Commiting all the Matlab Codes

BW_IIR filter.m

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+%IIR BUTTERWORTH FILTER
+syms s
+kp=-2;
+ks=-10;
+wp=20;
+ws=30;
+j=sqrt(-1);
+N=log((10^(-kp/10)-1)/(10^(-ks/10)-1))/(2*log(wp/ws))
+N=round(N)+1
+wc=wp/(10^(-kp/10)-1)^(1/(2*N))
+H1=1/(s+1);
+H2=1/(s^2+1.414*s+1);
+H3=1/((s^2+s+1)*(s+1));
+H4=1/((s^2+0.765368*s+1)*(s^2+1.84776*s+1));
+H5=1/((s+1)*(s^2+0.6180*s+1)*(s^2+1.6180*s+1));
+
+if N==1
+H(s)=H1;
+elseif N==2
+H(s)=H2;
+elseif N==3
+H(s)=H3;
+elseif N==4
+H(s)=H4;
+elseif N==5
+H(s)=H5;
+end
+H(s)=H(s/wc)
+H(s)=H(j*wp)
+n=abs(H(s))
+
+m=20*log(H(s))
+%IIR BUTTERWORTH FILTER
+syms s
+kp=-2;
+ks=-10;
+wp=20;
+ws=30;
+j=sqrt(-1);
+N=log((10^(-kp/10)-1)/(10^(-ks/10)-1))/(2*log(wp/ws))
+N=round(N)+1
+wc=wp/(10^(-kp/10)-1)^(1/(2*N))
+H1=1/(s+1);
+H2=1/(s^2+1.414*s+1);
+H3=1/((s^2+s+1)*(s+1));
+H4=1/((s^2+0.765368*s+1)*(s^2+1.84776*s+1));
+H5=1/((s+1)*(s^2+0.6180*s+1)*(s^2+1.6180*s+1));
+
+if N==1
+H(s)=H1;
+elseif N==2
+H(s)=H2;
+elseif N==3
+H(s)=H3;
+elseif N==4
+H(s)=H4;
+elseif N==5
+H(s)=H5;
+end
+H(s)=H(s/wc)
+H(s)=H(j*wp)
+n=abs(H(s))
+
+m=20*log(H(s))

BW_IIR_filter.m

@@ -0,0 +1,64 @@
+%IIR BUTTERWORTH FILTER
+syms s
+kp=-2;
+ks=-10;
+wp=20;
+ws=30;
+j=sqrt(-1);
+N=log((10^(-kp/10)-1)/(10^(-ks/10)-1))/(2*log(wp/ws))
+N=round(N)+1
+wc=wp/(10^(-kp/10)-1)^(1/(2*N))
+H1=1/(s+1);
+H2=1/(s^2+1.414*s+1);
+H3=1/((s^2+s+1)*(s+1));
+H4=1/((s^2+0.765368*s+1)*(s^2+1.84776*s+1));
+H5=1/((s+1)*(s^2+0.6180*s+1)*(s^2+1.6180*s+1));
+
+if N==1
+H(s)=H1;
+elseif N==2
+H(s)=H2;
+elseif N==3
+H(s)=H3;
+elseif N==4
+H(s)=H4;
+elseif N==5
+H(s)=H5;
+end
+H(s)=H(s/wc)
+H(s)=H(j*wp)
+n=abs(H(s))
+
+m=20*log(H(s))
+%IIR BUTTERWORTH FILTER
+syms s
+kp=-2;
+ks=-10;
+wp=20;
+ws=30;
+j=sqrt(-1);
+N=log((10^(-kp/10)-1)/(10^(-ks/10)-1))/(2*log(wp/ws))
+N=round(N)+1
+wc=wp/(10^(-kp/10)-1)^(1/(2*N))
+H1=1/(s+1);
+H2=1/(s^2+1.414*s+1);
+H3=1/((s^2+s+1)*(s+1));
+H4=1/((s^2+0.765368*s+1)*(s^2+1.84776*s+1));
+H5=1/((s+1)*(s^2+0.6180*s+1)*(s^2+1.6180*s+1));
+
+if N==1
+H(s)=H1;
+elseif N==2
+H(s)=H2;
+elseif N==3
+H(s)=H3;
+elseif N==4
+H(s)=H4;
+elseif N==5
+H(s)=H5;
+end
+H(s)=H(s/wc)
+H(s)=H(j*wp)
+n=abs(H(s))
+
+m=20*log(H(s))

Chebyshev_IIR.m

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+%Chebyshev Filter
+syms s
+kp=-2;
+ks=-20;
+wp=1;
+ws=1.3;
+j=sqrt(-1);
+e=sqrt(((1/(10^(kp/20)))^2)-1);
+dp=1-(1/sqrt(1+(e^2)));
+ds=10^(ks/20);
+%discrimination factor
+d=sqrt(((1-dp)^(-2)-1)/((ds^(-2))-1));
+%selectivity factor
+k=wp/ws;
+N=(acosh(1/d))/(acosh(1/k));
+N=round(N)+1;
+%to find a and b
+
+a1=(1/2)*(((1+sqrt(1+e^2))/e)^(1/N));
+a2=(1/2)*(((1+sqrt(1+e^2))/e)^(-1/N));
+a=a1-a2;
+b=a1+a2;
+
+for k=1:1:N
+S(k+1)=(-a)*sin(((2*k)-1)*(pi/(2*N)));
+end
+
+for k=1:1:N
+w(k+1)=b*cos(((2*k)-1)*(pi/(2*N)));
+end
+for m=1:1:N
+l(m+1)=(s-(S(m)+(j*w(m))));
+end

DFT.m

@@ -0,0 +1,26 @@
+x = [1,2,3,4];
+N = length(x);
+% k = (1:N)
+X = zeros(1, N);
+j = sqrt(-1);
+disp("DFT of x(n) ")
+%DFT of x(n) 
+for k = 0:N-1
+ for n= 0:N-1
+ X(k+1) = X(k+1) + x(n+1)*(exp(-j * n * k *2 *pi / N))
+ end
+end
+ny = (1:N);
+X_mag = abs(X);
+X_phase = angle(X);
+figure("Name","DFT")
+subplot(2,1,1)
+stem(ny,X_mag,"LineWidth",3)
+xlabel("Frequency")
+ylabel("Mag")
+title("Magnitude plot")
+subplot(2,1,2)
+stem(ny, X_phase,"LineWidth",3)
+xlabel("Frequency")
+ylabel("Phase")
+title("Phase plot")

DFT2.m

@@ -0,0 +1,26 @@
+x = [1,2,3,4,5];
+N = length(x);
+% k = (1:N)
+X = zeros(1, N);
+j = sqrt(-1);
+disp("DFT of x(n) ")
+%DFT of x(n) 
+for k = 0:N-1
+ for n= 0:N-1
+ X(k+1) = X(k+1) + x(n+1)*(exp(-j * n * k *(2 *pi / N)))
+ end
+end
+ny = (1:N);
+X_mag = abs(X);
+X_phase = angle(X);
+figure("Name","DFT")
+subplot(2,1,1)
+stem(ny,X_mag,"LineWidth",3)
+xlabel("Frequency")
+ylabel("Mag")
+title("Magnitude plot")
+subplot(2,1,2)
+stem(ny, X_phase,"LineWidth",3)
+xlabel("Frequency")
+ylabel("Phase")
+title("Phase plot")

FFT.m

@@ -0,0 +1,67 @@
+syms Wnkm(k,m) Wnk(k)
+x = [1 2 3 4 5 6 7 8];
+N = length(x);
+f1 = (zeros(1,round(N/2)));
+f2 = (zeros(1,round(N/2)));
+y=1;
+%Decimating into EVEN and ODD
+for i=1:N
+ if rem(i,2)==0
+ f2(y) = x(i);
+ y=y+1;
+ else
+ f1(y) = x(i);
+end
+end
+j=sqrt(-1);
+Wnkm(k,m) = exp((-j*4*pi*k*m)/N);
+Wnk(k) = exp((-j*2*pi*k)/N);
+F1 = (zeros(1,round(N/2)));
+F2 = (zeros(1,round(N/2)));
+%F1(k)
+for k=1:(round(N/2))
+ for m=1:(round(N/2))
+ F1(k) = F1(k) + f1(m)*Wnkm(k-1,m-1);
+ end
+end
+%F2(k)
+for k=1:(round(N/2))
+ for m=1:(round(N/2))
+ F2(k) = F2(k) + f2(m)*Wnkm(k-1,m-1);
+ end
+end
+F1;
+F2;
+X1 = (zeros(1,round(N/2)));
+X2 = (zeros(1,round(N/2)));
+%X1(k) = X(k) and X2(k) = X(k+N/2)
+for k=1:(round(N/2))
+ X1(k) = F1(k) + Wnk(k-1)*F2(k);
+ X2(k) = F1(k) - Wnk(k-1)*F2(k);
+end
+X_without_fft = [X1,X2]
+%X_without_fft = 1×8 complex
+% 36.0000 + 0.0000i -4.0000 + 9.6569i -4.0000 + 4.0000i -4.0000 + 1.6569i 
+%⋯
+X_mag = abs(X_without_fft);
+X_phase = angle(X_without_fft);
+f = 1:N;
+figure("Name","FFT")
+subplot(3,1,1)
+stem(f,x,"filled","LineWidth",3)
+title("Input sequence")
+ylabel("x(n)")
+xlabel("N")
+grid
+subplot(3,1,2)
+stem(f,X_mag,"filled","LineWidth",3)
+title("Magnitude spectrum")
+ylabel("Magnitude")
+xlabel("Frequency")
+grid
+subplot(3,1,3)
+stem(f,X_phase,"filled","LineWidth",3)
+title("Phase spectrum")
+ylabel("Phase")
+xlabel("Frequency")
+grid

FIR.m

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+N=7;
+wc=1;
+alpha=(N-1)/2;
+n=0:1:N-1;
+%Desired impulse response
+for i=0:1:(N-1)
+ if(i~=alpha)
+ hd(i+1)=(sin(wc*(i-3))/(pi*(i-3)));
+ else
+ hd(i+1)=wc/pi;
+ end
+end
+subplot(5,1,1);
+stem(n,hd);
+xlabel('n');
+ylabel('hd(n)');
+title('Desired impulse response');
+wHm = zeros(1,7);
+%Hamming window
+for j=0: 6
+ wHm(j+1)=0.54-(0.46*cos(2*pi*j/(N-1)));
+end
+subplot(5,1,2);
+stem(n,wHm);
+xlabel('n');
+ylabel('whm(n)');
+title('Hamming window');
+%Impulse response
+hn=hd.*wHm;
+subplot(5,1,3);
+stem(n,hn);
+xlabel('n');
+ylabel('h(n)');
+title('Impulse response');
+hw=[];
+for w=0:(1/pi):pi
+ t=0;
+ temp=0;
+ const=hn(alpha+1);
+ for m=0:1:((N-3)/2)
+ temp=temp+(2.*hn(m+1).*cos(w.*(alpha-m)));
+ end
+ temp=temp+const;
+ hw=[hw, temp];
+end
+w=0:1/pi:pi;
+%Magnitude response
+subplot(5,1,4);
+stem(w,hw);
+xlabel('w');
+ylabel('|H(w)|');
+title('Magnitude response');
+phase=-w*alpha;
+subplot(5,1,5);
+stem(w,phase);
+xlabel('w');
+ylabel('Phase');
+title('Phase response');

FIR1.m

@@ -0,0 +1,49 @@
+wc=1;
+N=51;
+alpha=(N-1)/2;
+n=0:1:N-1;
+%Rectangular window
+for j=0:1:(N-1)
+ wR(j+1)=1;
+end
+subplot(5,1,1);
+stem(n,wR);
+xlabel('n');
+ylabel('wR(n)');
+title('Rectangular window');
+%Bartlett window
+for j=0:1:(N-1)
+ wBr(j+1)=1-(2.*abs(j-((N-1)/2)))/(N-1);
+end;
+subplot(5,1,2);
+stem(n,wBr);
+xlabel('n');
+ylabel('wBr(n)');
+title('Bartlett window');
+%Hamming window
+for j=0:1:(N-1)
+ wHm(j+1)=0.54-(0.46*cos(2*pi*j/(N-1)));
+end;
+subplot(5,1,3);
+stem(n,wHm);
+xlabel('n');
+ylabel('whm(n)');
+title('Hamming window');
+%Hanning window
+for j=0:1:(N-1)
+ wHn(j+1)=0.5-(0.5*cos(2*pi*j/(N-1)));
+end;
+subplot(5,1,4);
+stem(n,wHn);
+xlabel('n');
+ylabel('whn(n)');
+title('Hanning window');
+%Blackmann window
+for j=0:1:(N-1)
+ wBl(j+1)=0.42-(0.5*(cos(2*pi*j/(N-1))))+(0.08*(cos(4*pi*j/(N-1))));
+end;
+subplot(5,1,5);
+stem(n,wBl);
+xlabel('n');
+ylabel('wbl(n)');
+title('Blackmann window');