Help me sketch the sprectrum of this signal.

Hi there,

I am really stuggling with two things:

First I would like to sketch the spectrum of this signal:

y(t) = cos(760*pi*t)*(4+3*cos(20*pi*t))

I would like the magnitude plot and the phase plot. I have been trying the following to no avail....

%%Time specifications:
   Fs = 1000;                      % samples per second
   dt = 1/Fs;                     % seconds per sample
   StopTime = 1;                  % seconds
   t = (0:dt:StopTime-dt)';
   N = size(t,1);
   %%Sine wave:
   x = (cos(760*pi*t)).*(4+3*cos(20*pi*t));
   %%Fourier Transform:
   X = fftshift(fft(x));
   %%Frequency specifications:
   dF = Fs/N;                      % hertz
   f = -Fs/2:dF:Fs/2-dF;           % hertz
   %%Plot the spectrum:
   figure;
   plot(f,abs(X)/N);
   xlabel('Frequency (in hertz)');
   title('Magnitude Response');

My second issue is very similar: Sketch the spectrum ( BOTH REAL AND IMAGINERY PARTS ) for:

x(t)=(10*cos(1000*pi*t+pi/6)) + (7*cos(500*pi*t-pi/3)) - (4cos(1500*pi*t))

I appreciate everyone's help. Best regards Paul

Answer 1

[Nishitha Ayyalapu]

doc angle
doc real
doc imag

1.) For Phase Respone

plot(f,angle(X));

2.) To plot real and imaginary parts

plot(f,real(X))
plot(f,imag(X))

[Paul]

I'm still stuggling to get this to work...

From what I beleive the phase diagram and magnitude diagram should both have lines coming up or down from the x axis.

I can't get this to work.

Any help please

Answer 2

[Paul]

I still can't get this to work. Any input?