Help me undersandand Frequency Vector and index vector in fourier transform

I have strated learning and I am new to Matlab and fourier transform I am Struggling to understand the concept of the frequency vector and index vector in this code below. I will be grateful if someone can explain what is frequency vector (Fv) and index vector (Iv) and what the code for both at Fv, Iv and FTs_plot is doing.

L = numel(t);                                                   % Vector Length
Fs = 1/Ts;                                                      % Sampling Frequency
Fn = Fs/2;                                                      % Nyquist Frequency
FTs = fft(s)/L;                                                 % Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                             % Frequency Vector
Iv = 1:numel(Fv);                                               % Index Vector
FTs_plot = abs(FTs(Iv))/max(abs(FTs(Iv)));                      % Normalised Fourier Transform

Answer 1

[Star Strider]

That is my code, so I will do my best to explain it.

The frequency vector ‘Fv’ here defines the frequencies for a one-sided Fourier transform, going from 0 Hz (d-c) to the Nyquist frequency. The length is determined by half the length of the original signal vector (+1 since it begins at 0). (Since the time vector is always a vector and not a matrix, and the signal could be a matrix, it is easier to use the time vector to determine the length of the signal.) The length of the two-sided Fourier transform (most easily appreciated after using fftshift on it) is the same as the length of the original signal vector (unless the length is increased by zero-padding it, that being a separate discussion).

The index vector ‘Iv’ just makes plotting and other references to the one-sided fft result easier. It is equal to the number of elements in the frequency vector, so the lengths match when plotted or otherwise processed.

With respect to ‘FTS_plot’, I am not certain what this code refers to (with this, I will have posted 13495 Answers, and I do not remember all of them), however it appears that it was intended to plot the normalised fft, so that the highest value is 1 and everything else is between 0 and 1. That is not how I usually plot fft results, so there must have been a specific reason for it.

If you have any further questions about my code here, I will do my best to address them.

[S Pro]

Hi Star. I appreciate your response thanks. This is samll part of your code i took from this forum. The full code is as follow

D = load('time_domain.txt');
t = D(:,1);
s = D(:,2);
L = numel(t);                                                   % Vector Length
Ts = mean(diff(t));                                             % Sampling Interval
Fs = 1/Ts;                                                      % Sampling Frequency
Fn = Fs/2;                                                      % Nyquist Frequency
FTs = fft(s)/L;                                                 % Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                             % Frequency Vector
Iv = 1:numel(Fv);                                               % Index Vector
FTs_plot = abs(FTs(Iv))/max(abs(FTs(Iv)));                      % Normalised Fourier Transform
figure
plot(Fv, FTs_plot)
grid
xlim([0 0.5])

I have few other questions if you don't mind answering.

1. Why did we include o HZ (DC ) in the fourier transform? many of tutorials i have been following on the internet recommends removing DC before performing FFT.

2. why do halve the Length of the signal in the Fv?

3. Is the FTs_plot simply normalising the mangtitudes of frequency components with respect to the highest frequency magnitude in the signal (i.e fundamental frequency magnitude)?

Thanks in advance for your time.

[Star Strider]

1. That varies, depending on the signal. A signal with a mean at or near 0 does not have to have the mean value of the signal (the d-c component) removed from it first. I always include it because it is part of the signal.

2. To plot or otherwise process) a one-sided Fourier transform.

3. Yes. (I thought I explained that in my original post.)

[S Pro]

thank you so much for your help

[Star Strider]

As always, my pleasure!