DSP Viva

 

 Code: //Circular Shift of a sequence clc; clear all; close; //Circular time shifting property x=input('Enter the input signal'); l=input('Enter the units of shift'); nx=length(x); n1=[0:1:nx-1]; n2=pmodulo(n1-l,nx); y=x(n2+1); disp('Circularly time shifted signal==>'); disp(y); Yk=zeros(1,nx); Xk=fft(x); for j=0:nx-1 Yk(j+1)=Xk(j+1)*exp((-1*%i*2*%pi*j*l)/nx) End disp('DFT of Circularly time shifted signal using the property==>'); disp(round(Yk)); Yk1=fft(y); disp('DFT of Circularly time shifted signal is ==>'); disp((Yk1)); Code: clc; clear all; close; //Circular time reversal property x=[1 2 3 4 6 8]; disp('Input signal x(n)==>'); disp(x); Xk=fft(x); disp('DFT of x(n)==>'); disp(Xk); nx=length(x); n1=[0:1:nx-1]; n2=pmodulo(-n1,nx); y=x(n2+1); disp('Circularly time reversed signal x(-n)==>'); disp(y); //DFT of x(-n) is X(-k) N=length(x); k=n1; k1=pmodulo(-k,N); Yk=Xk(k1+1); disp('DFT of Circularly ti...

 Code: //To calculate DFT of the sequence: clear all; clc; close; x=input(" Input sequence x :- ") nl=input("length of input sequence :- ") if length(x)<nl then x=[x zeros(1,nl-length(x))] end n=0:nl-1; k=0:nl-1; //dft Xdft= x*exp(-%i*((2*%pi)/nl)* k'*n); //dft formula Xdft1=fft(x); // direct Command //Idft Xidft = (Xdft*exp(%i*((2*%pi)/nl)* k'*n))/nl; //idft formula Xidft1=ifft(X); /// direct command figure(1); //input sequence subplot(2,2,1); a=gca(); a.x_location="origin"; a.y_location="origin"; plot2d3(n,x) ylabel("x[n]"); xlabel("n"); title("Input sequence"); //DFT sequence 'Xdft' subplot(2,2,2); a=gca(); a.x_location="origin"; a.y_location="origin"; plot2d3(k,Xdft) ylabel("Y[k]"); xlabel("k"); title("DFT sequence"); //IDFT sequence 'Xidft' subplot(2,2,3); a=gca(); a.x_location="origin"; a.y_location="origin"; plot2d...

 Code: clc; clear all; close; //input sequences x=[1,2,0,3,4,1]; h=[2,0,1,3,1]; //find length of input sequences nx=length(x); nh=length(h); N=nx+nh-1; // Length of linear convolution M=max(nx,nh); // Length of circular convolution Y1=conv(x,h);//Linear convolution //Circular convolution x_len=[x,zeros(1,M-nx)]; h_len=[h,zeros(1,M-nh)]; DFT_x=fft(x_len); DFT_h=fft(h_len); DFT_xh=DFT_x.*DFT_h; circ_xh=ifft(DFT_xh); //Circular Convolution from linear convolution for i=1:M if (i<=(N-M)) then Y2 (i)=Y1(i)+Y1(i+M); else Y2(i)=Y1(i); end end //linear cnvolution from circular convolution X=[x,zeros(1,nh-1)]; H=[h,zeros(1,nx-1)]; x_dft=fft(X); h_dft=fft(H); xh_dft=x_dft.*h_dft; Y3= ifft(xh_dft); //Display various sequences on console window disp(x,"Input Sequence x"); disp(h,"Input Sequence h"); disp(Y1,"Linearly Convolved sequence using conv function"); disp(circ_xh,"Circularly Convolved sequence using fft function"); disp(Y3," Linear Convolutio...

 Code: clc; clear all; close; //linear convolution x=[1,2,3,4,5];// First Signal y=[1,2,1,2];// Second Signal y=mtlb_fliplr(y); nx=length(x); ny=length(y); N=nx+ny-1; n1=0:nx-1; n2=0:ny-1; n=0:nx+ny-2; X_lin=[x,zeros(1,ny-1)]; //append zeros to make length equal to nx+nh-1 Y_lin=[y,zeros(1,(nx-1))]; //append zeros to make length equal to nx+nh-1 // Formation of Toeplitz Matrix for i=1:N for j=1:N if (i<j) then Y2_lin(i,j)=0; else Y2_lin(i,j)=Y_lin(i-j+1); end end end rxy_lin=Y2_lin*X_lin'; // matrix multiplication to obtain linear correlation disp('The first signal x(n) is '); disp(x); disp('The second signal y(n) is '); disp(y); disp('The toeplitz matrix of y(n)to calculate linear correlation is '); disp(Y2_lin); disp('The linear correlation for x(n)and y(n) is '); disp(rxy_lin'); //Plotting of the signals figure(1); subplot(2,2,1); a=gca(); a.x_location="origin"; a.y_location="origin"; plot2d3(n1,x); a.children.children.f...

 Code: clc; clear all; close; //linear convolution x=[1,2,3,4,5]; // First Signal h=[1,2,1,2]; // Second Signal nx=length(x); nh=length(h); N=nx+nh-1; n1=0:nx-1; n2=0:nh-1; n=0:nx+nh-2; X_lin=[x,zeros(1,nh-1)]; //append zeros to make length equal to nx+nh-1 H_lin=[h,zeros(1,(nx-1))]; //append zeros to make length equal to nx+nh-1 // Formation of Toeplitz Matrix for i=1:N for j=1:N if (i<j) then X2_lin(i,j)=0; else X2_lin(i,j)=X_lin(i-j+1); end end end Y_lin=X2_lin*H_lin';// matrix multiplication to obtain linear convolution disp('The first signal x(n) is '); disp(x); disp('The second signal h(n) is '); disp(h); disp('The toeplitz matrix of x(n) to calculate linear convolution is '); disp(X2_lin); disp('The linear convolution for x(n)and h(n) is '); disp(Y_lin'); //Plotting of the signals figure(1); subplot(2,2,1); a=gca(); a.x_location="origin"; a.y_location="origin"; plot2d3(n1,x); a.children.children.foreground=5; xtitle(...