scipy.signal.unit_impulse

scipy.signal.unit_impulse(shape, idx=None, dtype=<class 'float'>)

Unit impulse signal (discrete delta function) or unit basis vector.

Parameters

shapeint or tuple of int

Number of samples in the output (1-D), or a tuple that represents the shape of the output (N-D).

idxNone or int or tuple of int or ‘mid’, optional

Index at which the value is 1. If None, defaults to the 0th element. If idx='mid', the impulse will be centered at shape // 2 in all dimensions. If an int, the impulse will be at idx in all dimensions.

dtypedata-type, optional

The desired data-type for the array, e.g., numpy.int8. Default is numpy.float64.

Returns

yndarray

Output array containing an impulse signal.

Notes

The 1D case is also known as the Kronecker delta.

New in version 0.19.0.

Examples

An impulse at the 0th element (\(\delta[n]\)):

>>> from scipy import signal
>>> signal.unit_impulse(8)
array([ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.])

Impulse offset by 2 samples (\(\delta[n-2]\)):

>>> signal.unit_impulse(7, 2)
array([ 0.,  0.,  1.,  0.,  0.,  0.,  0.])

2-dimensional impulse, centered:

>>> signal.unit_impulse((3, 3), 'mid')
array([[ 0.,  0.,  0.],
       [ 0.,  1.,  0.],
       [ 0.,  0.,  0.]])

Impulse at (2, 2), using broadcasting:

>>> signal.unit_impulse((4, 4), 2)
array([[ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  0.]])

Plot the impulse response of a 4th-order Butterworth lowpass filter:

>>> imp = signal.unit_impulse(100, 'mid')
>>> b, a = signal.butter(4, 0.2)
>>> response = signal.lfilter(b, a, imp)

>>> import matplotlib.pyplot as plt
>>> plt.plot(np.arange(-50, 50), imp)
>>> plt.plot(np.arange(-50, 50), response)
>>> plt.margins(0.1, 0.1)
>>> plt.xlabel('Time [samples]')
>>> plt.ylabel('Amplitude')
>>> plt.grid(True)
>>> plt.show()