.. 4.6

Fourier Analysis
================

**Objective**

Learn about Fourier Transform of a signal. Time and Frequency domain
representations.

**Procedure**

-  Connect SQ1 to A1 and WG to A2. Put A1 in AC coupled mode (slide
   switch on the box)
-  Enable A1 and A2, select 4 volt scale
-  Set both WG and SQ1 to 500Hz
-  Press the FFT button

**Discussion**

In the Fourier transform plot, frequency is on the x-axis and the y-axis
shows the relative strength of the frequency components of the signal.
This is called the frequency domain
representation (http://en.wikipedia.org/wiki/Fourier\_transform).
For the sine wave there is only one dominant peak, the smaller ones are
a measure of distortion of the sine wave.

A square wave function can be represented as
:math:`f(\theta) = \sin(\theta) + \sin(3\theta)/3 + \sin(5\theta)/5 + ⋯`. In the
Fourier transform of a square wave of frequency f , there will be a 3\ f
component (having an amplitude of one third of f ), 5\ f component
(amplitude one fifth) etc. as shown in the figure.

.. image:: pics/sqwaveFFT.png
	   :width: 300px
.. image:: pics/sinewaveFFT.png
	   :width: 300px
