Add functions fftfreq, rfftfreq #33
Merged
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This PR adds two functions that return the integer frequency (or wavenumber) values involved in the discrete Fourier transform performed, in the same order as the Fourier coefficients are returned by the corresponding transform calls. In particular,
fftfreq(n)returns the frequency values that correspond to the coefficients calculated byfft(n)or equivalentlyzfftf(n, ...), in the standard order (zero frequency first).rfftfreq(n)returns the frequency values that correspond to the coefficients calculated byrfft(n)or equivalentlydfftf(n, ...), in the standard order (zero frequency first).My main motivation for writing
fftfreqis its use in spectral methods for integrating PDEs, where multiplying the original Fourier coefficients by the imaginary unit and their frequencies is used to calculate the Fourier coefficients of the derivative of the original data. That property is also employed in two of the tests included forfftfreq.Note that the functions return the integer frequency values; they do not divide by the FFT's length. Returning integer values also has the benefit that when/if multiplied by the user's real or complex data, the result gets automatically promoted to the real or complex precision used.
All tests run successfully in my local build.