# Nyquist-Shannon Sampling Theorem

Nyquist-Shannon Sampling Theorem It’s safe to say that the invention of the computer has changed the world we live in forever. Digital technology is so pervasive in modern life that it’s hard to imagine what things were like before this revolution occurred. Digital audio technology has made huge advances in the last 20 years as well. We now have the ability to record and transmit digital audio wirelessly, which is a miracle in and of itself. In this article, we’re going to dig a little deeper into a fundamental theorem in the realm of signal processing that plays an integral […]

# Dynamic Range Control Using Compression

Dynamic Range Control Using Compression Dynamic range compression sounds scary. Almost like some kind of horrible disease or ailment. Fortunately, the concept isn’t as bad (or confusing) as it sounds. Compression is a form of dynamic range control, and an important topic in signal processing, audio engineering, acoustics, and music production. Let’s break it down! Boring Terminology If you’re not a nerd, you may fall asleep reading this. But I’d argue that knowing these things will help you understand compression and other dynamic range control methods. Do not read while driving or operating heavy machinery. Dynamic – describes something that […]

# Harmonics & Additive Synthesis

Harmonics & Additive Synthesis A waveform is a periodic mathematical function (or sum of functions) defined by frequency, amplitude and phase. Frequency is the number of full cycles or periods that the waveform goes through in one second. And a harmonic is a waveform with a frequency that is a perfect integer multiple of the frequency of any given fundamental waveform. When the frequency is not an integer multiple of the fundamental frequency, we call it an inharmonic. Harmonics and inharmonics are both grouped into a larger category that we call partials. Partials are all of the simple component waveforms […]

# Audio Signal Filtering

Audio Signal Filtering Your pool guy would tell you they keep things out of your pool. Your car guy would tell you they keep things out of your engine. Your computational fluid dynamics guy (you have one of those, right?) would tell you they keep things out of your Navier-Stokes equations. And I’d tell you that filters keep things out of your audio signal. Fourier analysis and theory says that a signal (electrical, audio, electromagnetic, etc.) can be decomposed into an infinite number of different sinusoidal waveforms all with different frequencies, amplitudes, and phases. A filter in electrical engineering, communications, […]

# Frequency Modulation

Frequency Modulation Frequency modulation, also known as FM, is a signal processing method used around the world in radio broadcasting, radar, medicine, music production, and a load of other technologies. And yes, that’s what the “FM” stands for in FM radio. But what is it exactly, and how does it work? This article will demystify the concept for you. Modulation The word “modulate” really just means to instantaneously change some property of a signal waveform using a different waveform. When one signal waveform “modulates” another, it changes a property of the signal being modulated. We call the signal being modulated […]

# Waveform Phase & Phase Cancellation

Waveform Phase & Phase Cancellation In order to understand music production, we first need to understand how waveform phase and phase cancellation can effect the interactions between waveforms. Without a fundamental understanding of this subject, it may become difficult to identify and pinpoint phase problems, especially when we’re dealing with audio. Sinusoidal Functions Sine waves are periodic mathematical functions represented by the equation y(t) = A sin(ωt + θ). It may look confusing to those of us who have never been exposed to it, but this equation basically says that the y-value (height) in a time-versus-height graph depends on the […]

# Spectral Analysis & Fast Fourier Transforms

The Fourier Transform Arguably one of the most important developments in applied mathematics in modern times is the Fourier transform. The Fourier transform is a mathematical operation that takes any waveform and breaks it down into individual component sine waves at different frequencies and amplitudes. These are then represented by peaks in a frequency spectrum, and this whole process is called spectral analysis. A waveform as a summation of many simple sine waves is a concept seen in all oscillatory physical phenomena, including electromagnetic radiation, AC electricity, rotational motion, and the most important one for our purposes… sound. Let’s dig […]