>> 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')

>> 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=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=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')

>> b=[5,2];a=[1, -0.8];>> freqz(b,a)

>> b=[5 -0.4];a=[1 0.4];>> zplane(b,a) >> freqz(b,a)

>> b=[0.15,0,-0.15]; a=[1,0,0.7];>> zplane(b,a) >> freqz(b,a)

>> 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)

>> 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=0.8;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=0.785;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=0.815;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=0.98;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)

“Clean” ECG signal

“Noisy” ECG signal