How to plot the actual frequency range for the FFT plot?

Question

奥刘 2023-4-16

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https://ww2.mathworks.cn/matlabcentral/answers/1948018-how-to-plot-the-actual-frequency-range-for-the-fft-plot

评论： Star Strider 2023-4-17

Suppose I have a complex linear frequency modulated signal, where the frequency of it sweeps from 9.975 GHz to 10.025 GHz with 50 MHz bandwidth and the time duration is 10

. As my sampling frequency is fixed as 51.2 MHz, the FFT plot of the signal is shown below,

The corresponding code is given below.

clear all;

close all;

clc;

%% Signal parameter

c = 3e8; % speed of light

fc= 10e9; % carrier frequency

lambda = c/fc; % wave length

B = 50e6; % bandwidth

Tchirp = 1e-5; % duration time

slope = B / Tchirp; % slope

Nr = 513; % number

fs = (Nr-1)/Tchirp; % sampling frequency

t = linspace(0,Tchirp,Nr);

t(Nr)=[];

St = exp(1j*2*pi*((fc-B/2)*t + (slope*t.^2)/2)); % signal

St_all = [St];

figure; % check fft plot

plot(abs(fft(St_all)));

As my signal ranges from 9.975 GHz to 10.025 GHz. What is the actual frequency for x axis here? Why the FFT plot will include the current period of signal and an adjacent period here? Meanwhile, is there any way to present the whole 50 MHz of signal in a single FFT plot?

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Answer 1

Star Strider 2023-4-16

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在 MATLAB Online 中打开

One approach —

%% Signal parameter

c = 3e8; % speed of light

fc= 10e9; % carrier frequency

lambda = c/fc; % wave length

B = 50e6; % bandwidth

Tchirp = 1e-5; % duration time

slope = B / Tchirp; % slope

Nr = 513; % number

fs = (Nr-1)/Tchirp; % sampling frequency

t = linspace(0,Tchirp,Nr);

t(Nr)=[];

St = exp(1j*2*pi*((fc-B/2)*t + (slope*t.^2)/2)); % signal

St_all = [St];

L = numel(St_all)

L = 512

FT_St = fft(St_all)/L;

Fv = linspace(0, 1, fix(L/2)+1)*fs/2; % Frequency Vector

Iv = 1:numel(Fv); % Index Vector

figure; % check fft plot

plot(Fv, abs(fft(St_all(Iv))));

xlabel('Frequency (Hz)')

ylabel('Magnitude (units)')

xlim([min(Fv) max(Fv)])

The code for ‘Fv’ originates in the documentation for fft in R2015b. I have used it since, although other ways to calculate the frequency for a one-sided fft that produce the same result are equally valid. The ‘Iv’vector simply make subsequent addressing easier. It is not required.

.

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奥刘 2023-4-17

@Star Strider Thanks! I will check the modulate function

Star Strider 2023-4-17

My pleasure!

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Answer 2

Paul 2023-4-16

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1948018-how-to-plot-the-actual-frequency-range-for-the-fft-plot#answer_1216623

编辑：Paul 2023-4-16

在 MATLAB Online 中打开

clear all;
close all;
clc;
%% Signal parameter
c = 3e8;                    % speed of light
fc= 10e9;                   % carrier frequency
lambda = c/fc;              % wave length
B = 50e6;                   % bandwidth
Tchirp = 1e-5;                   % duration time
slope = B / Tchirp;              % slope
Nr = 513;                  % number 
fs = (Nr-1)/Tchirp;                                         % sampling frequency
t = linspace(0,Tchirp,Nr);
t(Nr)=[];                                                
St = exp(1j*2*pi*((fc-B/2)*t + (slope*t.^2)/2));         % signal
St_all = [St];

Frequency vector corresponding to St_all

N = numel(St_all);

f = (0:(N-1))/N*fs;

figure; % check fft plot

plot(f,abs(fft(St_all)));

xlabel('Hz')

The reason that all the action is around 4.22e7 Hz is because the sampling frequency

fs
fs = 5.1200e+07

is way too small relative the base sinusoidal frequency

fc - B/2
ans = 9.9750e+09

The 4.22e7 result is the aliased frequency.

If we make the sampling frequency more than two times larger than the base frequency

fs = (fc - B/2)*5                                        % sampling frequency
fs = 4.9875e+10

then we get this result:

t = linspace(0,Tchirp,round(Tchirp*fs));                                                
St = exp(1j*2*pi*((fc-B/2)*t + (slope*t.^2)/2));         % signal
St_all = [St];

Frequency vector corresponding to St_all

N = numel(St_all);

f = (0:(N-1))/N*fs;

figure; % check fft plot

plot(f,abs(fft(St_all)))

xlabel('Hz')

xlim([9e9 11e9])

xline(fc-B/2,'r')