[Numpy-discussion] interpolating arrays (?)

[Warren Focke]

Would you consider Fourier interpolation?

interpolated = FFT.inverse_real_fft(FFT.real_fft(data), desiredLength) * \
	desiredLength / len(data)

This works whether desiredLength is less or greater than len(data).  The
trick here is that inverse_real_fft discards data or zero-pads at high
frequencies.  I keep toying with the idea of modifying the complex
version to do the same, I cannot imagine a use for the current behavior
(truncate or pad at small negative frequencies).

There can be some pretty wierd edge effects, they can often be defeated
with padding, or, better yet, overlapping segments.  Geting that right
might be harder than fixing your approach.

It has the nice feature that it is information-preserving:  if you
interpolate to a higher number of points, then back to the original, you
should get the same numbers back, give or take a little bit of rounding
error.

Warren Focke

On Mon, 22 Mar 2004, Ray Schumacher wrote:

> Howdy,
>
> I'd like to resize an array (1-dimensional) a of length n into an array of
> n+x, and interpolate the values as necessary.
> x might be+/-200, len(a) is usually ~500
>
> I tried it in pure Python but it's not quite right yet. (rubberBand, below)
> Someone out there must have done this... and linear interpolation for
> values is probably sufficient (instead of bi-cubic or some such)
>
> Cheers,
> Ray
>
>
>
>
> ==================================================================
>          startSlice = 10000
>          endOfSlice =
> 10000+int(round(self.samplesPerRotation))    #self.samplesPerRotation=661
>          ## self.dataArray is about len=200,000 of Int
>
>          for delta in range(-2,3):
>              ## interpolate the different slices to the original length
> 	  ##  0 should return the same array, this is a test
>              newArray = self.rubberBand(
>                                  self.dataArray[startSlice:endOfSlice+delta],
>                                  round(self.samplesPerRotation))
>              print len(self.dataArray[startSlice:endOfSlice+delta]),
> len(newArray),
>              ## show the result
>              print delta, Numeric.sum(self.dataArray[startSlice:endOfSlice]
> - newArray)
>
>      def rubberBand(self, data, desiredLength):
>          """ alias/interpolate the data so that it is adjusted to the
> desired array length"""
>          currentLength = float(len(data))
>
>          ## positive if the new array is to be longer
>          difference = desiredLength - currentLength
>          #print  difference, desiredLength, currentLength
>
>          ## set up the desired length array
>          newData = Numeric.zeros(desiredLength, Numeric.Float)
>
>          ## accounts for binary rounding errors
>          smallNum = 2**-14
>
>          for index in range(desiredLength):
>              ## find the ratio of the current index to the desired length
>              ratio = index / float(desiredLength)
>
>              ## find the same (float) position in the old data
>              currIndex = int(ratio * currentLength)
>              ## find the decimal part
>              decimalPart = (ratio * currentLength) - currIndex
>              print index, currIndex, decimalPart,
>              if(decimalPart>smallNum):
>                  ## interpolate
>                  newData[index] = ((1 - decimalPart) * data[currIndex] +
> decimalPart * data[currIndex+1])
>                  print data[currIndex], data[currIndex+1], newData[index]
>              else:
>                  newData[index] = data[currIndex]
>                  print 'else',data[currIndex], newData[index]
>
>          return newData
>
>
>
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