# Waveform: Wikis

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# Encyclopedia

Sine, square, triangle, and sawtooth waveforms
A sine, square, and sawtooth wave at 440 hz

Waveform means the shape and form of a signal such as a wave moving in a solid, liquid or gaseous medium.

In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph of the varying quantity against time or distance. An instrument called an oscilloscope can be used to pictorially represent the wave as a repeating image on a CRT or LCD screen.

By extension of the above, the term 'waveform' is now also sometimes used to describe the shape of the graph of any varying quantity against time.

## Examples of waveforms

Common periodic waveforms include (t is time):

• Sine wave: sin (2 π t). The amplitude of the waveform follows a trigonometric sine function with respect to time.
• Square wave: saw(t) − saw (t − duty). This waveform is commonly used to represent digital information. A square wave of constant period contains odd harmonics that fall off at −6 dB/octave.
• Triangle wave: (t − 2 floor ((t + 1) /2)) (−1)floor ((t + 1) /2). It contains odd harmonics that fall off at −12 dB/octave.
• Sawtooth wave: 2 (t − floor(t)) − 1. This looks like the teeth of a saw. Found often in time bases for display scanning. It is used as the starting point for subtractive synthesis, as a sawtooth wave of constant period contains odd and even harmonics that fall off at −6 dB/octave.

Other waveforms are often called composite waveforms and can often be described as a combination of a number of sinusoidal waves or other basis functions added together.

The Fourier series describes the decomposition of periodic waveforms, such that any periodic waveform can be formed by the sum of a fundamental component and harmonic components. Finite-energy non-periodic waveforms can be analyzed into sinusoids by the Fourier transform.

# Simple English

The waveform is the shape of a wave as it travels. There are many different waveforms. They are usually a shape which is repeated over and over (a "periodic waveform"). A common waveform is the sine wave. It is normally not possible to see a waveform without some device.

## Root mean square

The amplitude of a waveform may change a lot. Even though it changes, the waveform has a root mean square (rms) value. For example: in the UK, the AC mains supply is a sine wave and has a voltage of 240 V. This is an rms voltage. The actual voltage varies:

$V_\left\{\mbox\left\{peak\right\}\right\} = \sqrt 2 \times V_\left\{\mbox\left\{rms\right\}\right\} = \sqrt 2 \times 240 = \pm 339.411255... V$

The amplitude of the sine wave keeps changing from -339.4 V to +339.4 V.

Root mean square is important. It lets us work out many useful things, like power and heating in a wire.

This table has information about working out the rms for some waveforms.

Wave type rms amplitude
Sine wave $A_\left\{\mbox\left\{rms\right\}\right\} = \frac\left\{A_\left\{\mbox\left\{peak\right\}\right\}\right\}\left\{\sqrt 2\right\}$
Square wave $A_\left\{\mbox\left\{rms\right\}\right\} = A_\left\{\mbox\left\{peak\right\}\right\}$
Triangular wave $A_\left\{\mbox\left\{rms\right\}\right\} = \frac\left\{A_\left\{\mbox\left\{peak\right\}\right\}\right\}\left\{\sqrt 3\right\}$