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	<h1 id="firstHeading" class="firstHeading" >Waveform</h1>
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		<div id="contentSub"><span class="mw-redirectedfrom">&#160;&#160;(Redirected from <a href="/w/index.php?title=Waveforms&amp;redirect=no" class="mw-redirect" title="Waveforms">Waveforms</a>)</span></div>
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		<div id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><div class="mw-parser-output"><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Waveform_(disambiguation)" class="mw-disambig" title="Waveform (disambiguation)">Waveform (disambiguation)</a>.</div>
<div class="thumb tright"><div class="thumbinner" style="width:352px;"><a href="/wiki/File:Waveforms.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Waveforms.svg/350px-Waveforms.svg.png" decoding="async" width="350" height="299" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Waveforms.svg/525px-Waveforms.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Waveforms.svg/700px-Waveforms.svg.png 2x" data-file-width="620" data-file-height="530" /></a>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Waveforms.svg" class="internal" title="Enlarge"></a></div><a href="/wiki/Sine_wave" title="Sine wave">Sine</a>, <a href="/wiki/Square_wave" title="Square wave">square</a>, <a href="/wiki/Triangle_wave" title="Triangle wave">triangle</a>, and <a href="/wiki/Sawtooth_wave" title="Sawtooth wave">sawtooth</a> waveforms</div></div></div>
<div class="thumb tright"><div class="thumbinner" style="width:222px;"><div class="mediaContainer" style="width:220px"><audio id="mwe_player_0" controls="" preload="none" style="width:220px" class="kskin thumbimage" data-durationhint="6" data-startoffset="0" data-mwtitle="440_Hertz_Sine_Square_Saw.wav" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/25/440_Hertz_Sine_Square_Saw.wav/440_Hertz_Sine_Square_Saw.wav.ogg" type="audio/ogg; codecs=&quot;vorbis&quot;" data-title="Ogg Vorbis" data-shorttitle="Ogg Vorbis" data-transcodekey="ogg" data-width="0" data-height="0" data-bandwidth="82216" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/2/25/440_Hertz_Sine_Square_Saw.wav/440_Hertz_Sine_Square_Saw.wav.mp3" type="audio/mpeg" data-title="MP3" data-shorttitle="MP3" data-transcodekey="mp3" data-width="0" data-height="0" data-bandwidth="144936" /><source src="//upload.wikimedia.org/wikipedia/commons/2/25/440_Hertz_Sine_Square_Saw.wav" type="audio/wav" data-title="Original WAV file (8.45 Mbps)" data-shorttitle="WAV source" data-width="0" data-height="0" data-bandwidth="8448000" /></audio></div>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:440_Hertz_Sine_Square_Saw.wav" class="internal" title="Enlarge"></a></div>A sine, square, and sawtooth wave at 440 Hz</div></div></div>
<div class="thumb tright"><div class="thumbinner" style="width:222px;"><div class="mediaContainer" style="width:220px"><audio id="mwe_player_1" controls="" preload="none" style="width:220px" class="kskin thumbimage" data-durationhint="3" data-startoffset="0" data-mwtitle="Tearwave.wav" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/93/Tearwave.wav/Tearwave.wav.mp3" type="audio/mpeg" data-title="MP3" data-shorttitle="MP3" data-transcodekey="mp3" data-width="0" data-height="0" data-bandwidth="94176" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/93/Tearwave.wav/Tearwave.wav.ogg" type="audio/ogg; codecs=&quot;vorbis&quot;" data-title="Ogg Vorbis" data-shorttitle="Ogg Vorbis" data-transcodekey="ogg" data-width="0" data-height="0" data-bandwidth="105512" /><source src="//upload.wikimedia.org/wikipedia/commons/9/93/Tearwave.wav" type="audio/wav" data-title="Original WAV file (5.64 Mbps)" data-shorttitle="WAV source" data-width="0" data-height="0" data-bandwidth="5644800" /></audio></div>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Tearwave.wav" class="internal" title="Enlarge"></a></div>A composite waveform that is shaped like a teardrop.</div></div></div>
<div class="thumb tright"><div class="thumbinner" style="width:222px;"><div class="mediaContainer" style="width:220px"><audio id="mwe_player_2" controls="" preload="none" style="width:220px" class="kskin thumbimage" data-durationhint="5" data-startoffset="0" data-mwtitle="22b02.wav" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f8/22b02.wav/22b02.wav.ogg" type="audio/ogg; codecs=&quot;vorbis&quot;" data-title="Ogg Vorbis" data-shorttitle="Ogg Vorbis" data-transcodekey="ogg" data-width="0" data-height="0" data-bandwidth="153456" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/f/f8/22b02.wav/22b02.wav.mp3" type="audio/mpeg" data-title="MP3" data-shorttitle="MP3" data-transcodekey="mp3" data-width="0" data-height="0" data-bandwidth="253088" /><source src="//upload.wikimedia.org/wikipedia/commons/f/f8/22b02.wav" type="audio/wav" data-title="Original WAV file (11.29 Mbps)" data-shorttitle="WAV source" data-width="0" data-height="0" data-bandwidth="11289600" /></audio></div>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:22b02.wav" class="internal" title="Enlarge"></a></div>A waveform generated by a <a href="/wiki/Synthesizer" title="Synthesizer">synthesizer</a></div></div></div>
<p>In <a href="/wiki/Electronics" title="Electronics">electronics</a>, <a href="/wiki/Acoustics" title="Acoustics">acoustics</a>, and related fields, the <b>waveform</b> of a <a href="/wiki/Signal" title="Signal">signal</a> is the shape of its <a href="/wiki/Graph_of_a_function" title="Graph of a function">graph</a> as a function of time, independent of its time and <a href="/wiki/Magnitude_(mathematics)" title="Magnitude (mathematics)">magnitude</a> <a href="/wiki/Scale_(ratio)" title="Scale (ratio)">scales</a> and of any displacement in time.<sup id="cite_ref-techWeb_1-0" class="reference"><a href="#cite_note-techWeb-1">&#91;1&#93;</a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2">&#91;2&#93;</a></sup>
</p><p>In electronics, the term is usually applied to <a href="/wiki/Periodic_function" title="Periodic function">periodically</a> varying <a href="/wiki/Voltage" title="Voltage">voltages</a>, <a href="/wiki/Electric_current" title="Electric current">currents</a>, or <a href="/wiki/Electromagnetic_field" title="Electromagnetic field">electromagnetic fields</a>.  In acoustics, it is usually applied to steady periodic <a href="/wiki/Sound" title="Sound">sounds</a>—variations of <a href="/wiki/Air_pressure" class="mw-redirect" title="Air pressure">pressure</a> in air or other media.  In these cases, the waveform is an attribute that is independent of the <a href="/wiki/Frequency" title="Frequency">frequency</a>, <a href="/wiki/Amplitude" title="Amplitude">amplitude</a>, or <a href="/wiki/Phase_shift" class="mw-redirect" title="Phase shift">phase shift</a> of the signal.  The term can also be used for non-periodic signals, like <a href="/wiki/Chirp" title="Chirp">chirps</a> and <a href="/wiki/Pulse_(signal_processing)" title="Pulse (signal processing)">pulses</a>.
</p><p>The waveform of an electrical signal can be visualized in an <a href="/wiki/Oscilloscope" title="Oscilloscope">oscilloscope</a> or any other device that can capture and plot its value at various times, with a suitable <a href="/wiki/Scale_(ratio)" title="Scale (ratio)">scales</a> in the time and value axes.  The <a href="/wiki/Electrocardiography" title="Electrocardiography">electrocardiograph</a> is a <a href="/wiki/Medicine" title="Medicine">medical</a> device to record the waveform of the electric signals that are associated with the beating of the <a href="/wiki/Heart" title="Heart">heart</a>; that waveform has important <a href="/wiki/Diagnosis" title="Diagnosis">diagnostic</a> value.  <a href="/wiki/Waveform_generator" class="mw-redirect" title="Waveform generator">Waveform generators</a>, that can output a periodic voltage or current with one of several waveforms, are a common tool in electronics laboratories and workshops.
</p><p>The waveform of a steady periodic sound affects its <a href="/wiki/Timbre" title="Timbre">timbre</a>.  <a href="/wiki/Synthesizer" title="Synthesizer">Synthesizers</a> and modern <a href="/wiki/Keyboard_(instrument)" class="mw-redirect" title="Keyboard (instrument)">keyboards</a> can generate sounds with many complicated waveforms.<sup id="cite_ref-techWeb_1-1" class="reference"><a href="#cite_note-techWeb-1">&#91;1&#93;</a></sup>
</p>
<div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="#Examples"><span class="tocnumber">1</span> <span class="toctext">Examples</span></a></li>
<li class="toclevel-1 tocsection-2"><a href="#See_also"><span class="tocnumber">2</span> <span class="toctext">See also</span></a></li>
<li class="toclevel-1 tocsection-3"><a href="#References"><span class="tocnumber">3</span> <span class="toctext">References</span></a></li>
<li class="toclevel-1 tocsection-4"><a href="#Further_reading"><span class="tocnumber">4</span> <span class="toctext">Further reading</span></a></li>
<li class="toclevel-1 tocsection-5"><a href="#External_links"><span class="tocnumber">5</span> <span class="toctext">External links</span></a></li>
</ul>
</div>

<h2><span class="mw-headline" id="Examples">Examples</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Waveform&amp;action=edit&amp;section=1" title="Edit section: Examples">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>Simple examples of <b>periodic waveforms</b> include the following, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle t}">
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        <mi>&#x03D5;<!-- ϕ --></mi>
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</p>
<ul><li><a href="/wiki/Sine_wave" title="Sine wave">Sine wave</a><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle (t,\lambda ,a,\phi )=a\sin {\frac {2\pi t-\phi }{\lambda }}}">
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</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09862825292ad564ca2a036f4008127088bc97a5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.005ex; width:26.075ex; height:5.509ex;" alt="{\displaystyle (t,\lambda ,a,\phi )=a\sin {\frac {2\pi t-\phi }{\lambda }}}"/></span>. The amplitude of the waveform follows a <a href="/wiki/Trigonometric" class="mw-redirect" title="Trigonometric">trigonometric</a> sine function with respect to time.</li>
<li><a href="/wiki/Square_wave" title="Square wave">Square wave</a><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle (t,\lambda ,a,\phi )={\begin{cases}a,&amp;(t-\phi ){\bmod {\lambda }}&lt;{\text{duty}}\\-a,&amp;{\text{otherwise}}\end{cases}}}">
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    <annotation encoding="application/x-tex">{\displaystyle (t,\lambda ,a,\phi )={\begin{cases}a,&amp;(t-\phi ){\bmod {\lambda }}&lt;{\text{duty}}\\-a,&amp;{\text{otherwise}}\end{cases}}}</annotation>
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</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ecf05e83ed4ffd11cc1131d11ded8bd9449dd4f7" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:43.048ex; height:6.176ex;" alt="{\displaystyle (t,\lambda ,a,\phi )={\begin{cases}a,&amp;(t-\phi ){\bmod {\lambda }}&lt;{\text{duty}}\\-a,&amp;{\text{otherwise}}\end{cases}}}"/></span>. This waveform is commonly used to represent digital information. A square wave of constant <a href="/wiki/Frequency" title="Frequency">period</a> contains odd <a href="/wiki/Harmonic" title="Harmonic">harmonics</a> that decrease at −6&#160;dB/octave.</li>
<li><a href="/wiki/Triangle_wave" title="Triangle wave">Triangle wave</a><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle (t,\lambda ,a,\phi )={\frac {2a}{\pi }}\arcsin \sin {\frac {2\pi t-\phi }{\lambda }}}">
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</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4418a6b032743e31cb8ee3a7b198945c565d3b78" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.005ex; width:34.423ex; height:5.509ex;" alt="{\displaystyle (t,\lambda ,a,\phi )={\frac {2a}{\pi }}\arcsin \sin {\frac {2\pi t-\phi }{\lambda }}}"/></span>. It contains odd <a href="/wiki/Harmonic" title="Harmonic">harmonics</a> that decrease at −12&#160;dB/octave.</li>
<li><a href="/wiki/Sawtooth_wave" title="Sawtooth wave">Sawtooth wave</a><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle (t,\lambda ,a,\phi )={\frac {2a}{\pi }}\arctan \tan {\frac {2\pi t-\phi }{2\lambda }}}">
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<p>The <a href="/wiki/Fourier_series" title="Fourier series">Fourier series</a> 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 <a href="/wiki/Fourier_transform" title="Fourier transform">Fourier transform</a>.
</p><p>Other periodic waveforms are often called composite waveforms and can often be described as a combination of a number of sinusoidal waves or other <a href="/wiki/Basis_functions" class="mw-redirect" title="Basis functions">basis functions</a> added together.
</p>
<h2><span class="mw-headline" id="See_also">See also</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Waveform&amp;action=edit&amp;section=2" title="Edit section: See also">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<ul><li><a href="/wiki/AC_waveform" class="mw-redirect" title="AC waveform">AC waveform</a></li>
<li><a href="/wiki/Arbitrary_waveform_generator" title="Arbitrary waveform generator">Arbitrary waveform generator</a></li>
<li><a href="/wiki/Crest_factor" title="Crest factor">Crest factor</a></li>
<li><a href="/wiki/Continuous_waveform" class="mw-redirect" title="Continuous waveform">Continuous waveform</a></li>
<li><a href="/wiki/Envelope_(music)" title="Envelope (music)">Envelope (music)</a></li>
<li><a href="/wiki/Frequency_domain" title="Frequency domain">Frequency domain</a></li>
<li><a href="/wiki/Phase_offset_modulation" title="Phase offset modulation">Phase offset modulation</a></li>
<li><a href="/wiki/Spectrum_analyzer" title="Spectrum analyzer">Spectrum analyzer</a></li>
<li><a href="/wiki/Waveform_monitor" title="Waveform monitor">Waveform monitor</a></li>
<li><a href="/wiki/Waveform_viewer" title="Waveform viewer">Waveform viewer</a></li>
<li><a href="/wiki/Wave_packet" title="Wave packet">Wave packet</a></li></ul>
<h2><span class="mw-headline" id="References">References</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Waveform&amp;action=edit&amp;section=3" title="Edit section: References">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<style data-mw-deduplicate="TemplateStyles:r1011085734">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist">
<div class="mw-references-wrap"><ol class="references">
<li id="cite_note-techWeb-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-techWeb_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-techWeb_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r999302996">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://techterms.com/definition/waveform">"Waveform Definition"</a>. <i>techterms.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2015-12-09</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=techterms.com&amp;rft.atitle=Waveform+Definition&amp;rft_id=http%3A%2F%2Ftechterms.com%2Fdefinition%2Fwaveform&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AWaveform" class="Z3988"></span></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">David Crecraft, David Gorham, <i>Electronics</i>, 2nd ed., <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&#160;<a href="/wiki/Special:BookSources/0748770364" title="Special:BookSources/0748770364">0748770364</a>, CRC Press, 2002, p. 62</span>
</li>
</ol></div></div>
<h2><span class="mw-headline" id="Further_reading">Further reading</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Waveform&amp;action=edit&amp;section=4" title="Edit section: Further reading">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<ul><li>Yuchuan Wei, Qishan Zhang. <i>Common Waveform Analysis: A New And Practical Generalization of Fourier Analysis.</i> Springer US, Aug 31, 2000</li>
<li>Hao He, Jian Li, and Petre Stoica. <a rel="nofollow" class="external text" href="http://www.sal.ufl.edu/book/">Waveform design for active sensing systems: a computational approach</a>. Cambridge University Press, 2012.</li>
<li>Solomon W. Golomb, and Guang Gong. <a rel="nofollow" class="external text" href="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</a>. Cambridge University Press, 2005.</li>
<li>Jayant, Nuggehally S and Noll, Peter. <i>Digital coding of waveforms: principles and applications to speech and video</i>. Englewood Cliffs, NJ, 1984.</li>
<li>M. Soltanalian. <a rel="nofollow" class="external text" href="http://theses.eurasip.org/theses/573/signal-design-for-active-sensing-and/download/">Signal Design for Active Sensing and Communications</a>. Uppsala Dissertations from the Faculty of Science and Technology (printed by Elanders Sverige AB), 2014.</li>
<li>Nadav Levanon, and Eli Mozeson. Radar signals. Wiley. com, 2004.</li>
<li>Jian Li, and Petre Stoica, eds. Robust adaptive beamforming. New Jersey: John Wiley, 2006.</li>
<li>Fulvio Gini, Antonio De Maio, and Lee Patton, eds. Waveform design and diversity for advanced radar systems. Institution of engineering and technology, 2012.</li>
<li>John J. Benedetto, Ioannis Konstantinidis, and Muralidhar Rangaswamy. "<a rel="nofollow" class="external text" href="http://ieeexplore.ieee.org/xpl/login.jsp?tp=&amp;arnumber=4775877">Phase-coded waveforms and their design</a>." <i>IEEE Signal Processing Magazine</i>, 26.1 (2009): 22–31.</li></ul>
<h2><span class="mw-headline" id="External_links">External links</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Waveform&amp;action=edit&amp;section=5" title="Edit section: External links">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
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<td class="mbox-image"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="noviewer" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></td>
<td class="mbox-text plainlist">Wikimedia Commons has media related to <i><b><a href="https://commons.wikimedia.org/wiki/Category:Waveforms" class="extiw" title="commons:Category:Waveforms"><span style="">Waveforms</span></a></b></i>.</td></tr>
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<ul><li><a rel="nofollow" class="external text" href="http://www.adventurekid.se/akrt/waveforms/">Collection of single cycle waveforms</a> sampled from various sources</li></ul>
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<ul><li><a href="/wiki/Colors_of_noise" title="Colors of noise">Colors of noise</a></li>
<li><a href="/wiki/Fundamental_frequency" title="Fundamental frequency">Fundamental frequency</a></li>
<li><i><a href="/wiki/Jivari" title="Jivari">Jivari</a></i></li>
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<li><a href="/wiki/Microtonal_music" title="Microtonal music">Microinflection</a></li>
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<li><a href="/wiki/Rustle_noise" title="Rustle noise">Rustle noise</a></li>
<li><i><a href="/wiki/Sawari" title="Sawari">Sawari</a></i></li>
<li><a href="/wiki/Spectral_envelope" title="Spectral envelope">Spectral envelope</a></li>
<li><a href="/wiki/Sympathetic_string" title="Sympathetic string">Sympathetic string</a></li>
<li><a href="/wiki/Tonality" title="Tonality">Tonality</a></li>
<li><a class="mw-selflink selflink">Waveform</a></li></ul>
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<ul><li><a href="/wiki/Sine_wave" title="Sine wave">Sine wave</a></li>
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<ul><li><a href="/wiki/Pulse_wave" title="Pulse wave">Rectangular wave</a></li>
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<li><a href="/wiki/Square_wave" title="Square wave">Square wave</a></li>
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