Fourier Transform of a Radar Signal

I am taking the fourier transform of a radar signal (1st image below), when I take the fourier transform I should get a single frequency at 3kHz. However I am not, instead I am getting(2nd image). I think there is an issue on how I am defining 'fs', but I am not sure how to fix it. Thank you!

Here is my code:

Fs = 125e3; % Sample Frequency in Hz

signal_with_bias = csvread('noball.csv',1,0);

sig_i = signal_with_bias(:,1); %in_phase signal

sig_i = sig_i - mean(sig_i); %remove bias

sig_q = signal_with_bias(:,2);%quad_signal

sig_q = sig_q - mean(sig_q); %remove bias

signal = complex(sig_i, sig_q); %the complex signal

N =length(signal); %number sample

t = (0:1:N-1)/Fs; %time period

fs = Fs*((0:1:N-1)-(N/2))/N; %range of frequency that was measured.

w = hann(N); %hanning window

ff=fft((signal .*w)); %fourier transform of the signal

%Plot Complex Signal

figure(1)

plot(t,real(signal), 'r', t,imag(signal), 'k');

title('Signal'); xlabel('time(s)'); ylabel('Voltage(V)');

legend('real', 'imaginary');

%Plot the Power Spectrum

figure(2)

plot(fs, abs(real(ff))); %Frequency Vs. Power

title('Power Spectrum'); xlabel('Frequency(Hz)'); ylabel('Magnitude');

[Honglei Chen]

From the plot of your signal, there are a lot of frequency components in it. Why would you expect a single peak in FFT? For that to happen, you will have a single frequency sinusoid, which is not the case for your radar signal.

[Shanice Kelly]

We had a single frequency of interest and there was only a metal plate in front of the radar. Our professor hinted that we should be seeing a single frequency. I’m starting to suspect there was something wrong with our sampling parameters. Thank you for the help!

Answer 1

[Jerome Blair]

You should be plotting abs(ff), not abs(real(ff)). The spectrum of this signal is not a single line at 3kHz. It should be a bunch of lines separated by 3kHz centered around a much higher frequency.

Why does the frequency axis start at 0 when fs starts at -62.5 kHz?

[Shanice Kelly]

First, thank you so much for the help! I left the frequency axis at 0 because I am unsure what 'fs' is suppose to be defined as. That is where I am mostly confused. The signal plotted is exactly same as the signal on the oscilloscope, so the data acquisition software is working fine. Our frequency was set at 9875MHz, the difference frequency was 3 kHz, the sample frequency 125kHz and the number of samples were 1000.

This is what the fft plot looks like when I plot abs(ff) and I shift the frequency axis over. Thank you again!