Editing Waveform

{{Short description|Shape and form of a signal}}
{{Other uses}}

[[File:Waveforms.svg|thumb|350px|[[sine wave|Sine]], [[Square wave (waveform)|square]], [[triangle wave|triangle]], and [[sawtooth wave|sawtooth]] waveforms.]]
[[File:440 Hertz Sine Square Saw.wav|right|thumb|A sine, square, and sawtooth wave at 440 Hz]]
[[File:Tearwave.wav|right|thumb|A composite waveform that is shaped like a teardrop.]]
[[File:22b02.wav|right|thumb|A waveform generated by a [[synthesizer]]]]

In [[electronics]], [[acoustics]], and related fields, the '''waveform''' of a [[signal]] is the shape of its [[Graph of a function|graph]] as a function of time, independent of its time and [[Magnitude (mathematics)|magnitude]] [[Scale (ratio)|scale]]s and of any displacement in time.<ref name=techWeb>{{Cite web|title = Waveform Definition|url = http://techterms.com/definition/waveform|website = techterms.com|access-date = 2015-12-09}}</ref><ref>David Crecraft, David Gorham, ''Electronics'', 2nd ed., {{isbn|0748770364}}, CRC Press, 2002, p. 62</ref> ''[[Periodic waveform]]s'' repeat regularly at a constant [[wave period|period]]. The term can also be used for non-periodic or aperiodic signals, like [[chirp]]s and [[pulse (signal processing)|pulse]]s.<ref name="IEV">{{cite web | title=IEC 60050 — Details for IEV number 103-10-02: "waveform" | website=International Electrotechnical Vocabulary | url=https://www.electropedia.org/iev/iev.nsf/display?openform&ievref=103-10-02 | language=ja | access-date=2023-10-18}}</ref>

In electronics, the term is usually applied to time-varying [[voltage]]s, [[electric current|current]]s, or [[electromagnetic field]]s.  In acoustics, it is usually applied to steady periodic [[sound]]s — variations of [[air pressure|pressure]] in air or other media.  In these cases, the waveform is an attribute that is independent of the [[frequency]], [[amplitude]], or [[phase shift]] of the signal.

The waveform of an electrical signal can be visualized with an [[oscilloscope]] or any other device that can capture and plot its value at various times, with suitable [[scale (ratio)|scales]] in the time and value axes.  The [[electrocardiography|electrocardiograph]] is a [[medicine|medical]] device to record the waveform of the electric signals that are associated with the beating of the [[heart]]; that waveform has important [[diagnosis|diagnostic]] value.  [[Waveform generator]]s, which can output a periodic voltage or current with one of several waveforms, are a common tool in electronics laboratories and workshops.

The waveform of a steady periodic sound affects its [[timbre]].  [[Synthesizer]]s and modern [[keyboard (instrument)|keyboards]] can generate sounds with many complex waveforms.<ref name=techWeb/>

== Common periodic waveforms ==

Simple examples of periodic waveforms include the following, where <math>t</math> is [[time]], <math>\lambda</math> is [[wavelength]], <math>a</math> is [[amplitude]] and <math>\phi</math> is [[Phase (waves)|phase]]:

*[[Sine wave]]: <math display="inline">(t, \lambda, a, \phi) = a\sin \frac{2\pi t - \phi}{\lambda}.</math> The amplitude of the waveform follows a [[trigonometric]] sine function with respect to time.
*[[Square wave (waveform)|Square wave]]: <math display="inline">(t, \lambda, a, \phi) = \begin{cases}
a, (t-\phi) \bmod \lambda < \text{duty} \\
-a, \text{otherwise}
\end{cases}.</math> This waveform is commonly used to represent digital information. A square wave of constant [[frequency|period]] contains odd [[harmonic]]s that decrease at −6&nbsp;dB/octave.
*[[Triangle wave]]: <math display="inline">(t, \lambda, a, \phi) = \frac{2a}{\pi} \arcsin \sin \frac{2\pi t - \phi}{\lambda}.</math> It contains odd [[harmonic]]s that decrease at −12&nbsp;dB/octave.
*[[Sawtooth wave]]: <math display="inline">(t,\lambda, a, \phi) = \frac{2a}{\pi} \arctan \tan \frac{2\pi t - \phi}{2\lambda}.</math> 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 [[frequency|period]] contains odd and even [[harmonic]]s that decrease at −6 [[decibel|dB]]/octave.

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]].

Other periodic 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.

==See also==
* [[Arbitrary waveform generator]]
* [[Carrier wave]]
* [[Crest factor]]
* [[Continuous waveform]]
* [[Envelope (music)]]
* [[Frequency domain]]
* [[Phase offset modulation]]
* [[Spectrum analyzer]]
* [[Waveform monitor]]
* [[Waveform viewer]]
* [[Wave packet]]

==References==
{{Reflist}}

==Further reading==
*Yuchuan Wei, Qishan Zhang. ''Common Waveform Analysis: A New And Practical Generalization of Fourier Analysis.'' Springer US, Aug 31, 2000 
* Hao He, [[Jian Li (engineer)|Jian Li]], and [[Peter Stoica|Petre Stoica]]. [http://www.sal.ufl.edu/book/ Waveform design for active sensing systems: a computational approach]. Cambridge University Press, 2012.
* Solomon W. Golomb, and [[Guang Gong]]. [http://www.cambridge.org/us/academic/subjects/computer-science/cryptography-cryptology-and-coding/signal-design-good-correlation-wireless-communication-cryptography-and-radar 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. [http://theses.eurasip.org/theses/573/signal-design-for-active-sensing-and/download/ Signal Design for Active Sensing and Communications]. Uppsala Dissertations from the Faculty of Science and Technology (printed by Elanders Sverige AB), 2014.
* Nadav Levanon, and Eli Mozeson. Radar signals. Wiley. com, 2004.
* Jian Li, and Petre Stoica, eds. Robust adaptive beamforming. New Jersey: John Wiley, 2006.
* Fulvio Gini, Antonio De Maio, and Lee Patton, eds. Waveform design and diversity for advanced radar systems. Institution of engineering and technology, 2012.
* {{cite journal | url=https://ieeexplore.ieee.org/document/4775877 | doi=10.1109/MSP.2008.930416 | bibcode=2009ISPM...26...22B | title=Phase-Coded Waveforms and Their Design | last1=Benedetto | first1=J. J. | last2=Konstantinidis | first2=I. | last3=Rangaswamy | first3=M. | journal=IEEE Signal Processing Magazine | date=2009 | volume=26 | issue=1 | page=22 }}

==External links==
{{Commons category|Waveforms}}
* [http://www.adventurekid.se/akrt/waveforms/ Collection of single cycle waveforms] sampled from various sources

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{{Waveforms}}
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[[Category:Waveforms| ]]