# why FFT used in matlab???

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#### Nosheen

##### Member level 1 dft 60 hz matlab

hi there...

why FFT used in matlab???
can anyone give me the background and signal's theory abt it....

#### Dmitrij purpose of fft

Your question is really strange for me. I supposed all participants of this prestigious forum are aware of Fourier transform and such questions will never arise in their minds. It's difficult to answer this question. Take any book on DSP (I insistently recommend you Oppenheim "Digital Signal processing"), read it very carefully and pay attention to the paragraphs, devoted to Fourier analysis. Try to understand the sense of applying Fourier tranform in Signal Processing. If you succeed in this, your question will be solved automatically.

If anything won't be clear, let me know. No doubt, I'll help with great pleasure.

With respect,

Dmitrij

### Nosheen

Points: 2

#### wajahat computer cannot calculate continuous signal

Hi Nosheen , this is a very insightful question.

Now u see fourier transform is a function of continuous frequeny ω.continuous variable has infinite values.

Your computer can't calculate these infinite values in limited time that we have.

To overcome this discrepancy fft is used which reduces the computational load and allows us to determine dft in lessor time.

Two names outstand in this regard cooley and tuckey.
please see cooley and tuckey algorithm.

i hope this clarifies your problem.

regards

wajahat

### Nosheen

Points: 2

#### Nosheen

##### Member level 1 what is the purpose of fft

i actually meant to say that whats the purpose of FFT??
is it provide the magnitude of highest frequency component or else...

replies r most welcome

regardz
Nosheen

##### Newbie level 2 determine dft using matlab

FFT is a computationally effective method of calculating the Discrete Fourier Transform
(DFT) of a signal.

DFT of a time domain signal will give you information about it's spectral composition.
That is , the different frequencies that make up the signal.

A quick example :

Consider a signal that contains multiple frequencies. FFT of the signal will show you the magnitude of the various frequencies present in the signal. It is also important to note that the results of the FFT may not be accurate. This, however, is beyond the scope of this thread. Please refer any standard text on more information regarding the use of FFT and spectral leakage.

Matlab code
===================================================

t = 0:0.001:0.6; % time
x = sin(2*pi*60*t)+sin(2*pi*91*t); % Signal with frequencies of 60 ,91 Hz
plot(x(1:50))
title('Signal in time-domain')
xlabel('Time (seconds)')

Y = fft(x,512); %perform 512 point FFT

sample_rate = 1000; %Sample rate = 1000 Hz

Pyy = Y.* conj(Y) / 512; % Magnitude of the frequency (since it is a complex
% number)
f = sample_rate*(0:256)/512; %frequency vector
plot(f,Pyy(1:257))
title('Frequency content of x')
xlabel('Frequency (Hz)')

### Nosheen

Points: 2

#### nnm

##### Junior Member level 3 what is fft used for

Physical significant is that , converting time domain to frequency domain for analyze the frequency,

#### niagara

##### Newbie level 3 what is fft used for?

There are several ways to calculate the Discrete Fourier Transform (DFT), such as solving
simultaneous linear equations or the correlation method and by FFT method.The FFT is a clever algorithm for rapidly calculating the DFT.Using the FFT,convolution by multiplication in the frequency domain can be hundreds of times faster than conventional convolution. Problems that take hours of calculationtime are reduced to only minutes.

### Nosheen

Points: 2

#### mihirtronics

##### Junior Member level 2 sampling an infinite signal using fft in matlab

FFT is not a transform..its a quick method to perform DFT... saves on computational steps like addition, multiplication and ofcourse saves time!

#### viralv11

##### Newbie level 3 why is fft used?

FFT stands 4 fast fourier transform

It is very imp to find dft.

#### goosecool

##### Junior Member level 3 solving fourier transform matlab

Nosheen said:
i actually meant to say that whats the purpose of FFT??
is it provide the magnitude of highest frequency component or else...

replies r most welcome

regardz
Nosheen

Your question should have been what is the purpose of FFT in general? Matlab is just a programming/testing environment for mathematical modelling so they provide FFT as a tool. What's important to know is that they use an algorithm called FFTW (Fastest Fourier Transform in the West).
Now coming to FFT; FFT is an algorithm which computes N point DFT of N sample points of a signal. Fourier theorized that any periodic signal can be represented as a sum of sines and cosines. Fourier's transform was the method he gave to do so. Now, for a continuous signal, Fourier's method needs infinite sine and cosine terms, rendering the Fourier transform unusable in real situations. DFT provided a way to do fourier analysis on a sampled representation of a signal. Since DFT is a computationally expensive process Cooley and Tukey gave an algorithm which cleverly exploited the symmetry in DFT computations to calculate DFT with less operations. This algorithm is called FFT.

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