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>> n=-50:50; wc=0.4*pi; >> hn=sinc(n*wc/pi)*wc/pi; >> stem(n,hn); title('Ideal LPF with cutoff frequency = 0.4 \pi')
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>> w=linspace(0,pi,512); mag_hw=cos(w/2); >> [h,w1]=freqz([0.5 0.5],[1]); >> subplot(2,1,1); plot(w/pi,mag_hw);title('|H(\omega)|of first order FIR LPF:analytical solution') >> subplot(2,1,2); plot(w1/pi,abs(h));title('|H(\omega)|of first order FIR LPF:FREQZ')
![>> w=linspace(0,pi,512); mag_hw=cos(w/2); >> [h,w1]=freqz([ ],[1]); >> subplot(2,1,1); plot(w/pi,mag_hw);title( |H(\omega)|of first order FIR LPF:analytical solution ) >> subplot(2,1,2); plot(w1/pi,abs(h));title( |H(\omega)|of first order FIR LPF:FREQZ )](http://images.slideplayer.com/12/3396272/slides/slide_2.jpg ">> w=linspace(0,pi,512); mag_hw=cos(w/2); >> [h,w1]=freqz([ ],[1]); >> subplot(2,1,1); plot(w/pi,mag_hw);title( |H(\omega)|of first order FIR LPF:analytical solution ) >> subplot(2,1,2); plot(w1/pi,abs(h));title( |H(\omega)|of first order FIR LPF:FREQZ )")
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>> w=linspace(0,pi,512); mag_hw=sin(w/2); >> [h,w1]=freqz([0.5 -0.5],[1]); >> subplot(2,1,1); plot(w/pi,mag_hw);title('|H(\omega)|of first order FIR HPF:analytical solution') >> subplot(2,1,2); plot(w1/pi,abs(h));title('|H(\omega)|of first order FIR HPF:FREQZ')
![>> w=linspace(0,pi,512); mag_hw=sin(w/2); >> [h,w1]=freqz([ ],[1]); >> subplot(2,1,1); plot(w/pi,mag_hw);title( |H(\omega)|of first order FIR HPF:analytical solution ) >> subplot(2,1,2); plot(w1/pi,abs(h));title( |H(\omega)|of first order FIR HPF:FREQZ )](http://images.slideplayer.com/12/3396272/slides/slide_3.jpg ">> w=linspace(0,pi,512); mag_hw=sin(w/2); >> [h,w1]=freqz([ ],[1]); >> subplot(2,1,1); plot(w/pi,mag_hw);title( |H(\omega)|of first order FIR HPF:analytical solution ) >> subplot(2,1,2); plot(w1/pi,abs(h));title( |H(\omega)|of first order FIR HPF:FREQZ )")
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>> w=linspace(0,pi,512); mag_hw=abs(sinc(w*(M+1)/2/pi)./sinc(w/2/pi)); >> b=ones(1,M+1)/(M+1);a=[1]; >> [h,w1]=freqz(b,a); >> subplot(2,1,1); plot(w/pi,mag_hw);title('|H(\omega)|of moving average filter (M=10):analytical solution') >> subplot(2,1,2); plot(w1/pi,abs(h));title('|H(\omega)|of moving average filter (M=10):FREQZ')
![>> w=linspace(0,pi,512); mag_hw=abs(sinc(w*(M+1)/2/pi)./sinc(w/2/pi)); >> b=ones(1,M+1)/(M+1);a=[1]; >> [h,w1]=freqz(b,a); >> subplot(2,1,1); plot(w/pi,mag_hw);title( |H(\omega)|of moving average filter (M=10):analytical solution ) >> subplot(2,1,2); plot(w1/pi,abs(h));title( |H(\omega)|of moving average filter (M=10):FREQZ )](http://images.slideplayer.com/12/3396272/slides/slide_4.jpg ">> w=linspace(0,pi,512); mag_hw=abs(sinc(w*(M+1)/2/pi)./sinc(w/2/pi)); >> b=ones(1,M+1)/(M+1);a=[1]; >> [h,w1]=freqz(b,a); >> subplot(2,1,1); plot(w/pi,mag_hw);title( |H(\omega)|of moving average filter (M=10):analytical solution ) >> subplot(2,1,2); plot(w1/pi,abs(h));title( |H(\omega)|of moving average filter (M=10):FREQZ )")
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>> b=[5,2];a=[1, -0.8]; >> freqz(b,a)
![>> b=[5,2];a=[1, -0.8]; >> freqz(b,a)](http://images.slideplayer.com/12/3396272/slides/slide_8.jpg ">> b=[5,2];a=[1, -0.8]; >> freqz(b,a)")
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>> b=[5 -0.4];a=[1 0.4]; >> zplane(b,a) >> freqz(b,a)
![>> b=[5 -0.4];a=[1 0.4]; >> zplane(b,a) >> freqz(b,a)](http://images.slideplayer.com/12/3396272/slides/slide_9.jpg ">> b=[5 -0.4];a=[1 0.4]; >> zplane(b,a) >> freqz(b,a)")
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>> b=[0.15,0,-0.15]; a=[1,0,0.7]; >> zplane(b,a) >> freqz(b,a)
![>> b=[0.15,0,-0.15]; a=[1,0,0.7]; >> zplane(b,a) >> freqz(b,a)](http://images.slideplayer.com/12/3396272/slides/slide_10.jpg ">> b=[0.15,0,-0.15]; a=[1,0,0.7]; >> zplane(b,a) >> freqz(b,a)")
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>> b=poly([0.9*exp(j*pi/2) 0.9*exp(-j*pi/2)]) b = 1.0000 -0.0000 0.8100 >> a=poly([0.8 -0.8]) a = 1.0000 0 -0.6400 >> zplane(b,a) >> freqz(b,a)
![>> b=poly([0.9*exp(j*pi/2) 0.9*exp(-j*pi/2)]) b = >> a=poly([ ]) a = >> zplane(b,a) >> freqz(b,a)](http://images.slideplayer.com/12/3396272/slides/slide_11.jpg ">> b=poly([0.9*exp(j*pi/2) 0.9*exp(-j*pi/2)]) b = >> a=poly([ ]) a = >> zplane(b,a) >> freqz(b,a)")
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>> R=0.9;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> G=(1-R)*sqrt(1-2*R*cos(2*w0)+R^2); >> b=[G]; a=[1 a1 a2]; >>zplane(b,a) >> freqz(b,a)
![>> R=0.9;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> G=(1-R)*sqrt(1-2*R*cos(2*w0)+R^2); >> b=[G]; a=[1 a1 a2]; >>zplane(b,a) >> freqz(b,a)](http://images.slideplayer.com/12/3396272/slides/slide_12.jpg ">> R=0.9;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> G=(1-R)*sqrt(1-2*R*cos(2*w0)+R^2); >> b=[G]; a=[1 a1 a2]; >>zplane(b,a) >> freqz(b,a)")
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>> R=0.8;r=0.7;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)
![>> R=0.8;r=0.7;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)](http://images.slideplayer.com/12/3396272/slides/slide_13.jpg ">> R=0.8;r=0.7;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)")
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>> R=0.8;r=0.785;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)
![>> R=0.8;r=0.785;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)](http://images.slideplayer.com/12/3396272/slides/slide_14.jpg ">> R=0.8;r=0.785;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)")
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>> R=0.8;r=0.815;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)
![>> R=0.8;r=0.815;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)](http://images.slideplayer.com/12/3396272/slides/slide_15.jpg ">> R=0.8;r=0.815;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)")
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>> R=0.98;r=1;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)
![>> R=0.98;r=1;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)](http://images.slideplayer.com/12/3396272/slides/slide_16.jpg ">> R=0.98;r=1;w0=pi/3; >> a1=-2*R*cos(w0);a2=R^2; >> b1=-2*r*cos(w0);b2=r^2; >> b=[1 b1 b2];a=[1 a1 a2]; >> zplane(b,a) >> freqz(b,a)")
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“Noisy” ECG signal
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