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I am making an experiment using sound source and microphones. I use metronome as the sound source, so I can consider it as impulse sound. I placed the microphones at different places about 1 meter above the floor. I use a recording system to get a sound file from each microphone. However I noticed that the acquired sound waveform from each microphone is different. For example let's say that one impulse sound is about 300K samples (48K sampling rate). The waveform of sound in microphone 1 and microphone 2 is similar only about the first 500 samples, mic 1 and mic 3 is similar only about the first 200 samples and so on. My guess that it is caused by the reverberation from the environment. Using Matlab function to find the delay is only good when I use only the first 200 samples.

Question:

  1. Can I consider this as low SNR?
  2. Can I use only the first 200 samples for each impulse sound as to improve the SNR?

Thank you.

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  • $\begingroup$ What are you actually trying to do with the metronome and the 2 microphones? There will be reflections off the walls and the floor. 500 samples is only 3.6 meters. $\endgroup$
    – IanJ
    May 16, 2021 at 19:05

2 Answers 2

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If the SNR is limited by reflections in the room, and the impulse response of the channel from the source to a specific microphone is unknown, then the received signal can be used to determine the impulse response of the channel (together with a known transmitter signal that is spectrally rich in content) and with that equalize the received signal. However 200 samples would likely be far too insufficient for this purpose. In channel equalization we are basically solving for inverse convolution a system of overdetermined equations such that each output (sample) represents a sum of prior samples with unknown weights (which we solve for). These prior samples must extend over the significant duration of the channel impulse response, and then we need several samples to determine a least squared solution: each new sample provides us a new equation, and we would like to have more equations than unknowns as the accuracy of the solution will be improved the more equations we can use -- up to the limits of assumed stationarity in the channel statistics (the channel will change with time, so up to a point further inputs will contribute no further improvement, and then it will actually degrade the result).

200 samples at 48 KSps is only 4.16 ms. I believe typical channel impulse responses for a small room can be in the 100's of ms but I am less familiar with audio engineering to have confidence in that. But to equalize the channel to improve SNR by eliminating reflections/reverb I would recommend determining the impulse response time of the channel and then using at least 5 times more samples than that for the channel estimation with a known spectrally rich signal (white noise such as a maximum length sequence or frequency chirp). The equalization filter itself once the coefficients are determined would be the length of the channel response.

Once all channels are equalized for each microphone, assuming the remaining background noise is white and uncorrelated, further SNR improvement can be gained by coherently summing the microphone outputs: align their delay and sum each signal weighted by the SNR for that microphone for optimal ratio combining. If all microphones have the same SNR, this will provide a $\sqrt{N}$ SNR improvement where $N$ is the number of microphones.

If SNR is not limited by reflections in the room or other coherent sources, then any number of samples from multiple microphones can be added to get the $\sqrt{N}$ SNR gain assuming the coherent signals are aligned and the noise is uncorrelated on each microphone.

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You may be able to get better results by using an MLS signal instead of a metronome impulse and then correlating the mic output to that signal to extract the max possible sample time before a reflection is received; I haven’t done this myself but I believe the result is that you can get the longer sample length needed for low frequency measurements. https://en.m.wikipedia.org/wiki/Maximum_length_sequence

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