Advanced Digital Signal Processing

What is Fourier Transform : Fourier Transform is a incredible method of finding the frequencies present in a signal. When we apply fourier transform we get a impulse at that particular sinusoidal frequency present in the incoming signal. Suppose that the signal is generated using three frequencies fm1 , fm2 and fm3. Now when we observe the fourier transform of this signal we can see three impulses at fm1 , fm2 and fm3. So in this program we are going to generate a random signal and note down the frequencies present in that signal. The after applying fourier transform we can check whether we have impulses at that frequencies or not. Algorithm : Step 1 : We are going to generate a random signal. Step 2 : Apply fourier transform to that signal. Step 3 : Verify. Program Code :  clc clear all close all fs=input('Enter the sampling frequency'); t=0:1/fs:1; X=sin(2*pi*0*t); n=input('Enter the number of frequencies'); frequencies=[]; for i=1:n  ...

dftidft3 clc clear all close all X=input( 'Enter the Input Sequence' ); N=input( 'Enter the value of N such taht N-point DFT is to be calculated' ); %Inputs are taken% n=0:1:N-1; k=0:1:N-1; nk=n'*k; %n transpose * k gives us a N*N matrix% W=exp(-(j*2*pi)/N); % Twiddle Factor % Wnk=W.^nk; % Twiddle Factor matrix is generated % Y= Wnk*X' ; % Twiddle factor matrix multiplied by X transpose% %Reason behing going to Transopose of the input matrix is : when we enter a matrix sequence we usually use ROW Matrix, in order to convert ROW to COLUMN we are using Transpose% L=length(Y); n=0:1:L-1; figure,plot(n,abs(Y)),title( 'Magnitude Response of DFT' ) figure, plot(n, angle(Y)), title( 'Phase Response of DFT' ) %MAGNITUDE and PHASERESPONSE OF DFT SIGNAL IS PLOTTED% W=exp((j*2*pi)/N); % Twiddle Factor % Wnk=(W.^nk)/N; % Twiddle Factor matrix is generated % Yinv= Wnk*Y ; % Twiddle factor matrix multiplied by Y% L=length...

dftidft1 clc clear all close all X=input( 'Enter the Input Sequence' ); N=input( 'Enter the Value of N such that N-point DFT is to be Calculated' ); % INPUTS ARE GIVEN % Y= fft(X,N) %DFT IS CALCULATED% L=length(Y); n=0:1:L-1; figure,plot(n,abs(Y)),title( 'Magnitude Response of DFT' ) figure, plot(n, angle(Y)), title( 'Phase Response of DFT' ) %MAGNITUDE and PHASERESPONSE OF DFT SIGNAL IS PLOTTED% Yinv=ifft(Y,N) %IDFT IS CALCULATED% figure,plot(n,abs(Yinv)),title( 'Magnitude Response of IDFT' ) figure, plot(n, angle(Yinv)), title( 'Phase Response of IDFT' ) %MAGNITUDE and PHASERESPONSE OF ORIGINAL SIGNAL IS PLOTTED% Error using input Cannot call INPUT from EVALC. Error in dftidft1 (line 5) X=input('Enter the Input Sequence'); Published with MATLAB® R2013b

dftidft2 clc clear all close all X=input( 'Enter the Input Sequence' ); N=input( 'Enter the N value such that N-point DFT is calculated' ); %Inputs are given% L=length(X); if N>L X=[X zeros(1,N-L)]; else X=X(1:N); end %Adjusting the Length of the input Sequence by appending Zeros or truncating the sequence% for k=1:N key=0; for n=1:N key=key+X(n)*exp(-(j*2*pi*(k-1)*(n-1))/N); end Y(k)=key; end %DFT is calculated% Y %DFT is printed% L=length(Y); n=0:1:L-1; figure,plot(n,abs(Y)),title( 'Magnitude Response of DFT' ) figure, plot(n, angle(Y)), title( 'Phase Response of DFT' ) %MAGNITUDE and PHASERESPONSE OF DFT SIGNAL IS PLOTTED% for k=1:N key=0; for n=1:N key=key+Y(n)*exp((j*2*pi*(k-1)*(n-1))/N); end Yinv(k)=key/N; end %IDFT is calculated% Yinv L=length(Y); n=0:1:L-1; figure,plot(n,abs(Yinv)),title( 'Magnitude Response of IDFT' ) figure, plot(n, ang...

The program code is : clc clear all close all X1=input('ENTER THE SEQUENCE 1 >'); i1=input('ENTER THE STARTING INDEX OF THE SEQUENCE 1 >'); X2=input('ENTER THE SEQUENCE 2 >'); i2=input('ENTER THE STARTING INDEX OF THE SEQUENCE 2 >'); m1=length(X1); m2=length(X2); if(m1>m2)     Y=cconv(X1,X2,m1)     n3=(i1+i2):(i1+i2+m1-1); else     Y=cconv(X1,X2,m2)     n3=(i1+i2):(i1+i2+m2-1); end Yref=conv(X1,X2) n1=i1:i1+m1-1; n2=i2:i2+m2-1; n4=(i1+i2):(length(Yref)-1+i1+i2); subplot(4,1,1) stem(n1,X1,'r') xlabel('n'); ylabel('Amplitude'); title('Sequence 1'); subplot(4,1,2) stem(n2,X2,'g') xlabel('n'); ylabel('Amplitude'); title('Sequence 2'); subplot(4,1,3) stem(n3,Y,'c') xlabel('n'); ylabel('Amplitude'); title('Circular Convolution of the Above two sequences'); subplo...

The program code is : clc clear all close all X1=input('ENTER THE SEQUENCE 1 >'); i1=input('ENTER THE STARTING INDEX OF THE SEQUENCE 1 >'); X2=input('ENTER THE SEQUENCE 2 >'); i2=input('ENTER THE STARTING INDEX OF THE SEQUENCE 2 >'); m1=length(X1); m2=length(X2); Y=conv(X1,X2) n1=i1:i1+m1-1; n2=i2:i2+m2-1; n3=(i1+i2):(i1+i2+length(Y)-1); subplot(3,1,1) stem(n1,X1,'r') xlabel('n'); ylabel('Amplitude'); title('Sequence 1'); subplot(3,1,2) stem(n2,X2,'g') xlabel('n'); ylabel('Amplitude'); title('Sequence 2'); subplot(3,1,3) stem(n3,Y,'c') xlabel('n'); ylabel('Amplitude'); title('Linear Convolution of the Above two sequences'); output : Please feel free to ask your questions in the comment session