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# He ohio s ate t university slide 12 fir design example

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Unformatted text preview: 0.2 0.22 −50 0.295 0.3 T.H.E OHIO S ATE T UNIVERSITY Slide # 11 FIR Design Example 2 Speciﬁcations:   ECE 600 FIR Design   !  ¥  ¡ £ ¥  Linear phase samples per second rad/sec -3 dB cutoff at 50 dB attenuation, or more, past rad/sec T.H.E OHIO S ATE T UNIVERSITY Slide # 12 FIR Design Example 2, continued Filter order Impulse response    ¥  §  ¨ ¦   !  §   ¥ § § ¥ Cutoff at midpoint of transition band (by symmetry):   ¨ T.H.E OHIO S ATE T UNIVERSITY Slide # 13 !  ¨  ECE 600 FIR Design else ¨ ¨   ¢ ¢  ! ¦ § " !  § ¨    ¤  ¦ ¥  ¤ ¢ £¡ ¤    § ¡ ¢¡ ¨  ! ¡   ¤   ¦  ¦§  © ¢ ¤ ¥£ Shifted and windowed IDTFT: FIR Design Example 2, continued and reducing ¥  Inspect frequency response and iterate, altering >> h=fir1(28,0.335,hamming(29)); %...or >> n=[-14:14];h=(sin(0.335*pi*n))./(pi*n);h(15)=0.335; % >> h=h.*hamming(29)'; >> [H,omega]=freqz(h,1,1024); >> subplot(2,1,1);plot(omega/pi,20*log10(abs(H)));grid;axis([0 1 -70 10]) >> subplot(2,2,3);plot(omega/pi,20*log10(abs(H)));grid >> hold on; plot([0 0.3],-3*[1 1],'r');hold off;axis([0.25 0.33 -5 1]); >> subplot(2,2,4);plot(omega/pi,20*log10(abs(H)));grid >> hold on; plot([0.46 0.5],-50*[1 1],'r');hold off;axis([0.4 0.5 -60 -30]); 10 0 −10 −20 −30 −40 −50 −60 −70 0 0.1 0.2 0.3 0.4 0.5 0.6 1 −45 −3 −50 −4 −55 −5 ECE 600 FIR Design 1 −40 −2 0.9 −35 −1 0.8 −30 0 0.7 0.26 0.28 0.3 0.32 −60 0.4 0.42 0.44 0.46 0.48 0.5 T.H.E OHIO S ATE T UNIVERSITY Slide # 14 Minimize mainlobe width such that energy in sidelobes does not exceed a given percentage of total (and approximate prolate spheriodal with Bessel functions) Family of windows described by a zeroth order modiﬁed Bessel function Parameter tolerance allows trade-off between transition bandwidth and approximation ¨ ¦¡ ¦  ¦ § ¤ ¨ #  §     ¦ §   ¨   ¥ ...
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