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The sequence of N complex numbers x0, ..., xN−1 is transformed into the sequence of N complex numbers X0, ..., XN−1 by the DFT according to the formula:
where e is the base of the natural logarithm, is the imaginary unit (i2 = − 1), and π is Pi. The transform is sometimes denoted by the symbol , as in or .
fourier transform is like denoting the amplitude at every infinitesimal frequency and then joining all those points. incase you sample that curve at discrete points, it becomes dft.
FFT is an efficient method of calculating the DFT of a signal.
to calculate DFT it need computations of the order of square N.
FFT need computation of the order of NlogN.As the value of N(no of samples increases)
the computational advantage is immense.
As about the difference betwenn FS,FT,DFS,DFT i will try to come back.
@adsl
thats right,upto my knowledge we cannot do a continuous fourier transform on any digital machine. thats why if you give the input in the discrete form it means that you have sampled the original analog signal and then given it to the computer to take an fft(or dft(there is no ft in matlab)) of it.
FS: is used for signals which is continous and periodic..
FT: is used for signals which is continous and aperiodic...
DFT: is used for signals which is discrete and periodic.....
DTFT: is used for signals which is discrete and aperiodic.....
To calculate FT for a discrete signal is done by just sampling the continous signal and transforming it. And we should make sure that the continous signal is not periodic
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