# [Numpy-discussion] (no subject)

Cera, Tim tim at cerazone.net
Tue Sep 3 21:05:43 EDT 2013

```> 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)[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

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