Modal Beamforming¶
Submodules for modal beamforming
Angular¶
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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)
Radial¶
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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.
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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.
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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.