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_upfirdn.py
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/
_upfirdn.py
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# Code adapted from "upfirdn" python library with permission:
#
# Copyright (c) 2009, Motorola, Inc
#
# All Rights Reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# * Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# * Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# * Neither the name of Motorola nor the names of its contributors may be
# used to endorse or promote products derived from this software without
# specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
# IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
# THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
import numpy as np
from ._upfirdn_apply import _output_len, _apply
__all__ = ['upfirdn', '_output_len']
def _pad_h(h, up):
"""Store coefficients in a transposed, flipped arrangement.
For example, suppose upRate is 3, and the
input number of coefficients is 10, represented as h[0], ..., h[9].
Then the internal buffer will look like this::
h[9], h[6], h[3], h[0], // flipped phase 0 coefs
0, h[7], h[4], h[1], // flipped phase 1 coefs (zero-padded)
0, h[8], h[5], h[2], // flipped phase 2 coefs (zero-padded)
"""
h_padlen = len(h) + (-len(h) % up)
h_full = np.zeros(h_padlen, h.dtype)
h_full[:len(h)] = h
h_full = h_full.reshape(-1, up).T[:, ::-1].ravel()
return h_full
class _UpFIRDn(object):
def __init__(self, h, x_dtype, up, down):
"""Helper for resampling"""
h = np.asarray(h)
if h.ndim != 1 or h.size == 0:
raise ValueError('h must be 1D with non-zero length')
self._output_type = np.result_type(h.dtype, x_dtype, np.float32)
h = np.asarray(h, self._output_type)
self._up = int(up)
self._down = int(down)
if self._up < 1 or self._down < 1:
raise ValueError('Both up and down must be >= 1')
# This both transposes, and "flips" each phase for filtering
self._h_trans_flip = _pad_h(h, self._up)
def apply_filter(self, x):
"""Apply the prepared filter to a 1D signal x"""
output_len = _output_len(len(self._h_trans_flip), len(x),
self._up, self._down)
out = np.zeros(output_len, dtype=self._output_type)
_apply(np.asarray(x, self._output_type), self._h_trans_flip, out,
self._up, self._down)
return out
def upfirdn(h, x, up=1, down=1, axis=-1):
"""Upsample, FIR filter, and downsample
Parameters
----------
h : array_like
1-dimensional FIR (finite-impulse response) filter coefficients.
x : array_like
Input signal array.
up : int, optional
Upsampling rate. Default is 1.
down : int, optional
Downsampling rate. Default is 1.
axis : int, optional
The axis of the input data array along which to apply the
linear filter. The filter is applied to each subarray along
this axis. Default is -1.
Returns
-------
y : ndarray
The output signal array. Dimensions will be the same as `x` except
for along `axis`, which will change size according to the `h`,
`up`, and `down` parameters.
Notes
-----
The algorithm is an implementation of the block diagram shown on page 129
of the Vaidyanathan text [1]_ (Figure 4.3-8d).
.. [1] P. P. Vaidyanathan, Multirate Systems and Filter Banks,
Prentice Hall, 1993.
The direct approach of upsampling by factor of P with zero insertion,
FIR filtering of length ``N``, and downsampling by factor of Q is
O(N*Q) per output sample. The polyphase implementation used here is
O(N/P).
.. versionadded:: 0.18
Examples
--------
Simple operations:
>>> from scipy.signal import upfirdn
>>> upfirdn([1, 1, 1], [1, 1, 1]) # FIR filter
array([ 1., 2., 3., 2., 1.])
>>> upfirdn([1], [1, 2, 3], 3) # upsampling with zeros insertion
array([ 1., 0., 0., 2., 0., 0., 3., 0., 0.])
>>> upfirdn([1, 1, 1], [1, 2, 3], 3) # upsampling with sample-and-hold
array([ 1., 1., 1., 2., 2., 2., 3., 3., 3.])
>>> upfirdn([.5, 1, .5], [1, 1, 1], 2) # linear interpolation
array([ 0.5, 1. , 1. , 1. , 1. , 1. , 0.5, 0. ])
>>> upfirdn([1], np.arange(10), 1, 3) # decimation by 3
array([ 0., 3., 6., 9.])
>>> upfirdn([.5, 1, .5], np.arange(10), 2, 3) # linear interp, rate 2/3
array([ 0. , 1. , 2.5, 4. , 5.5, 7. , 8.5, 0. ])
Apply a single filter to multiple signals:
>>> x = np.reshape(np.arange(8), (4, 2))
>>> x
array([[0, 1],
[2, 3],
[4, 5],
[6, 7]])
Apply along the last dimension of ``x``:
>>> h = [1, 1]
>>> upfirdn(h, x, 2)
array([[ 0., 0., 1., 1.],
[ 2., 2., 3., 3.],
[ 4., 4., 5., 5.],
[ 6., 6., 7., 7.]])
Apply along the 0th dimension of ``x``:
>>> upfirdn(h, x, 2, axis=0)
array([[ 0., 1.],
[ 0., 1.],
[ 2., 3.],
[ 2., 3.],
[ 4., 5.],
[ 4., 5.],
[ 6., 7.],
[ 6., 7.]])
"""
x = np.asarray(x)
ufd = _UpFIRDn(h, x.dtype, up, down)
return np.apply_along_axis(ufd.apply_filter, axis, x)