`scipy.signal._waveforms:unit_impulse`

source: /scipy/signal/_waveforms.py :584

Signature

def unit_impulse ( shape , idx = None , dtype = <class 'float'> )

Summary

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

Parameters

shape : int or tuple of int: Number of samples in the output (1-D), or a tuple that represents the shape of the output (N-D).
idx : None 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.
dtype : data-type, optional: The desired data-type for the array, e.g., numpy.int8. Default is numpy.float64.

Returns

y : ndarray: Output array containing an impulse signal.

Notes

In digital signal processing literature the unit impulse signal is often represented by the Kronecker delta. ^[1] I.e., a signal $u_{k} [n]$ , which is zero everywhere except being one at the $k$ -th sample, can be expressed as

u_{k} [n] = δ [n - k] \equiv δ_{n, k} .

Furthermore, the unit impulse is frequently interpreted as the discrete-time version of the continuous-time Dirac distribution. ^[2]

Array API Standard Support

unit_impulse 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                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

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

from scipy import signal

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signal.unit_impulse(8)

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

signal.unit_impulse(7, 2)

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2-dimensional impulse, centered:

signal.unit_impulse((3, 3), 'mid')

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Impulse at (2, 2), using broadcasting:

signal.unit_impulse((4, 4), 2)

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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)

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import numpy as np
import matplotlib.pyplot as plt

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plt.plot(np.arange(-50, 50), imp)
plt.plot(np.arange(-50, 50), response)

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plt.margins(0.1, 0.1)

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plt.xlabel('Time [samples]')
plt.ylabel('Amplitude')

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plt.grid(True)
plt.show()

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