EXPERIMENT 1 - INTRODUCTIONAIM 1) To plot sinc(an)2) To plot spectrum of sinc(an)MATLAB Code % Plot Sinc Functiona = 0.5n = -20 : 0.1 : 20y = sinc(a*n)plot (n,y)OUTPUT-

MATLAB CODE-% Plot spectrum of Sinc Functiona = 1n = -5: 0.1 : 5plot(n,abs(fftshift(fft(sinc(a*n),201))))OUTPUT-

EXPERIMENT 2 DFT AND ITS PROPERTIES-IAIM Verify following properties of Discrete Fourier Transform (DFT) Convolution Time shifting Frequency shiftingMATLAB CODE-%DFT TWO SIGNALSX1 = [zeros(1,20) ones(1,20) zeros(1,20)]X2 = [zeros(1,15) ones(1,30) zeros(1,15)]n = 1 : 1 : 60stem(n,X1)stem(n,X2)OUTPUT

%DFT-CONVOLUTIONMATLAB CODE- x1 = [zeros(1,20) ones(1,20) zeros(1,20)]x2 = [zeros(1,15) ones(1,30) zeros(1,15)]dftx1 = fft(x1,128)dftx2 = fft(x2,128)stem(conv(x1,x2))stem(ifft(times(dftx1,dftx2)))OUTPUT-

MATLAB CODE- %DFT-TIME SHIFTINGx = [zeros(1,20) ones(1,20) zeros(1,20)]dftx = fft(x,60)n = 1:1:60dftx1 = times(dftx, exp(5*i*2*pi*n/60)stem(dftx1)stem(x)OUTPUT-

MATLAB CODE-%DFT-FREQUENCY SHIFTINGx = [zeros(1,20) ones(1,20) zeros(1,20)]n = 1 : 1 : 60x1 = times(x, exp(5*i*2*pi*n/60))dftx = fft(x,60)dftx1 = fft(x1,60)stem(n,abs(fft(x,60)))stem(n,abs(fft(x1,60)))OUTPUT-