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The Matlab fast Fourier transform
<fft> of a linearly discrete function y(fn) of the frequency fn
with steps of df, is a linearly discrete function
Y(tn) of the time tn (impulse response) with steps of dt, n Î [1..N]. With the inverse
Fourier transform <ifft>, y(fn) is calculated from Y(tn).
Optimal calculation is found when N=2m, m integer. To obtain a
linear scale from negative to positive positions, the Matlab function
<fftshift> has to be applied to the discrete Fourier transform, i.e.
<fftshift(fft)> or <fftshift(ifft)>. The definition of fn
and tn are
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(D-12) |
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(D-13) |
The relation between df and dt are
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(D-14) |
If fn (or tn) is
not symmetric across zero, a constant phase shift factor is added to the
Fourier or inverse Fourier transform. To increase the Fourier transform
resolution, padding with zeros is possible directly with Matlab by calling the
function with a size parameter, i.e. <fft(y(tn),M)>. In this case, the
number M replace the parameter N in the equations (D-12), (D-14)
and (D-13). It should be remembered that the maximal frequency that can
be found by iFFT is determined by dt
as fN=1/dt.
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