# Waveform

Waveform quite literally means the shape and form of a signal, such as a wave moving across the surface of water, or the vibration of a plucked string.

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 used loosely to describe the shape of the graph of any periodically varying quantity against time.

## Examples of waveforms

Periodic sound waveforms also have distinctive timbres: see psychoacoustics.

Common waveforms include

• Sine wave: sin(2 π t). The amplitude of the waveform follows a trigonometric sine function with respect to time.
• 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.
• Square wave: saw(x) − saw(x − duty). This waveform is commonly used to represent digital information. It is square wave of constant period contains odd harmonics that fall off at −6 dB/octave.
• Trapezoidal wave: This is a combination of a square wave and a sawtooth wave.
• Triangle wave: (t − 2 floor((t + 1)/2)) (−1)floor((t + 1)/2). This is the integral of the square wave. It contains odd harmonics that fall off at −12 dB/octave.
• Ocean wave: This is a characteristic form of a wave in a liquid medium

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

The Fourier transform describes the composition of distorted waveforms, such that any periodic waveform can be formed by the sum of a fundamental component and harmonic components.

Fourier analysis provides a method for decomposing a measured waveform into its harmonic components. This is readily achieved with a sampling instrument, which samples the waveform using an analog-to-digital converter and then applies a software discrete Fourier transform to find the mix of harmonic components which make up the waveform.

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