# Rotate a signal

import sys
IN_COLAB = 'google.colab' in sys.modules

# Install s2fft and data if running on google colab.
if IN_COLAB:
    !pip install s2fft &> /dev/null

This tutorial demonstrates how to use S2FFT to rotate a signal on the sphere. A signal can be rotated in pixel space, however this can introduce artifacts. The best way to perform a rotation is through spherical harmonic space using the Wigner d-matrices, that is:

• forward spherical harmonic transform

• rotation on the flm coefficients

• inverse spherical harmonic transform

Specifically, we will adopt the sampling scheme of McEwen & Wiaux (2012). For our purposes here we’ll just generate a random bandlimited signal.

import jax
jax.config.update("jax_enable_x64", True)

import numpy as np
import s2fft

L = 128
sampling = "mw"
rng = np.random.default_rng(12346161)
flm = s2fft.utils.signal_generator.generate_flm(rng, L)
f = s2fft.inverse(flm, L)

Execute the rotation steps

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First, we will run the JAX function to compute the spherical harmonic transform of our signal

flm = s2fft.forward_jax(f, L, reality=True)

Now apply the rotation (here pi/2 in each of alpha, beta, gamma) on the harmonic coefficients flm

flm_rotated = s2fft.rotate_flms(flm, L, (np.pi/2, np.pi/2,np.pi/2))

Finally, we will run the JAX function to compute the inverse spherical harmonic transform to get back to pixel space

f_rotated = s2fft.inverse_jax(flm_rotated, L, reality=True)