MATLAB : Fourier transform

By Nuno Nogueira, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=3912826

MATLAB has been  crucial programming language across worldwide that let us express matrix and array mathematics directly. In signal processing and communication it plays vital role in analysing and exploring time series data in time domain or frequency domain. For analysing non periodic signals in frequency domain we use Fourier transform instead of Fourier series ,which is used to express periodic signals in terms of infinite sum of sinusoidal terms .  

Fourier transform can exist for :

     1. Energy signals

     2. Power signals 

     3. Impulse signals 

That means absolutely integrable signals can have their Fourier transform only. 

Formula for Fourier transform; 

 Then its come to use Fourier transform in MATLAB. So here is the code for Fourier transform of sinusoidal wave , for any other signal we can define that signal as y. :

Here is the output image

Fourier transform consist of both absolute and complex values. Here's a glimpse of some absolute and complex values.

 So for plotting we will take absolute values only, that's why we have used 'abs' function. So here's the way to understand the basics of Fourier transform.