On Thu, Mar 26, 2009 at 7:17 PM, Michael Gilbert < michael.s.gilb...@gmail.com> wrote:
> On Thu, 26 Mar 2009 16:56:13 -0700 Lutz Maibaum wrote: > > > Hello, > > > > I just started to use python and numpy for some numerical analysis. I > > have a question about the definition of the inverse Fourier transform. > > The user gives the formula (p.180) > > > > x[m] = Sum_k X[k] exp(j 2pi k m / n) > > > > where X[k] are the Fourier coefficients, and n is the length of the > arrays. > > > > The online documentation > > (http://docs.scipy.org/doc/numpy/reference/routines.fft.html), on the > > other hand, states that there is an additional factor of 1/n, which is > > required to make ifft() the inverse of fft(). Is this a misprint in > > the user guide? > > this documentation is saying that the difference between the equations > for the fft and ifft is a factor of 1/n (not the numpy implementations). > if you do > > output = numpy.ifft( numpy.fft( input ) ) > > and you get output = input, then the normalizations are appropriately > weighted. > > the "correct" normalization (from a mathemetician viewpoint) is actually > 1/sqrt (n) so that the fft is the same function as the ifft, but > computer implementations tend not to do this since the sqrt takes a lot > more operations than plain old 1/n. > > mike > _______________________________________________ > Numpy-discussion mailing list > Numpy-discussion@scipy.org > http://mail.scipy.org/mailman/listinfo/numpy-discussion >
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