217 lines
7.7 KiB
Python
217 lines
7.7 KiB
Python
|
# 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, mode_enum
|
||
|
|
|
||
|
|
__all__ = ['upfirdn', '_output_len']
|
||
|
|
|
||
|
|
_upfirdn_modes = [
|
||
|
|
'constant', 'wrap', 'edge', 'smooth', 'symmetric', 'reflect',
|
||
|
|
'antisymmetric', 'antireflect', 'line',
|
||
|
|
]
|
||
|
|
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
|
||
|
|
def _check_mode(mode):
|
||
|
|
mode = mode.lower()
|
||
|
|
enum = mode_enum(mode)
|
||
|
|
return enum
|
||
|
|
|
||
|
|
|
||
|
|
class _UpFIRDn:
|
||
|
|
"""Helper for resampling."""
|
||
|
|
|
||
|
|
def __init__(self, h, x_dtype, up, down):
|
||
|
|
h = np.asarray(h)
|
||
|
|
if h.ndim != 1 or h.size == 0:
|
||
|
|
raise ValueError('h must be 1-D 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)
|
||
|
|
self._h_trans_flip = np.ascontiguousarray(self._h_trans_flip)
|
||
|
|
self._h_len_orig = len(h)
|
||
|
|
|
||
|
|
def apply_filter(self, x, axis=-1, mode='constant', cval=0):
|
||
|
|
"""Apply the prepared filter to the specified axis of N-D signal x."""
|
||
|
|
output_len = _output_len(self._h_len_orig, x.shape[axis],
|
||
|
|
self._up, self._down)
|
||
|
|
# Explicit use of np.int64 for output_shape dtype avoids OverflowError
|
||
|
|
# when allocating large array on platforms where np.int_ is 32 bits
|
||
|
|
output_shape = np.asarray(x.shape, dtype=np.int64)
|
||
|
|
output_shape[axis] = output_len
|
||
|
|
out = np.zeros(output_shape, dtype=self._output_type, order='C')
|
||
|
|
axis = axis % x.ndim
|
||
|
|
mode = _check_mode(mode)
|
||
|
|
_apply(np.asarray(x, self._output_type),
|
||
|
|
self._h_trans_flip, out,
|
||
|
|
self._up, self._down, axis, mode, cval)
|
||
|
|
return out
|
||
|
|
|
||
|
|
|
||
|
|
def upfirdn(h, x, up=1, down=1, axis=-1, mode='constant', cval=0):
|
||
|
|
"""Upsample, FIR filter, and downsample.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
h : array_like
|
||
|
|
1-D 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.
|
||
|
|
mode : str, optional
|
||
|
|
The signal extension mode to use. The set
|
||
|
|
``{"constant", "symmetric", "reflect", "edge", "wrap"}`` correspond to
|
||
|
|
modes provided by `numpy.pad`. ``"smooth"`` implements a smooth
|
||
|
|
extension by extending based on the slope of the last 2 points at each
|
||
|
|
end of the array. ``"antireflect"`` and ``"antisymmetric"`` are
|
||
|
|
anti-symmetric versions of ``"reflect"`` and ``"symmetric"``. The mode
|
||
|
|
`"line"` extends the signal based on a linear trend defined by the
|
||
|
|
first and last points along the ``axis``.
|
||
|
|
|
||
|
|
.. versionadded:: 1.4.0
|
||
|
|
cval : float, optional
|
||
|
|
The constant value to use when ``mode == "constant"``.
|
||
|
|
|
||
|
|
.. versionadded:: 1.4.0
|
||
|
|
|
||
|
|
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).
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [1] P. P. Vaidyanathan, Multirate Systems and Filter Banks,
|
||
|
|
Prentice Hall, 1993.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
Simple operations:
|
||
|
|
|
||
|
|
>>> import numpy as np
|
||
|
|
>>> 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.])
|
||
|
|
>>> 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])
|
||
|
|
>>> 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])
|
||
|
|
|
||
|
|
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)
|
||
|
|
# This is equivalent to (but faster than) using np.apply_along_axis
|
||
|
|
return ufd.apply_filter(x, axis, mode, cval)
|