how to take psd

i want to take psd for following signal.

x=sin(2*pi*19000*t)+cos(2*pi*2000*t)+randn(size(t))+tan(2*f);

Can someone help me please?

Answer 1

[David Wilson]

Bit hard to help since you haven't given us some key information, but assuming you are sampling at a reasonable sampling rate, and forthe moment we will drop the noise term, then

Ts = 1e-5; % sample time 
Fs = 1/Ts; % sampling frequency 
t = [0:Ts:0.001]'; 
f = 1000; % ??? (who knows?) 
x=sin(2*pi*19000*t)+cos(2*pi*2000*t)+ 0*randn(size(t))+tan(2*f);

plot(t,x,'.-')

This will give a time plot ofthe signal. Always a good idea to look at that.

Now you were asked for a PSD, and typing

help psd

indicates we should use periodgram. Have a look at the help file, and you will see

periodogram(x,[],'twosided',512,Fs)

two clear peaks; one at 2 kHz and one at 19 kHz, just like in your original generating formula. What a coincidence!

Answer 2

[David Wilson]

If you want, the noise term will simply smudge the results.