How to plot the frequency response of a discrete cosine function?

My attempt:

I tried doing it but I can't get the freq response to be plotted between pi and pi. Any help would be appreciated.

Answer 1

[Rick Rosson]

   L = 1000;
   n = 0:L-1;

   x1 = fftshift(fft(x))/L;

   dw = 2*pi/L;
   w = -pi:dw:pi-dw;

   stem(w,mag);

[Daniel Ramirez]

Thank you Rick. I got the magnitude right this time. But the phase plot I get a a lot of fluctuations, like noise.

 L = 1000;
   n = 0:L-1;
   x=5*cos((0.13*pi*n)+(pi/13));

   x1 = fftshift(fft(x))/L;
   dw = 2*pi/L;
   w = -pi:dw:pi-dw;
   mag=abs(x1)
   stem(w,mag);
   title('Magnitude Plot');
   phase=angle(x1);
   figure
   plot(w,phase)
   title('Phase Plot');

[Rick Rosson]

   phase = angle(x1);
   phase(mag<0.01) = nan;
   figure;
   plot(w,phase/pi);
   ylabel('Phase Angle (pi-radians)');

[Daniel Ramirez]

Rick sorry but I still can't get the phase response. I uploaded the image.

 L = 1000;
   n = 0:L-1;
   x=5*cos((0.13*pi*n)+(pi/13));
  x1 = fftshift(fft(x))/L;
   dw = 2*pi/L;
   w = -pi:dw:pi-dw;
   mag=abs(x1)
   stem(w,mag);
   title('Magnitude Plot');
   phase = angle(x1);
   phase(mag<0.01) = nan;
   figure;
   plot(w,phase/pi);
   ylabel('Phase Angle (pi-radians)');

[Rick Rosson]

Try using stem instead of plot:

   stem(w,phase/pi);

[Daniel Ramirez]

Thank you so much Rick. It's working now.