diric — SciPy v1.15.2 Manual (original) (raw)

scipy.special.

scipy.special.diric(x, n)[source]#

Periodic sinc function, also called the Dirichlet function.

The Dirichlet function is defined as:

diric(x, n) = sin(x * n/2) / (n * sin(x / 2)),

where n is a positive integer.

Parameters:

xarray_like

Input data

nint

Integer defining the periodicity.

Returns:

diricndarray

Examples

import numpy as np from scipy import special import matplotlib.pyplot as plt

x = np.linspace(-8np.pi, 8np.pi, num=201) plt.figure(figsize=(8, 8)); for idx, n in enumerate([2, 3, 4, 9]): ... plt.subplot(2, 2, idx+1) ... plt.plot(x, special.diric(x, n)) ... plt.title('diric, n={}'.format(n)) plt.show()

The following example demonstrates that diric gives the magnitudes (modulo the sign and scaling) of the Fourier coefficients of a rectangular pulse.

Suppress output of values that are effectively 0:

np.set_printoptions(suppress=True)

Create a signal x of length m with k ones:

m = 8 k = 3 x = np.zeros(m) x[:k] = 1

Use the FFT to compute the Fourier transform of x, and inspect the magnitudes of the coefficients:

np.abs(np.fft.fft(x)) array([ 3. , 2.41421356, 1. , 0.41421356, 1. , 0.41421356, 1. , 2.41421356])

Now find the same values (up to sign) using diric. We multiply by k to account for the different scaling conventions ofnumpy.fft.fft and diric:

theta = np.linspace(0, 2*np.pi, m, endpoint=False) k * special.diric(theta, k) array([ 3. , 2.41421356, 1. , -0.41421356, -1. , -0.41421356, 1. , 2.41421356])