# Why Fourier Transform?

Ever heard that shhhhhh……… sound most often from mic?

Disturbing enough? What’s that? Let’s Decode!

When we speak the signal practically looks kind of like this in the oscilloscope!

Figure 1 Noise in Time Domain

Or maybe worse like below-

Figure 2 Noise in Time Domain

This contains not only our voice but also the noise from our surroundings.

Suppose you are talking to your mom. Your voice is the original signal here and the freaking out music your neighbor is playing right now is the noise here! Now, in any type of communication system this noise can be a problem doing miscommunication! The main signal can get distorted too!

We need to remove this noise!

To solve a problem, we need to detect that problem first, right?

Here, noise is our main problem! So, we need to detect that first!

Figure 2 was a time domain representation of a signal and from this we cannot differentiate between what is our voice and what is noise! And if we can’t separate noise, we won’t be able to remove it!

Thus, we need another representation to detect the noise! That’s where Fourier Transform came with a solution!

Let, this is your voice signal. For analysis purpose, we use sinusoidal waveform of 24 Hz.

In frequency domain, your voice signal looks like this! A peak at 24 Hz!

Now, you add noise of 74Hz, and the signal looks like this!

In frequency domain-

Here, other than the main signal another peak at 73 Hz had been seen which denotes the noise.

Now, we can use a filter to remove this noise from the spectrum! Remember filters? Just take it as a regular water filter!

A water filter removes all kinds of unwanted components from your water!

Our digital or analog filter also does the same.!

In MATLAB, we are using some filtering codes to remove the noise! Not mentioning those codes here to maintain simplicity.

After filtering the spectrum looks like this!

No other components other than 24 Hz are present after filtering which means the noise has been removed!

So, where was the Fourier Transform here?

Without moving to frequency domain, we would not be able to detect the noise. This is how Fourier helped us.

This was just a mere example. The area of Fourier Transform is vast! With time we will know more!

Author: Asfia Ahmed Khan (EEE,CUET)

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