What does two sided spectrum represent in fft function of MATLAB? Can someone explain fft and its plot in MATLAB?

close all;

clear all;

clc;

Fs = 1000; % Sampling frequency

T = 1/Fs; % Sampling period

L = 1500; % Length of signal

t = (0:L-1)*T; % Time vector

S = sin(2*pi*50*t) ;

plot (S)

Y=fft (S);

figure

% Y = fft(S);

P2 = abs(Y/L); % find absolute value.normalization

I should get fft at 50Hz. But after plotting P2 it shows above plot.

What is step by step explanation for fft in MATLAB?

[Adam]

You need to create your frequency vector to plot the spectrum against, rather than just indices, as is done in examples in

doc fft

Those examples just plot a single-sided spectrum for the positive frequencies, which is usually all you want unless you especially want to do things with negative frequencies. Unless you have a complex signal the negative half of the spectrum will just mirror the positive half about either 0 or the nyquist frequency. It isn't something that is useful in most cases.