Microphone spotformer

This code is the matlab implementation of a microphone spotformer. A microphone spotformer is basically a beamformer that attempts to attenuate or amplify sounds from certain regions-of-interest.

Overview

As input, the spotformer takes the target locations, the interfer locations and the microphone locations. Some additional user parameters are required as well, such as the size of the region. The inputs are used to construct a spatial correlation or covariance matrix. These matrices are used to minimise the energy from the interferer regions with respect to that from the target regions.

A few examples are provided.

• Example 1: An anechoic scenario with a single interferer and a single target source. The weights are precomputed. This is handy when needing to reuse the same weights for multiple sound excerpts.
• Example 2: A slightly reverberant (T60 $\approx$ 120 ms) scenario with a single interferer and a single target source. The weights are computed when using the spotformer.
• Example 3: A more reverberant scenario (T60 $\approx$ 300 ms) with one interfer and one target source.
• Example 4: A slightly reverberant scenario (T60 $\approx$ 120 ms) with four interferers and two target sources.

All examples use eight microphones and have white Gaussian noise at the interferers. Note that other types of playback signal and different numbers of microphones also work. Audio excerpts of the examples can be found in the folder Example_Audio

The covariance matrices are computed through spatial integration. For this, a numerical integration method is needed. I used the Fast Clenshaw-Curtis quadrature function by G. von Winckel, published under a permissive license. Note that this is a different integration method than that used in the original paper ([1]). I did some small experiments (nothing on which you can draw a definitive conclusion!) and it appeared that the Clenshaw-Curtis quadrature gave more accurate results than the Gauss-Hermite quadrature method used in [1] (though it should be noted that they integrate over a different range). It is also worth investigating the accuracy at higher frequencies, since these methods do not deal very well with oscillatory integrals.

The code was tested on Ubuntu, MATLAB R2024a.

How to use the spotformer

Using the microphone spotformer is relatively straightforward and consists of three steps:

• Initialising the spotformer object;
• Computing the microphone weights given a microphone location, target location, and interferer location;
• Applying the microphone weights to compute the output signal.

Performing these steps looks as follows:

Spotformer = MicSpotformer(c, fs, window_length, pad_length, N_int, IntWinRad, TarWinRad, nSigma2, numSigma2, rebRatio, flag_full_axis, analysis_window, synthesis_window)
Spotformer.fnc_comp_weights(location_interferer, location_target, location_microphone)
output_audio = Spotformer.comp_output(received_audio)

With:

• c: the speed of sound. Usually c=343 meters/second.
• fs: the sampling rate. For speech, often fs=16000 samples/second (or Hz).
• window_length: the length of the speech segments. Usually a single segment is about 16 ms, so window_length=0.016 seconds.
• pad_length: the padding length. I used 16 ms here as well. So pad_length=0.016 seconds.
• N_int: the integrals involved in computing the spatial covariance matrices are computed numerically. N is the number of integration points per dimension and there is a trade-off between accuracy and speed. I typically use N=10 or N=20.
• IntWinRad and TarWinRad. The spatial covariance matrices are defined through a Gaussian distribution. The distribution effectively allows you to indicate how sure you are about the position of the targer and the interferer. TarWinRad and IntWinRad are the $3\sigma$ values of the distribution. Typically they are about 0.2 m to 0.5 m.
• nSigma2: can be used for setting microphone self-noise. Effectively adds a scaled identity matrix to the spatial covariance matrices.
• numSigma2: regularisation term (I usually use numSigma2=1e-10). Ensures matrices are positive definite in presence of numerical inaccuracies.
• rebRatio: allows for setting the direct-to-reverberant ratio of the covariance matrix describing the late-reverberation. At the moment it is a scalar, but ideally it should be frequency dependent.
• flag_full_axis: set to true to use the full frequency axis instead of the half frequency axis. I'm not sure if I tested for true.
• analysis_window: window for framing input audio. Only analysis_window = sqrthann is possible.
• synthesis_window: window for synthesising output audio. Only synthesis_window = sqrthann is possible.
• location_interferer, location_target, location_microphone: The locations of the microphones, targets and interferes in meters. Each location is a matrix of size $N_\text{{interferer, target, microphone}}\times 3$. Typically, you have more microphones than targets and interferers, i.e. $N_\text{mic}>N_\text{target} + N_\text{interferer}$.
• received_audio: the received audio is the microphone signal as an $\text{lengthAudio}\times N_\text{microphones}$ matrix.
• output_audio: this is the output of the spotformer and is a $\text{lengthAudio}\times 1$ vector.

Licensing

The examples make use of the room-impulse response generator from E. Habets (MIT license). You might need to compile this for your system. The sound excerpt is taken from the movie 'Sprite Fight' by Blender Studio (Creative Commons Attribution 1.0 License).

Citation information

The spotformer implemented in this repository is my interpretation of the following paper:

[1] J. Martinez, N. Gaubitch and W. B. Kleijn, "A robust region-based near-field beamformer," 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , South Brisbane, QLD, Australia, 2015, pp. 2494-2498, doi: 10.1109/ICASSP.2015.7178420.

Please cite them if you use this implementation. Citation information:

@INPROCEEDINGS{7178420,
  author={Martinez, Jorge and Gaubitch, Nikolay and Kleijn, W. Bastiaan},
  booktitle={2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, 
  title={A robust region-based near-field beamformer}, 
  year={2015},
  volume={},
  number={},
  pages={2494-2498},
  keywords={Robustness;Microphones;Speech;Reverberation;Arrays;Array signal processing;near-field beamformer;generalized eigenvalue problem;robust beamformer;microphone arrays;reverberation},
  doi={10.1109/ICASSP.2015.7178420}}

We used a variant of this implementation in our ICASSP paper "Loudspeaker Beamforming to Enhance Speech Recognition Performance of Voice Driven Applications". If you use this implementation please consider citing us. Citation information:

@INPROCEEDINGS{10889702,
  author={de Groot, D. and Karslioglu, B. and Scharenborg, O. and Martinez, J.},
  booktitle={ICASSP 2025 - 2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  title={Loudspeaker Beamforming to Enhance Speech Recognition Performance of Voice Driven Applications},
  year={2025},
  volume={},
  number={},
  pages={1-5},
  keywords={Loudspeakers;Performance evaluation;Acoustic distortion;Array signal processing;Signal processing algorithms;Acoustics;Robustness;Distortion measurement;Speech processing;Automatic speech recognition;Spotforming;beamforming;speech recognition}
  doi={10.1109/ICASSP49660.2025.10889702}}