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

Notes

The algorithm is an implementation of the block diagram shown on page 129 of the Vaidyanathan text (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).

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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 :None:None:`"line"` extends the signal based on a linear trend defined by the first and last points along the axis .

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cval : float, optional

The constant value to use when mode == "constant" .

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Returns

y : ndarray

The output signal array. Dimensions will be the same as x except for along :None:None:`axis`, which will change size according to the h, :None:None:`up`, and down parameters.

Upsample, FIR filter, and downsample.

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.]])
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._upfirdn.upfirdn scipy.signal._signaltools.resample_poly

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