Avik Pal EE 5355 project 3A X(n) = 1, 2, 3, 4, 5, 4, 3, 2, 1 Y(n)= -0.0001, 0.0007, -0.0004, -0.0049, 0.0087, 0.0140, -0.0441,-0.0174, 0.1287, 0.0005, -0.2840, -0.0158, 0.5854, 0.6756, 0.3129, 0.0544 1), Discrete convolution directly. Sketch the result. Programming: clc clear all close all X=[1 2 3 4 5 4 3 2 1]; %stem(X); title('sequence X') Y=[-0.0001,0.0007,-0.0004,-0.0049,0.0087,0.0140,-0.0441,-0.0174,0.1287,0.0005,-0.2840,-0.0158,0.5854,0.6756,0.3129,0.0544]; %stem(Y); title('sequence Y') %convolution graph% W=conv(X,Y); figure; stem(W); title('convolution graph'); ylabel('--Amplitude--'); xlabel('--time-') Visualization :Avik Pal EE 5355 project 3A Convolution between X and Y Observation: At first, I take the sequence of values in X and Y matrix.X matrix is of 1*9 dimension and Y matrix is of 1*16 dimension. Then I use conv() function to get the convoultion between two sequences. 2) Use DFT/FFT approach. Show that both give the same results. Programming: %Using FFT% n=length(X);%length of sequence X% m=length(Y);%length of y% N=n+m-1;%calculating the lenght% x=zeros(N,1); for i=1:length(X) if n==length(X) x(i)=X(i); end end y=zeros(N,1);Avik Pal EE 5355 project 3A for j=1:length(Y) if m==length(Y) y(j)=Y(j); end end Xf=fft(x);%fft of new sequence x% Yf=fft(y);%fft of new sequence y% Z=Xf.*Yf; z=ifft(Z); figure; stem(z); xlabel('time'); ylabel('magnitude'); title('Convolution of sequences using fft'); Visualization: using fft Matlab Programming: clc clear all close allAvik Pal EE 5355 project 3A X=[1 2 3 4 5 4 3 2 1]; %stem(X); %title('sequence X') Y=[-0.0001,0.0007,-0.0004,-0.0049,0.0087,0.0140,-0.0441,-0.0174,0.1287,0.0005,-0.2840,-0.0158,0.5854,0.6756,0.3129,0.0544]; %stem(Y); %title('sequence Y') %convolution graph% W=conv(X,Y); figure; stem(W); title('convolution graph'); ylabel('--Amplitude--'); xlabel('--time-') %Using FFT% n=length(X);%length of sequence X% m=length(Y);%length of y% N=n+m-1;%calculating the lenght% x=zeros(N,1); for i=1:length(X) if n==length(X) x(i)=X(i); end end y=zeros(N,1); for j=1:length(Y) if m==length(Y) y(j)=Y(j); end end Xf=fft(x);%fft of new sequence x% Yf=fft(y);%fft of new sequence y% Z=Xf.*Yf; z=ifft(Z); figure; stem(z); xlabel('time'); ylabel('magnitude'); title('Convolution of sequences using fft');Avik Pal EE 5355 project 3A Conclusion: In this project first I did convolution between two sequences x and y. both the sequence are in time domain. so I get the output W in time domain. So we use convolution in time domain to get the convolution between two signals.in figure 1 ,we can see that convolution graph between two sequences. In figure 2,I used fft to get the resultant. and from figure it is clearly vsble that both result are same .so in conclusion,we can say that convolution in time domain is equivalent to multiplication in frequency domain. I used fft to get the sequence in frequency domain.but it is needed to mention that I need to use zero padding to convert the sequence in frequency domain. and then I use fft to get sequence in frequency domain.then I multiply them and take inverse Fourier transform to get the resultant
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