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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.
"""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
"""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) self._h_trans_flip = np.ascontiguousarray(self._h_trans_flip)
"""Apply the prepared filter to the specified axis of a nD signal x""" output_len = _output_len(len(self._h_trans_flip), x.shape[axis], self._up, self._down) output_shape = np.asarray(x.shape) output_shape[axis] = output_len out = np.zeros(output_shape, dtype=self._output_type, order='C') axis = axis % x.ndim _apply(np.asarray(x, self._output_type), self._h_trans_flip, out, self._up, self._down, axis) return out
"""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) # This is equivalent to (but faster than) using np.apply_along_axis return ufd.apply_filter(x, axis) |