Extrapolatoin

[narahahn]

Example for modal analysis and sound field extrapolation

• capture the sound field of a monochromatic plane wave by an open circular array

• compute the circular harmonics expansion coefficients up to order N. As shown below, The CHT coefficients pm is obtained by multiplying the regularized radial weights dn with the IDFT of the captured signal p. No matrix computation is needed. The reason for using IDFT (not DFT) is due to our choice of the circular harmonics as np.exp(-1j*n*phi). https://github.com/spatialaudio/sfa-numpy/blob/3da5e01252f40a0ba8df2d701587ca9fcacd6b9e/examples/sound_field_extrapolation_open_circular_array_mono.py#L36-L38

• extrapolate the sound field on 2-dimensional grid points https://github.com/spatialaudio/sfa-numpy/blob/3da5e01252f40a0ba8df2d701587ca9fcacd6b9e/examples/sound_field_extrapolation_open_circular_array_mono.py#L40-L43

• results

CAUTION One line in regularize was commented out so that it works for mono-frequency cases. This issue is being handled in #4. https://github.com/spatialaudio/sfa-numpy/blob/3da5e01252f40a0ba8df2d701587ca9fcacd6b9e/micarray/modal/radial.py#L179-L183

[narahahn]

Additional note: Using IDFT for circular harmonics expansion works only if the microphone array is uniformly distributed on a circle and one of them is placed exactly at phi=0. If there is an angular offset, then a phase shift should be applied to the coefficients.