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# Waveform

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 Title: Waveform Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Waveform

Sine, square, triangle, and sawtooth waveforms
A sine, square, and sawtooth wave at 440 Hz
A composite waveform that is shaped like a teardrop.

A waveform is the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.

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 a wave as a repeating image on a screen. By extension, the term "waveform" also describes 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 decrease at −6 dB/octave.
• Triangle wave: (t − 2 floor ((t + 1) /2)) (−1)floor ((t + 1) /2). It contains odd harmonics that decrease 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 decrease 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 (possibly infinite) set of fundamental and harmonic components. Finite-energy non-periodic waveforms can be analyzed into sinusoids by the Fourier transform.

## References

• Yuchuan Wei, Qishan Zhang. Common Waveform Analysis: A New And Practical Generalization of Fourier Analysis. Springer US, Aug 31, 2000 - Technology & Engineering

• Hao He, Jian Li, and Petre Stoica. Waveform design for active sensing systems: a computational approach. Cambridge University Press, 2012.
• Solomon W. Golomb, and Guang Gong. Signal design for good correlation: for wireless communication, cryptography, and radar. Cambridge University Press, 2005.
• Jayant, Nuggehally S and Noll, Peter. Digital coding of waveforms: principles and applications to speech and video. Englewood Cliffs, NJ, 1984.
• M. Soltanalian. Signal Design for Active Sensing and Communications. Uppsala Dissertations from the Faculty of Science and Technology (printed by Elanders Sverige AB), 2014.