How to plot Fourier transform against frequency?

I am trying to plot the fourrier transform against frequency rather than bins. How do I do this? I belive the mistake is in creating f_axis

n = 400   %number of points
F1 = 3   %frequency 2
F2 = 2   %frequency 1
NT = 1.33   %number of periods

T = 2*pi/(F1-F2)   %one period
L = NT*T   %length of signal

m = zeros(1,n/20)
p = zeros(1,n/20)

for N =  20:20:n
    
    t = 0:L/N:L-L/N   % time axis given by N points counting from 0 to NT periods
    y = cos(t.*(F1+F2)).*cos(t.*(F1-F2))   %signal
    
    %%% Windowing %%%
    
    win = gausswin(N)
    y = y'.*win
    
    %%% Zero padding %%%
    
    Nz = 1000   % number of zeros to pad with
    y = [y' zeros(1,Nz)]
    
    %%% Fourier Transform %%%
    
    Y = fftshift(fft(y))
    
    %%% Extract the maxima %%%
    [pks,locs] = findpeaks(abs(Y))
    m(N/20) = m(N/20)+locs(3)
    p(N/20) = p(N/20)+locs(4)
    
end

%%% plot against frequecy rather than bins %%%

Ntotal = Nz + n
Df=1/((Ntotal)*L/n)
f_axis=(0:1:(Ntotal-1))*Df

Answer 1

[Star Strider]

I am not certain what you want to do.

Try this —

n = 400;   %number of points
F1 = 3;   %frequency 2
F2 = 2;   %frequency 1
NT = 1.33;   %number of periods

T = 2*pi/(F1-F2);   %one period
L = NT*T;   %length of signal

m = zeros(1,n/20);
p = zeros(1,n/20);
Nz = 1000;   % number of zeros to pad with


for N =  20:20:n
    
    t = 0:L/N:L-L/N;   % time axis given by N points counting from 0 to NT periods
    y = cos(t.*(F1+F2)).*cos(t.*(F1-F2));   %signal
    
    %%% Windowing %%%
    
    win = gausswin(N);
    y = y'.*win;
    
    %%% Zero padding %%%
    
%     Nz = 1000   % number of zeros to pad with
    y = [y' zeros(1,Nz)];
    
    %%% Fourier Transform %%%
    
    Y = fftshift(fft(y));    
    Fs = N/L;                                                                           % Sampling Frequency
    Fn = Fs/2;                                                                          % Nyquist Frequency
    Fv = linspace(-Fn, Fn, numel(t)+Nz);                                                % Frequency Vector (Assuming 'fftshift')
    
    figure                                                                              % Plot Fourier Transforms
    plot(Fv, abs(Y))
    grid
    xlabel('Frequency')
    ylabel('Amplitude')
    title(sprintf('N = %d',N))
    
    %%% Extract the maxima %%%
    [pks,locs] = findpeaks(abs(Y));
    m(N/20) = m(N/20)+locs(3);
    p(N/20) = p(N/20)+locs(4);
    
end

%%% plot against frequecy rather than bins %%%



Ntotal = Nz + n

Ntotal = 1400

Df=1/((Ntotal)*L/n)

Df = 0.0342

f_axis=(0:1:(Ntotal-1))*Df

f_axis = 1×1400

0 0.0342 0.0684 0.1026 0.1368 0.1710 0.2051 0.2393 0.2735 0.3077 0.3419 0.3761 0.4103 0.4445 0.4787 0.5129 0.5470 0.5812 0.6154 0.6496 0.6838 0.7180 0.7522 0.7864 0.8206 0.8548 0.8889 0.9231 0.9573 0.9915

.

[Jacob Duryee-Feeney]

I dont think I explained very well, sorry. The problem i am having is with plotting the fourier transform:

subplot(2,1,2)
plot(f,abs(Y), 'b')
xlabel('Frequency')
title('Fourier Transform')

does not give me the expected frequencies since the frequency axis is not correct. I need to fix the frequency axis of that graph so the fourier transform shows maximums at the correct frequencies.

[Star Strider]

My code plots the Fourier transfrom that is calculated in every iteration.

Here they are as subplots

n = 400;   %number of points
F1 = 3;   %frequency 2
F2 = 2;   %frequency 1
NT = 1.33;   %number of periods

T = 2*pi/(F1-F2);   %one period
L = NT*T;   %length of signal

m = zeros(1,n/20);
p = zeros(1,n/20);
Nz = 1000;   % number of zeros to pad with

figure
k = 0;

for N =  20:20:n
    k = k + 1;
    
    t = 0:L/N:L-L/N;   % time axis given by N points counting from 0 to NT periods
    y = cos(t.*(F1+F2)).*cos(t.*(F1-F2));   %signal
    
    %%% Windowing %%%
    
    win = gausswin(N);
    y = y'.*win;
    
    %%% Zero padding %%%
    
%     Nz = 1000   % number of zeros to pad with
    y = [y' zeros(1,Nz)];
    
    %%% Fourier Transform %%%
    
    Y = fftshift(fft(y));    
    Fs = N/L;                                                                           % Sampling Frequency
    Fn = Fs/2;                                                                          % Nyquist Frequency
    Fv = linspace(-Fn, Fn, numel(t)+Nz);                                                % Frequency Vector (Assuming 'fftshift')
    
    subplot(4,5,k)                                                                              % Plot Fourier Transforms
    plot(Fv, abs(Y))
    grid
    xlabel('Frequency')
    ylabel('Amplitude')
    title(sprintf('N = %d',N))
    
    %%% Extract the maxima %%%
    [pks,locs] = findpeaks(abs(Y));
    m(N/20) = m(N/20)+locs(3);
    p(N/20) = p(N/20)+locs(4);
    
end

%%% plot against frequecy rather than bins %%%



Ntotal = Nz + n

Ntotal = 1400

Df=1/((Ntotal)*L/n)

Df = 0.0342

f_axis=(0:1:(Ntotal-1))*Df

f_axis = 1×1400

0 0.0342 0.0684 0.1026 0.1368 0.1710 0.2051 0.2393 0.2735 0.3077 0.3419 0.3761 0.4103 0.4445 0.4787 0.5129 0.5470 0.5812 0.6154 0.6496 0.6838 0.7180 0.7522 0.7864 0.8206 0.8548 0.8889 0.9231 0.9573 0.9915

.

[Jacob Duryee-Feeney]

thank you. I am still not sure the FFT shows the correct frequencies though. Why is it showing a peak at f<1 when F1 and F2 are 2 and 3 respectively.

[Star Strider]

My plkeasuer.

It is showing the frequencies you defined (calculatted from the length of ‘t’ and ‘L’ and ‘N’) and since you want a double-sided Fourier transform, the frequency vector ‘Fv’ reflects that. The ‘locs’ vector are the absolute indices of the peaks. To experess them as frequencies, use:

PeakFreqs = Fv(locs);

Those frequencies should correspond to the double-sided Fourier transform plots.

This plots them, as requested. Experiment with it to get the result you want.