1# Code adapted from "upfirdn" python library with permission: 2# 3# Copyright (c) 2009, Motorola, Inc 4# 5# All Rights Reserved. 6# 7# Redistribution and use in source and binary forms, with or without 8# modification, are permitted provided that the following conditions are 9# met: 10# 11# * Redistributions of source code must retain the above copyright notice, 12# this list of conditions and the following disclaimer. 13# 14# * Redistributions in binary form must reproduce the above copyright 15# notice, this list of conditions and the following disclaimer in the 16# documentation and/or other materials provided with the distribution. 17# 18# * Neither the name of Motorola nor the names of its contributors may be 19# used to endorse or promote products derived from this software without 20# specific prior written permission. 21# 22# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS 23# IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, 24# THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 25# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR 26# CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 27# EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 28# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 29# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF 30# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING 31# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 32# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 33 34import numpy as np 35 36from ._upfirdn_apply import _output_len, _apply, mode_enum 37 38__all__ = ['upfirdn', '_output_len'] 39 40_upfirdn_modes = [ 41 'constant', 'wrap', 'edge', 'smooth', 'symmetric', 'reflect', 42 'antisymmetric', 'antireflect', 'line', 43] 44 45 46def _pad_h(h, up): 47 """Store coefficients in a transposed, flipped arrangement. 48 49 For example, suppose upRate is 3, and the 50 input number of coefficients is 10, represented as h[0], ..., h[9]. 51 52 Then the internal buffer will look like this:: 53 54 h[9], h[6], h[3], h[0], // flipped phase 0 coefs 55 0, h[7], h[4], h[1], // flipped phase 1 coefs (zero-padded) 56 0, h[8], h[5], h[2], // flipped phase 2 coefs (zero-padded) 57 58 """ 59 h_padlen = len(h) + (-len(h) % up) 60 h_full = np.zeros(h_padlen, h.dtype) 61 h_full[:len(h)] = h 62 h_full = h_full.reshape(-1, up).T[:, ::-1].ravel() 63 return h_full 64 65 66def _check_mode(mode): 67 mode = mode.lower() 68 enum = mode_enum(mode) 69 return enum 70 71 72class _UpFIRDn: 73 """Helper for resampling.""" 74 75 def __init__(self, h, x_dtype, up, down): 76 h = np.asarray(h) 77 if h.ndim != 1 or h.size == 0: 78 raise ValueError('h must be 1-D with non-zero length') 79 self._output_type = np.result_type(h.dtype, x_dtype, np.float32) 80 h = np.asarray(h, self._output_type) 81 self._up = int(up) 82 self._down = int(down) 83 if self._up < 1 or self._down < 1: 84 raise ValueError('Both up and down must be >= 1') 85 # This both transposes, and "flips" each phase for filtering 86 self._h_trans_flip = _pad_h(h, self._up) 87 self._h_trans_flip = np.ascontiguousarray(self._h_trans_flip) 88 self._h_len_orig = len(h) 89 90 def apply_filter(self, x, axis=-1, mode='constant', cval=0): 91 """Apply the prepared filter to the specified axis of N-D signal x.""" 92 output_len = _output_len(self._h_len_orig, x.shape[axis], 93 self._up, self._down) 94 # Explicit use of np.int64 for output_shape dtype avoids OverflowError 95 # when allocating large array on platforms where np.int_ is 32 bits 96 output_shape = np.asarray(x.shape, dtype=np.int64) 97 output_shape[axis] = output_len 98 out = np.zeros(output_shape, dtype=self._output_type, order='C') 99 axis = axis % x.ndim 100 mode = _check_mode(mode) 101 _apply(np.asarray(x, self._output_type), 102 self._h_trans_flip, out, 103 self._up, self._down, axis, mode, cval) 104 return out 105 106 107def upfirdn(h, x, up=1, down=1, axis=-1, mode='constant', cval=0): 108 """Upsample, FIR filter, and downsample. 109 110 Parameters 111 ---------- 112 h : array_like 113 1-D FIR (finite-impulse response) filter coefficients. 114 x : array_like 115 Input signal array. 116 up : int, optional 117 Upsampling rate. Default is 1. 118 down : int, optional 119 Downsampling rate. Default is 1. 120 axis : int, optional 121 The axis of the input data array along which to apply the 122 linear filter. The filter is applied to each subarray along 123 this axis. Default is -1. 124 mode : str, optional 125 The signal extension mode to use. The set 126 ``{"constant", "symmetric", "reflect", "edge", "wrap"}`` correspond to 127 modes provided by `numpy.pad`. ``"smooth"`` implements a smooth 128 extension by extending based on the slope of the last 2 points at each 129 end of the array. ``"antireflect"`` and ``"antisymmetric"`` are 130 anti-symmetric versions of ``"reflect"`` and ``"symmetric"``. The mode 131 `"line"` extends the signal based on a linear trend defined by the 132 first and last points along the ``axis``. 133 134 .. versionadded:: 1.4.0 135 cval : float, optional 136 The constant value to use when ``mode == "constant"``. 137 138 .. versionadded:: 1.4.0 139 140 Returns 141 ------- 142 y : ndarray 143 The output signal array. Dimensions will be the same as `x` except 144 for along `axis`, which will change size according to the `h`, 145 `up`, and `down` parameters. 146 147 Notes 148 ----- 149 The algorithm is an implementation of the block diagram shown on page 129 150 of the Vaidyanathan text [1]_ (Figure 4.3-8d). 151 152 The direct approach of upsampling by factor of P with zero insertion, 153 FIR filtering of length ``N``, and downsampling by factor of Q is 154 O(N*Q) per output sample. The polyphase implementation used here is 155 O(N/P). 156 157 .. versionadded:: 0.18 158 159 References 160 ---------- 161 .. [1] P. P. Vaidyanathan, Multirate Systems and Filter Banks, 162 Prentice Hall, 1993. 163 164 Examples 165 -------- 166 Simple operations: 167 168 >>> from scipy.signal import upfirdn 169 >>> upfirdn([1, 1, 1], [1, 1, 1]) # FIR filter 170 array([ 1., 2., 3., 2., 1.]) 171 >>> upfirdn([1], [1, 2, 3], 3) # upsampling with zeros insertion 172 array([ 1., 0., 0., 2., 0., 0., 3., 0., 0.]) 173 >>> upfirdn([1, 1, 1], [1, 2, 3], 3) # upsampling with sample-and-hold 174 array([ 1., 1., 1., 2., 2., 2., 3., 3., 3.]) 175 >>> upfirdn([.5, 1, .5], [1, 1, 1], 2) # linear interpolation 176 array([ 0.5, 1. , 1. , 1. , 1. , 1. , 0.5, 0. ]) 177 >>> upfirdn([1], np.arange(10), 1, 3) # decimation by 3 178 array([ 0., 3., 6., 9.]) 179 >>> upfirdn([.5, 1, .5], np.arange(10), 2, 3) # linear interp, rate 2/3 180 array([ 0. , 1. , 2.5, 4. , 5.5, 7. , 8.5, 0. ]) 181 182 Apply a single filter to multiple signals: 183 184 >>> x = np.reshape(np.arange(8), (4, 2)) 185 >>> x 186 array([[0, 1], 187 [2, 3], 188 [4, 5], 189 [6, 7]]) 190 191 Apply along the last dimension of ``x``: 192 193 >>> h = [1, 1] 194 >>> upfirdn(h, x, 2) 195 array([[ 0., 0., 1., 1.], 196 [ 2., 2., 3., 3.], 197 [ 4., 4., 5., 5.], 198 [ 6., 6., 7., 7.]]) 199 200 Apply along the 0th dimension of ``x``: 201 202 >>> upfirdn(h, x, 2, axis=0) 203 array([[ 0., 1.], 204 [ 0., 1.], 205 [ 2., 3.], 206 [ 2., 3.], 207 [ 4., 5.], 208 [ 4., 5.], 209 [ 6., 7.], 210 [ 6., 7.]]) 211 """ 212 x = np.asarray(x) 213 ufd = _UpFIRDn(h, x.dtype, up, down) 214 # This is equivalent to (but faster than) using np.apply_along_axis 215 return ufd.apply_filter(x, axis, mode, cval) 216