Understanding Sound from First Principles: Part 2

Author: Yusuf Brima

Introduction

We have made it thus far. For starters, please check out Part 1, where delved into the underlying principles of sound creation from physical systems that vibrate. It laid the foundation for this and subsequent parts of the series as we walk our way through the layers of abstractions from signals to AI audio systems. Today, we are briefly going to talk about the broad classification of signals (i.e., speech, electric current, electric voltage, EGG recordings e.t.c.). There has been a grounds well of interest in studying the underlying principles of singals in a plethora of STEM (even social sciences are joining the bandwagon so to speak). The goal of this intellectual sprint is to gain a deeper appriciation of the potential applications of AI in sound research leveraging on the already mature body of work there exist in the space of signal processing. It can be quite tempting to follow the andrinaline rush of pursuing end-to-end learning from audio signals introduces phantom problems and less expressive (aka black-boxed models). As you may have realized, using a principled multi-scaled approach that leverages existing domain knowledge in signal processing helps tremendously in building AI models for speech signals. Enough with the motivational speech. Let's get technical!

Sound can be classified into periodic and aperiodic waves. If you are wondering, you have a point. It is because it is derived from signal processing; imagine it as the umbrella that covers all kinds of signals. But our focus here is to study sound not the bells and whistles of signals in general. There are tons of text books, tutorials, you name it, that more than eloquently explain these notions. Our goal is to connect the dots, build the intuition and lay bare the possibility that you could have even discovered some of these algorithms. You may ponder, what is a periodic signal and does it have a connection with period of a wave? An answer to the for is: any sound wave that has a definite pattern and repeats itself at regular intervals can be called a periodic sound wave. There you have it. Suppose you have continuous time signal $ X(t)$ where $t \in \mathbb{R}$.