# Waveform

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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

• 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.
• 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.

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.