sincconv.py

#! /usr/bin/python
#
# Gaute Hope (gaute.hope@nersc.no) / 2015
#
# Uses a sinc-kernel to interpolate a discretely sampled signal by convolution.
#

import numpy as np

def conv_upsample (x, k, wn = None):

  """
  Use a convolution filter to resample the signal x with factor k. the
  resulting vector is not k-times bigger, but the sample rate is k-times
  greater.

  wn is window length. default is the length of the input signal.

  """

  if k == 1:
    return x
  elif k < 1:
    raise NotImplementedError ("k < 1")


  n  = len(x)
  nn = (n+1) * k

  if wn is None:
    wn = n

  wn = wn - 1

  sx = np.arange (1/k, wn / 2, 1/k)
  sx = np.r_[-sx[::-1], 0, sx]

  si = np.sinc (sx)

  y = np.zeros ((nn,))
  y[k::k] = x

  y = np.convolve (y, si, 'full')

  j = int(len(si)/2)
  y = y[j:-j]   # cut off convultion residue

  y = y[k:-k+1] # cut off sides outside the orignal first and last
                # sample point

  return y