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A bit of acoustics and signal processing for audio - Part I


The world of acoustics and signal processing for audio analysis is worth several book-length discussions. We might as well try to give an insight of our intentions within this world since we introduced ourselves in it by picking a digital microphone with a quite nice range of capabilities.

The very first thing we would like to do is to be able to perform weighting on the buffer we receive from the microphone through the I2S. To explain a bit further on what weighting is, it is no more than a transformation from the real-world sound pressure levels (SPL) travelling around in the air to what our ears can perceive. Just that.

Ear model

Image credit: Human hearing - DSP Guide

There are several studies and models of what we actually perceive and, depending on which is used, we have several types of the so called weighting functions. Some of them have been standarised for the purpose of SPL measurement, finding different types like A-weighting (the most common one), B-weighting, D (both in disuse) and others. In the frequency domain, they look like this:

Image credit: A-weighting - Wikipedia

This means that, even if there are high sound pressure levels floating around in the air, we might not hear them just because of the frequency they are at. Normally humans can hear from something around 20Hz to 20kHz, although most adults might not hear anything in out-of-laboratory conditions above 15kHz. Some animals though, can perceive a great range of frequencies, and for example mouses can hear up to 80kHz! So, now we know what this all is about, the I2S microphone is going to help us understand better how beluga whales communicate among themselves

But also! The I2S microphone is interesting in order to understand sources of urban noise pollution since it provides us with a raw SPL buffer we can play with. As well, we can obtain dBA levels (SPL with a-weighting correction) by processing this buffer in several ways and calculate the RMS level of the resulting signal. In Part II we will go through the mathematics of the signal processing itself and talk a bit about FFT, signal filtering and some other geeky stuff!

A bit of acoustics and signal processing for audio - Part II
A bit of acoustics and signal processing for audio - Part III