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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.]])
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