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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 repesent the wave as a repeating image on a CRT 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

Common waveforms include

• Sine wave: sin(2*Pi*t). The amplitude of the waveform follows a trigonometric sine function with respect to time.
• Sawtooth wave: 2*(t - floor(t)) - 1. Looks like the teeth of a saw. Found often in time bases for display scanning. Often 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. A square wave of constant period contains odd harmonics that fall off at -6 dB/octave.
• Trapezoidal wave: combination of a square wave and a sawtooth wave
• Triangle wave: (t - 2*floor((t + 1)/2)) * (-1)floor((t + 1)/2). Integral of the square wave. A triangle wave of constant period contains odd harmonics that fall off at -12 dB/octave.
• Ocean wave: 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 analogue to digital converter and then applies a software discrete Fourier transform to find the mix of harmonic components which make up the waveform.  