217 lines
7.7 KiB
Python
217 lines
7.7 KiB
Python
# Code adapted from "upfirdn" python library with permission:
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#
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# Copyright (c) 2009, Motorola, Inc
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#
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# All Rights Reserved.
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#
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# Redistribution and use in source and binary forms, with or without
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# modification, are permitted provided that the following conditions are
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# met:
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#
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# * Redistributions of source code must retain the above copyright notice,
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# this list of conditions and the following disclaimer.
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#
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# * Redistributions in binary form must reproduce the above copyright
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# notice, this list of conditions and the following disclaimer in the
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# documentation and/or other materials provided with the distribution.
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#
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# * Neither the name of Motorola nor the names of its contributors may be
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# used to endorse or promote products derived from this software without
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# specific prior written permission.
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#
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
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# IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
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# THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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import numpy as np
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from ._upfirdn_apply import _output_len, _apply, mode_enum
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__all__ = ['upfirdn', '_output_len']
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_upfirdn_modes = [
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'constant', 'wrap', 'edge', 'smooth', 'symmetric', 'reflect',
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'antisymmetric', 'antireflect', 'line',
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]
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def _pad_h(h, up):
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"""Store coefficients in a transposed, flipped arrangement.
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For example, suppose upRate is 3, and the
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input number of coefficients is 10, represented as h[0], ..., h[9].
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Then the internal buffer will look like this::
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h[9], h[6], h[3], h[0], // flipped phase 0 coefs
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0, h[7], h[4], h[1], // flipped phase 1 coefs (zero-padded)
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0, h[8], h[5], h[2], // flipped phase 2 coefs (zero-padded)
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"""
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h_padlen = len(h) + (-len(h) % up)
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h_full = np.zeros(h_padlen, h.dtype)
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h_full[:len(h)] = h
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h_full = h_full.reshape(-1, up).T[:, ::-1].ravel()
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return h_full
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def _check_mode(mode):
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mode = mode.lower()
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enum = mode_enum(mode)
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return enum
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class _UpFIRDn:
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"""Helper for resampling."""
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def __init__(self, h, x_dtype, up, down):
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h = np.asarray(h)
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if h.ndim != 1 or h.size == 0:
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raise ValueError('h must be 1-D with non-zero length')
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self._output_type = np.result_type(h.dtype, x_dtype, np.float32)
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h = np.asarray(h, self._output_type)
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self._up = int(up)
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self._down = int(down)
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if self._up < 1 or self._down < 1:
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raise ValueError('Both up and down must be >= 1')
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# This both transposes, and "flips" each phase for filtering
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self._h_trans_flip = _pad_h(h, self._up)
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self._h_trans_flip = np.ascontiguousarray(self._h_trans_flip)
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self._h_len_orig = len(h)
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def apply_filter(self, x, axis=-1, mode='constant', cval=0):
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"""Apply the prepared filter to the specified axis of N-D signal x."""
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output_len = _output_len(self._h_len_orig, x.shape[axis],
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self._up, self._down)
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# Explicit use of np.int64 for output_shape dtype avoids OverflowError
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# when allocating large array on platforms where intp is 32 bits.
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output_shape = np.asarray(x.shape, dtype=np.int64)
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output_shape[axis] = output_len
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out = np.zeros(output_shape, dtype=self._output_type, order='C')
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axis = axis % x.ndim
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mode = _check_mode(mode)
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_apply(np.asarray(x, self._output_type),
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self._h_trans_flip, out,
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self._up, self._down, axis, mode, cval)
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return out
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def upfirdn(h, x, up=1, down=1, axis=-1, mode='constant', cval=0):
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"""Upsample, FIR filter, and downsample.
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Parameters
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----------
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h : array_like
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1-D FIR (finite-impulse response) filter coefficients.
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x : array_like
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Input signal array.
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up : int, optional
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Upsampling rate. Default is 1.
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down : int, optional
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Downsampling rate. Default is 1.
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axis : int, optional
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The axis of the input data array along which to apply the
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linear filter. The filter is applied to each subarray along
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this axis. Default is -1.
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mode : str, optional
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The signal extension mode to use. The set
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``{"constant", "symmetric", "reflect", "edge", "wrap"}`` correspond to
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modes provided by `numpy.pad`. ``"smooth"`` implements a smooth
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extension by extending based on the slope of the last 2 points at each
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end of the array. ``"antireflect"`` and ``"antisymmetric"`` are
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anti-symmetric versions of ``"reflect"`` and ``"symmetric"``. The mode
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`"line"` extends the signal based on a linear trend defined by the
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first and last points along the ``axis``.
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.. versionadded:: 1.4.0
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cval : float, optional
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The constant value to use when ``mode == "constant"``.
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.. versionadded:: 1.4.0
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Returns
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-------
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y : ndarray
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The output signal array. Dimensions will be the same as `x` except
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for along `axis`, which will change size according to the `h`,
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`up`, and `down` parameters.
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Notes
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-----
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The algorithm is an implementation of the block diagram shown on page 129
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of the Vaidyanathan text [1]_ (Figure 4.3-8d).
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The direct approach of upsampling by factor of P with zero insertion,
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FIR filtering of length ``N``, and downsampling by factor of Q is
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O(N*Q) per output sample. The polyphase implementation used here is
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O(N/P).
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.. versionadded:: 0.18
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References
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----------
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.. [1] P. P. Vaidyanathan, Multirate Systems and Filter Banks,
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Prentice Hall, 1993.
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Examples
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--------
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Simple operations:
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>>> import numpy as np
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>>> from scipy.signal import upfirdn
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>>> upfirdn([1, 1, 1], [1, 1, 1]) # FIR filter
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array([ 1., 2., 3., 2., 1.])
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>>> upfirdn([1], [1, 2, 3], 3) # upsampling with zeros insertion
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array([ 1., 0., 0., 2., 0., 0., 3.])
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>>> upfirdn([1, 1, 1], [1, 2, 3], 3) # upsampling with sample-and-hold
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array([ 1., 1., 1., 2., 2., 2., 3., 3., 3.])
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>>> upfirdn([.5, 1, .5], [1, 1, 1], 2) # linear interpolation
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array([ 0.5, 1. , 1. , 1. , 1. , 1. , 0.5])
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>>> upfirdn([1], np.arange(10), 1, 3) # decimation by 3
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array([ 0., 3., 6., 9.])
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>>> upfirdn([.5, 1, .5], np.arange(10), 2, 3) # linear interp, rate 2/3
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array([ 0. , 1. , 2.5, 4. , 5.5, 7. , 8.5])
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Apply a single filter to multiple signals:
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>>> x = np.reshape(np.arange(8), (4, 2))
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>>> x
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array([[0, 1],
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[2, 3],
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[4, 5],
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[6, 7]])
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Apply along the last dimension of ``x``:
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>>> h = [1, 1]
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>>> upfirdn(h, x, 2)
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array([[ 0., 0., 1., 1.],
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[ 2., 2., 3., 3.],
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[ 4., 4., 5., 5.],
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[ 6., 6., 7., 7.]])
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Apply along the 0th dimension of ``x``:
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>>> upfirdn(h, x, 2, axis=0)
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array([[ 0., 1.],
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[ 0., 1.],
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[ 2., 3.],
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[ 2., 3.],
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[ 4., 5.],
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[ 4., 5.],
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[ 6., 7.],
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[ 6., 7.]])
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"""
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x = np.asarray(x)
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ufd = _UpFIRDn(h, x.dtype, up, down)
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# This is equivalent to (but faster than) using np.apply_along_axis
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return ufd.apply_filter(x, axis, mode, cval)
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