multi tone, different psd power

Hi, i am trying apply 4 frequencies tone to analyze spectrum.

Fs=1e6 dt=0:1/Fs:1-1/Fs Pc_amp=200e-6 f_ch_w=2000 ch_num=1 fc1=1000 fc2=fc1+1*ch_num*f_ch_w fc3=fc1+2*ch_num*f_ch_w fc4=fc1+3*ch_num*f_ch_w Pc=Pc_amp.*(cos(2*pi*fc1.*dt)+cos(2*pi*fc2.*dt)+cos(2*pi*fc3.*dt)+cos(2*pi*fc4.*dt))

L = length(Pc); Out_FFT_base = Pc; NFFT = 2^nextpow2(L); na=1 w=hanning(floor(L./na)); Out_FFT_base(L+1:NFFT)=zeros(1,NFFT-L); [Py_base,Fy] = pwelch(Out_FFT_base, w, 0, [], Fs);

but, not equal power@ 4 frequency components. may somebody help it?

Answer 1

[Jonas]

Δf=NFFTFs​​=1,048,5761,000,000​≈0.953674 Hz

Because Δf is not an integer divisor of the tone frequencies, none of the tones fall exactly on an FFT bin center, if you use L as NFFT, it is as expected

Fs = 1e6;
dt = 0:1/Fs:1-1/Fs;
Pc_amp = 200e-6;

% Tone frequencies
fc1 = 1000;
fc2 = 3000;
fc3 = 5000;
fc4 = 7000;

Pc = Pc_amp .* (cos(2*pi*fc1*dt) + cos(2*pi*fc2*dt) + ...
                cos(2*pi*fc3*dt) + cos(2*pi*fc4*dt));

L = length(Pc);
NFFT = L;
w = hanning(L);


[Py_base, Fy] = pwelch(Pc, w, 0, NFFT, Fs, 'power');

% Theoretical power per tone: (Pc_amp^2)/2 = 2e-8 V^2
plot(Fy, Py_base);
xlim([0 10000]);
grid on;
ylabel('Power (V^2)');
xlabel('Frequency (Hz)');