[Numpy-discussion] (no subject)

[Cera, Tim]

> I am trying to take the rfft of a numpy array, like this:
>>>> my_rfft = numpy.fft.rfft(my_numpy_array)
>
> and replace the amplitudes that can be obtained with:
>
>>>> my_amplitudes = numpy.abs(my_rfft)
>
> with amplitudes from an arbitrary numpy array's rFFT, which is to then be
> converted back using numpy.fft.irfft .  Alternately, some future plans will
> involve having to modify individual array element amplitudes directly based
> on other parameters.  I would think that modifying and re-synthesizing
> signals using FFT is a fairly common use-case, but my attempts at Googling
> example code have been fruitless.

I have FFT transform filter in my tidal analysis package.   See
http://sourceforge.net/apps/mediawiki/tappy/index.php?title=CompareTidalFilters
for a comparison and short description.

See my function below.  My earlier self made some poor variable name
choices.  The 'low_bound' variable is actually where frequencies
greater are set to zero ('factor[freq > low_bound] = 0.0'), then
factor is ramped from 0 at 'low_bound' to 1 at 'high_bound'.  To
filter out tidal signals if your water elevations are hourly then
'low_bound' = 1/30.0 and 'high_bound' = 1/40.0.  Having this gradual
change in the frequency domain rather than an abrupt change makes a
better filter.

def fft_lowpass(nelevation, low_bound, high_bound):
     """ Performs a low pass filter on the nelevation series.
     low_bound and high_bound specifies the boundary of the filter.
     """
     import numpy.fft as F
     if len(nelevation) % 2:
         result = F.rfft(nelevation, len(nelevation))
     else:
         result = F.rfft(nelevation)
     freq = F.fftfreq(len(nelevation))[:len(nelevation)/2]
     factor = np.ones_like(result)
     factor[freq > low_bound] = 0.0

     sl = np.logical_and(high_bound < freq, freq < low_bound)

     a = factor[sl]
     # Create float array of required length and reverse
     a = np.arange(len(a) + 2).astype(float)[::-1]

     # Ramp from 1 to 0 exclusive
     a = (a/a[0])[1:-1]

     # Insert ramp into factor
     factor[sl] = a

     result = result * factor
     print 'result=', len(result)
     relevation = F.irfft(result, len(nelevation))
     print 'result=', len(relevation)
     return relevation


Kindest regards,
Tim