Frequency Sampling

Objective 

Objective of this experiment is to design a Low pass, High pass, band pass and Band stop filters using Frequency Sampling Technique and plot the magnitude and phase response of the filter for various values of N

Low Pass filter design

Let us first design a low pass filter for the cutoff  frequency of 0.5*pi rad/sample of order 7. Observe the change in magnitude response by changing the Order N for various values.

CODE

N=7;

wc = 0.5*pi;

%Low pass Filter design

k =0:(2*pi/N):(2*pi);

k_valid = k <= wc;

k_index =find(k_valid ==1);

K=0:length(k_index)-1;

 % Write the reset of the code below 

 H=exp(-1i*(N-1)*pi.*(K)/N);

   for  n=0:N-1

    realpart=real(H(2:end).*exp(1i.*2*pi.*K(2:end)*n/N));

    h1(n+1)=(1/N)*(H(1)+2.*sum(realpart));

   end

  subplot(211)

  [H,W]=freqz(h1,1);

  plot(W,abs(H));

  set(gca,'XTick',0:pi/2:pi) 

  set(gca,'XTickLabel',{'0','\pi/2','\pi'})

  xlabel('\omega')

  ylabel('H(e^j^\omega)')

  title('Magnitude Response')

  grid on;

  subplot(212)

  plot(W,angle(H));

  set(gca,'XTick',0:pi/2:pi) 

  set(gca,'XTickLabel',{'0','\pi/2','\pi'})

  xlabel('\omega')

  ylabel('\theta(e^j^\omega)')

  title('Phase Response')

  grid on;

 % produce the graph as shown in the output section

OUTPUT

Now you should design the HP, BP and BS filters by modifying the above code accordingly