`scipy.signal._upfirdn:upfirdn`

source: /scipy/signal/_upfirdn.py :108

Signature

   def     upfirdn (    h    ,    x    ,    up    =  1   ,    down    =  1   ,    axis    =  -1   ,    mode    =  constant   ,    cval    =  0     )

Summary

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).

Array API Standard Support

upfirdn has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ⛔                   
JAX                   ⚠️ no JIT             ⛔                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

CuPy only supports mode="constant" and cval=0.0.

See dev-arrayapi for more information.

Examples

Simple operations:

import numpy as np
from scipy.signal import upfirdn

✓

upfirdn([1, 1, 1], [1, 1, 1])   # FIR filter
upfirdn([1], [1, 2, 3], 3)  # upsampling with zeros insertion
upfirdn([1, 1, 1], [1, 2, 3], 3)  # upsampling with sample-and-hold
upfirdn([.5, 1, .5], [1, 1, 1], 2)  # linear interpolation
upfirdn([1], np.arange(10), 1, 3)  # decimation by 3
upfirdn([.5, 1, .5], np.arange(10), 2, 3)  # linear interp, rate 2/3

✗

Apply a single filter to multiple signals:

x = np.reshape(np.arange(8), (4, 2))
x

✓

Apply along the last dimension of ``x``:

h = [1, 1]

✓

upfirdn(h, x, 2)

✗

Apply along the 0th dimension of ``x``:

upfirdn(h, x, 2, axis=0)