Waveform

Overview

A "waveform" is a mathematical or graphical curve used to describe the shape or "form" of a any manner of [wave]. The term "wave" is commonly used to describe a cyclical electromagnetic signal or acoustic signal because of the similarity to "waves" in a body of water.

Basics

At the most basic level, a “sine” waveform represents a single frequency or “pure tone.” Most audio waveforms consist of multiple frequencies with varying phase relationships; which results in a very different shape than a sine wave. Using the technique of Fourier analysis; even complex waveforms can be broken-down into the constituent sine wave components.

For more information on Fourier analysis; click here.

Because the constituent sine waves of a complex waveform add or subtract from each other due their phase relationship; the shape of the waveform can vary over time; even if the amplitude and frequency of the constituent sine waves do not. In a similar manner, even if the waveform consists purely of harmonic frequencies; the phase relationship of each harmonic frequency component will affect the shape of the resulting complex waveform. This is part of the reason why using square waves with a near zero rise-time or extremely short impulses in testing audio circuitry is usually not relevant to circuit performance with audio signals. The only way a "square edge" waveform can exist is if every harmonic frequency remains perfectly "in-phase" with each other, and harmonics extending into the hypersonic frequencies are included. Although it is possible to generate square or square-edge pulse waveforms using a synthesizer or test equipment; real-world music (and most other audio) never contains square edge waveforms because limiting the signal's frequency response will result in a finite rise-time (or in other words a less than infinitely steep slope to the rising edge of the waveform). Virtually all audio is frequency-band limited for a number of reasons; including real limitations in audio performance caused when higher-than-audio frequencies are allowed to pass though audio amplifiers or digital audio converters.

for more information on hypersonic frequencies in digital audio, click here

Examples

Two 1kHz sine waves “in-phase”

The scale for the blue sine wave has been offset slightly to make it possible to see the two waves as separate. This is two complete cycles. It is easy to see the relationship of the period to the frequency as the period of one cycle is 1 millisecond (one one-thousandth of a second) for a 1000 cycle-per-second (or one kilo-Hertz) sine wave.

Period = 1/frequency