sound_field_analysis example 1 - Ideal plane wave simulation

In the following notebook, the sound field of a plane wave impinging on a spherical microphone array is generated and visualized, both as an idealized plane wave as well as a "real" wave sampled by a microphone array.

Then, the impulse responses at two different looking direction are extraced using plane wave decomposition and compared. I can be shown that simulating the microphone introduces strong spatial aliasing in higher frequencies.

Setup

Configuration

First, the overall limit for the order in spherical domain is set. A lower order will allow for faster calculation time at a loss of fidelity in the radial spatial domain.

Then, a virtual microphone array that is to be simulated is configured by using three parameters:

• radius of the array
• sphere configuration (open, rigid or dual)
• transducers type (omni or cardioid)

For the spatial sampling, a quadrature grid is be generated using the gen.lebedev() module, which returnes a object holding the positions and weights of a specific Lebedev configuration.

Lastly, the wavetype ('plane') and the direction of the wave are defined. NFFT denotes the number of the FFT bins and fs the sampling frequency used for the simulation.

Simulated array data and radial filters

gen.ideal_wave() returns the spherical fourier coefficiens of a ideal plane wave as captured by an ideal array of the provided configuration. gen.sampled_wave() returns the spherical fourier coefficiens as captured by an simulated real array.

gen.radial_filter() returns the radial filters for the current array configuration, which is identical for both cases.

Visualization

To visualize the plane waves, the spherical fourier coefficients and the generated radial filters are passed to plot.makeMTX() along with a kr bin. The function returns the sound pressure at a resolution of 1 degree, which then can be visualized using plot.plot3D(). Several styles ('shape', 'sphere', 'flat') are available.

Extracting impulse responses

In order to extract the impulse response, a plane wave decomposition (PWD) is performed using process.plane_wave_decomp(). The output in the frequency domain can then simply be transformed to the time domain using process.iFFT(). We can calculate several looking directions at once by supplying a vector of azimuth / colatitude pairs.

For the ideal plane wave, the impulse response will be almost dirac impulse-like in the direction of the plane wave (azimuth = 0°, colatitude = 90°) and almost zero at a 90° angle (like azimuth = 90°, colatitude = 90°). The spatial resampling exhibit strong aliasing above a certain cutoff frequency (see spectrum), which results in temporal smearing in the time domain.

Plot time signal and frequency response