Sound Field Analysis Toolbox for NumPy/Python

The Sound Field Analysis Toolbox for NumPy/Python provides implementations of various techniques for the analysis of sound fields and beamforming using microphone arrays.

Source code and issue tracker:
https://github.com/spatialaudio/sfa-numpy
License:
MIT – see the file LICENSE for details.
Quick start:
  • Install NumPy, SciPy and for the examples Matplotlib
  • git clone https://github.com/spatialaudio/sfa-numpy.git
  • cd sfa-numpy
  • python setup.py install --user

Usage

Requirements

Obviously, you’ll need Python. We normally use Python 3.x, but it should also work with Python 2.x. NumPy and SciPy are needed for the calculations. If you also want to plot the resulting sound fields, you’ll need matplotlib.

Instead of installing all of them separately, you should probably get a Python distribution that already includes everything, e.g. Anaconda.

How to Get Started

Various examples are located in the directory

Modal Beamforming

Submodules for modal beamforming

Angular

micarray.modal.angular.sht_matrix(N, azi, elev, weights=None)[source]

(N+1)**2 x M SHT matrix

micarray.modal.angular.Legendre_matrix(N, ctheta)[source]

(N+1) x M matrix of weighted Legendre Polynominals 2*n+1/4*pi * P_n(ctheta)

micarray.modal.angular.grid_equal_angle(n)[source]

equi_angular grid on sphere. (cf. Rafaely book, sec.3.2)

micarray.modal.angular.grid_gauss(n)[source]

Gauss-Legendre sampling points on sphere. (cf. Rafaely book, sec.3.3)

Radial

micarray.modal.radial.spherical_pw(N, k, r, setup)[source]

Radial coefficients for a plane wave

Computes the radial component of the spherical harmonics expansion of a plane wave impinging on a spherical array.

\[\mathring{P}_n(k) = 4 \pi i^n b_n(kr)\]
Parameters:
  • N (int) – Maximum order.
  • k (array_like) – Wavenumber.
  • r (float) – Radius of microphone array.
  • setup ({‘open’, ‘card’, ‘rigid’}) – Array configuration (open, cardioids, rigid).
Returns:

numpy.ndarray – Radial weights for all orders up to N and the given wavenumbers.
micarray.modal.radial.spherical_ps(N, k, r, rs, setup)[source]

Radial coefficients for a point source

Computes the radial component of the spherical harmonics expansion of a point source impinging on a spherical array.

\[\mathring{P}_n(k) = 4 \pi (-i) k h_n^{(2)}(k r_s) b_n(kr)\]
Parameters:
  • N (int) – Maximum order.
  • k (array_like) – Wavenumber.
  • r (float) – Radius of microphone array.
  • rs (float) – Distance of source.
  • setup ({‘open’, ‘card’, ‘rigid’}) – Array configuration (open, cardioids, rigid).
Returns:

numpy.ndarray – Radial weights for all orders up to N and the given wavenumbers.
micarray.modal.radial.weights(N, kr, setup)[source]

Radial weighing functions

Computes the radial weighting functions for diferent array types (cf. eq.(2.62), Rafaely 2015).

For instance for an rigid array

\[b_n(kr) = j_n(kr) - \frac{j_n^\prime(kr)}{h_n^{(2)\prime}(kr)}h_n^{(2)}(kr)\]
Parameters:
  • N (int) – Maximum order.
  • kr (array_like) – Wavenumber * radius.
  • setup ({‘open’, ‘card’, ‘rigid’}) – Array configuration (open, cardioids, rigid).
Returns:

numpy.ndarray – Radial weights for all orders up to N and the given wavenumbers.
micarray.modal.radial.regularize(dn, a0, method)[source]

(cf. Rettberg, Spors : DAGA 2014)

micarray.modal.radial.diagonal_mode_mat(bk)[source]

Utilities

micarray.util.norm_of_columns(A, p=2)[source]

Vector p-norm of each column.

micarray.util.coherence_of_columns(A)[source]

Mutual coherence of columns of A.

micarray.util.asarray_1d(a, **kwargs)[source]

Squeeze the input and check if the result is one-dimensional.

Returns a converted to a numpy.ndarray and stripped of all singleton dimensions. Scalars are “upgraded” to 1D arrays. The result must have exactly one dimension. If not, an error is raised.