Hi Tim, Brilliant! Many thanks... I think this is exactly what I need, I owe you a beer (or other beverage of your choice). I'm now going to lock myself in the basement until I can work out an implementation of this for my use-case :) /Carl On Tue, Sep 3, 2013 at 9:05 PM, Cera, Tim <tim@cerazone.net> wrote:

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=CompareTidalFilt... 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 _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion