Fourier Transform
Fourier Transform is a very powerful tool that can able to convert any Time Domain Signal (periodic / non periodic) as a function of Frequency called Frequency Domain.
we can also convert from frequency domain to time domain by inverse fourier transform.
we can also convert from frequency domain to time domain by inverse fourier transform.
Here, w = 2.pi.f
F(w) is called as Fourier Transform & f(t) is called as Inverse Fourier Transform.
The time domain description tells you what sound you hear every instant, while the frequency domain description tells you, roughly,what instruments are involved in the ways & how they are played.
one of the most important properties of the Fourier transformation is that it converts calculus i.e differentiation and integration into algebra i.e multiplication and division. This underlies its
application to linear ordinary differential
equations and further to partial differential equation
Fourier Transform has many Application in many fields of science such as
Signal Analysis,Image Processing,Sound Filtering/Digital Filter-high pass low pass band pass etc,Data Compression,Solving Linear Partial Differential Equations,Communication,Optics,Geology,Astronomy,Antenna Designing and many moreand many
more.
in fact
any field of physical science that uses sinusoidal signals, such as
engineering, physics, applied mathematics, and chemistry.
let's take an example :-
lets observe fig 2 by looking at time domain we can't determine the frequency of resultant sound wave signal but by taking the transformation we can say that it contains three harmonic frequency of 50Hz,100Hz and 150Hz. similarly by taking the transformation of modulated signal at the receiver one can able to determine the carrier frequency and information signal frequency.
in modulation process i.e while signal is passing through the channel,noise is superimposed on the signal.by taking the Fourier transformation we can suppress the noise signal by designing the filter.that is the use of filter in signal processing.we can able to eliminate the unwanted frequency (particular or band of frequency ) by designing high pass, low pas , band pass filter. click here
let's take an example :-
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| Fig 1 |
lets observe fig 2 by looking at time domain we can't determine the frequency of resultant sound wave signal but by taking the transformation we can say that it contains three harmonic frequency of 50Hz,100Hz and 150Hz. similarly by taking the transformation of modulated signal at the receiver one can able to determine the carrier frequency and information signal frequency.
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| Fig 2 |
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| Square |
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| Sawtooth |
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| Pulse |
above fig shows how many harmonics of sine wave are used to approximate/generate the square wave,saw tooth & pulse.
