pisces.math_utils.random_fields.generate_white_noise_power_spectrum

pisces.math_utils.random_fields.generate_white_noise_power_spectrum(amplitude: float = 1.0) → Callable

Generate a white-noise (flat) power spectrum function.

A white-noise spectrum is defined by a constant power at all wavenumbers \(k\), i.e.

\[P(k) = A,\]

where \(A\) is the amplitude. This corresponds to a random field with equal variance contributed by all Fourier modes, independent of scale.

Parameters:

amplitude (float, optional) – Constant amplitude \(A\) of the power spectrum. Default is 1.0.

Returns:

A function P(kx, ky, ...) that takes arrays of wavenumber components and returns the constant power spectrum evaluated on that grid.

Return type:

Callable

Examples

from pisces.math_utils.random_fields import generate_white_noise_power_spectrum
L, n = 10.0, 128
k_grid = np.fft.fftfreq(n, d=L/n) * 2 * np.pi
power_spectrum = generate_white_noise_power_spectrum()
ps_array = power_spectrum(k_grid)

import matplotlib.pyplot as plt
plt.loglog(k_grid, ps_array)
plt.xlabel('Wavenumber k')
plt.ylabel('Power Spectrum P(k)')
plt.title('White Noise Power Spectrum')
plt.show()

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