Unit impulse signal in python

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

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

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.

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

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()