,17,10.2.4 Fixed Window Functions(V),P408 Table 10.2,Type of windowRelative Sidelob,18,10.2.4 Fixed Window Functions(VI),Example to illustrate the effect of windows N=50 P409,1810.2.4 Fixed Window Functio,19,10.2.4 Fixed Window Functions(VII),Compute impulse response of the desired,filter(according to the inverse Fourier equation),(2),Determine the suitable window by the minimum stopband attenuation and,(3),Determine the length of FIR by the transition width,(4)Obtain the designed FIR filter:,Steps for FIR filter design:,1910.2.4 Fixed Window Functio,20,Example 10.6 Page 410,Design an FIR lowpass digital filter with specifications:,the attenuation of the stopband should more than 40dB;,.,2),According to Table 10.2,we could select,Hanning,hamming,Blackman window,then,the bandwidth of the transition,band,should satisfy(,for,Hanning,),Type I:,N,=32;,Type II:,N,=33,10.2.4 Fixed Window Functions(VIII),1),i.e.,Please select a suitable window function and determine the smallest length of the window.,20Example 10.6 Page 410 Des,21,10.2.4 Fixed Window Functions,Example,Show that the ideal highpass transformer with a frequency response defined by,(1)Determine the impulse response hn,，,the relation of,and N?,(2)What type of linear-phase FIR filter?,(3)Write the impulse response hn,using the Hann windows-base method.,Solution:,2110.2.4 Fixed Window Functio,22,10.2.4 Fixed Window Functions,2210.2.4 Fixed Window Functio,23,10.2.4 Fixed Window Functions,（,2,）,If,N is even,when,the filter has linear phase,is integer,，,h,d,n is anti-symmetries,，,and hn=-hN-n,the filter is type III.,If,N is odd,isn,t integer,，,h,d,n is symmetries,，,and hn=hN-n,the filter is type II.,2310.2.4 Fixed Window Functio,24,10.2.4 Fixed Window Functions,（,3,）,2410.2.4 Fixed Window Functio,25,with,=,N/,2.,controls the side-lobe amplitudes(attenuation),cont
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