[Numpy-discussion] (no subject)

Carl Canuck carl.canuck.official at gmail.com
Tue Sep 3 22:04:13 EDT 2013


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 at 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=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
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