# Application Of Fourier Transform In Communication systems

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Application Of Fourier Transform

Fourier transform is a mathematical tool that breaks a function, a signal or a waveform into an another representation which is characterized by sin and cosines. In the theory of communication a signal is generally a voltage, and Fourier transform is essential mathematical tool which provides us an inside view of signal and its different domain, how it behaves when it passes through various communication channels, filters, and amplifiers and it also help in analyzing various problems.

Here are some applications of this transform:

1. Processing of signal: FT ( Fourier transform ) of a signal informs us what frequencies are present in our signal and in what proportions.

For example, Our phone buttons produce different sounds when we press them. It is because they are each composed of two different frequencies that combine tighter to produce the sound.

1. Data transmission: analysis of data transmission system where the signal which is transmitted is the Fourier transform and demodulator is discrete Fourier transform.

Example: frequency division multiplexing using parallel data transmission technique.

1. Sampling: The (Dirac) delta function or (unit) impulse signal, is denoted by .It is usually represented as a vertical arrow at the origin. It is not a true function, and undefined at t = 0. It is defined as a generalized function which satisfies the sampling property (or shifting property)

1. Spectral estimation is a signal processing method in which the frequency component of a

signal is characterized corresponds to spectral analysis. In communication engineering it is helpful in detecting the signal component (carrier ) which has the noise component in it.

1. Paley-Wiener criterion:

The necessary condition for the amplitude response

|H(?)| be realizable if

If H(?) does not satisfies above condition, it is unrealizable.

Author : Arusha Ahmed

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