mple, 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.]])
)