Double-sideband suppressed-carrier transmission

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noexcerpt noprint searchaux" style="display:none">Transmission method used in amateur radio</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Double-sideband_suppressed-carrier_transmission" title="Special:EditPage/Double-sideband suppressed-carrier transmission">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable 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Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Double-sideband+suppressed-carrier+transmission%22">"Double-sideband suppressed-carrier transmission"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Double-sideband+suppressed-carrier+transmission%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Double-sideband+suppressed-carrier+transmission%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Double-sideband+suppressed-carrier+transmission%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Double-sideband+suppressed-carrier+transmission%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Double-sideband+suppressed-carrier+transmission%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">September 2019</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p><b>Double-sideband suppressed-carrier transmission</b> (<b>DSB-SC</b>) is <a href="/wiki/Transmission_(telecommunications)" class="mw-redirect" title="Transmission (telecommunications)">transmission</a> in which frequencies produced by <a href="/wiki/Amplitude_modulation" title="Amplitude modulation">amplitude modulation</a> (AM) are symmetrically spaced above and below the <a href="/wiki/Carrier_frequency" class="mw-redirect" title="Carrier frequency">carrier frequency</a> and the carrier level is reduced to the lowest practical level, ideally being completely suppressed.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>In the DSB-SC modulation, unlike in AM, the wave carrier is not transmitted; thus, much of the power is distributed between the side bands, which implies an increase of the cover in DSB-SC, compared to AM, for the same power use. </p><p>DSB-SC transmission is a special case of <a href="/wiki/Double-sideband_reduced_carrier_transmission" class="mw-redirect" title="Double-sideband reduced carrier transmission">double-sideband reduced carrier transmission</a>. It is used for <a href="/wiki/Radio_Data_System" title="Radio Data System">radio data systems</a>. This mode is frequently used in <a href="/wiki/Amateur_radio" title="Amateur radio">amateur radio</a> voice communications, especially on <a href="/wiki/High_frequency" title="High frequency">high-frequency</a> bands </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Spectrum">Spectrum</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-sideband_suppressed-carrier_transmission&action=edit&section=1" title="Edit section: Spectrum"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>DSB-SC is basically an <a href="/wiki/Amplitude_modulation" title="Amplitude modulation">amplitude modulation</a> wave without the carrier, therefore reducing power waste, giving it a 50% efficiency. This is an increase compared to normal AM transmission (DSB) that has a maximum efficiency of 33.333%, since 2/3 of the power is in the carrier which conveys no useful information and both sidebands containing identical copies of the same information. <a href="/wiki/Single-sideband_modulation" title="Single-sideband modulation">Single Side Band Suppressed Carrier</a> (SSB-SC) is 100% efficient. </p><p>Spectrum plot of a DSB-SC signal: <span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Spectrum_DSBSC.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Spectrum_DSBSC.svg/300px-Spectrum_DSBSC.svg.png" decoding="async" width="300" height="230" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Spectrum_DSBSC.svg/450px-Spectrum_DSBSC.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8d/Spectrum_DSBSC.svg/600px-Spectrum_DSBSC.svg.png 2x" data-file-width="300" data-file-height="230" /></a></span> </p> <div class="mw-heading mw-heading2"><h2 id="Generation">Generation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-sideband_suppressed-carrier_transmission&action=edit&section=2" title="Edit section: Generation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>DSB-SC is generated by a mixer. The signal produced is the product of the message signal and a carrier signal. The mathematical representation of this process is shown below, where the <a href="/wiki/Prosthaphaeresis" title="Prosthaphaeresis">product-to-sum trigonometric identity</a> is used. </p> <dl><dd><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 \underbrace {V_{m}\cos \left(\omega _{m}t\right)} _{\mbox{Message}}\times \underbrace {V_{c}\cos \left(\omega _{c}t\right)} _{\mbox{Carrier}}=\underbrace {{\frac {V_{m}V_{c}}{2}}\left[\cos \left(\left(\omega _{m}+\omega _{c}\right)t\right)+\cos \left(\left(\omega _{m}-\omega _{c}\right)t\right)\right]} _{\mbox{Modulated Signal}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Message</mtext> </mstyle> </mrow> </munder> <mo>×</mo> <munder> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Carrier</mtext> </mstyle> </mrow> </munder> <mo>=</mo> <munder> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Modulated Signal</mtext> </mstyle> </mrow> </munder> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \underbrace {V_{m}\cos \left(\omega _{m}t\right)} _{\mbox{Message}}\times \underbrace {V_{c}\cos \left(\omega _{c}t\right)} _{\mbox{Carrier}}=\underbrace {{\frac {V_{m}V_{c}}{2}}\left[\cos \left(\left(\omega _{m}+\omega _{c}\right)t\right)+\cos \left(\left(\omega _{m}-\omega _{c}\right)t\right)\right]} _{\mbox{Modulated Signal}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a5b5ee2d07469277f5a570da3cda5e9ceec01d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.338ex; margin-right: -0.028ex; width:72.404ex; height:9.676ex;" alt="{\displaystyle \underbrace {V_{m}\cos \left(\omega _{m}t\right)} _{\mbox{Message}}\times \underbrace {V_{c}\cos \left(\omega _{c}t\right)} _{\mbox{Carrier}}=\underbrace {{\frac {V_{m}V_{c}}{2}}\left[\cos \left(\left(\omega _{m}+\omega _{c}\right)t\right)+\cos \left(\left(\omega _{m}-\omega _{c}\right)t\right)\right]} _{\mbox{Modulated Signal}}}"></span></dd></dl> <p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DSBSC_Modulation.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/DSBSC_Modulation.svg/399px-DSBSC_Modulation.svg.png" decoding="async" width="399" height="218" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/DSBSC_Modulation.svg/599px-DSBSC_Modulation.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/DSBSC_Modulation.svg/798px-DSBSC_Modulation.svg.png 2x" data-file-width="399" data-file-height="218" /></a></span> </p> <div class="mw-heading mw-heading2"><h2 id="Demodulation">Demodulation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-sideband_suppressed-carrier_transmission&action=edit&section=3" title="Edit section: Demodulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For DSBSC, Coherent Demodulation is done by multiplying the DSB-SC signal with the carrier signal (with the same phase as in the modulation process) just like the modulation process. This resultant signal is then passed through a low pass filter to produce a scaled version of the original message signal. </p> <dl><dd><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 \overbrace {{\frac {V_{m}V_{c}}{2}}\left[\cos \left(\left(\omega _{m}+\omega _{c}\right)t\right)+\cos \left(\left(\omega _{m}-\omega _{c}\right)t\right)\right]} ^{\mbox{Modulated Signal}}\times \overbrace {V'_{c}\cos \left(\omega _{c}t\right)} ^{\mbox{Carrier}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mover> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> </mrow> <mo>⏞</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Modulated Signal</mtext> </mstyle> </mrow> </mover> <mo>×</mo> <mover> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mover> <mrow> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mo>′</mo> </msubsup> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>⏞</mo> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Carrier</mtext> </mstyle> </mrow> </mover> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \overbrace {{\frac {V_{m}V_{c}}{2}}\left[\cos \left(\left(\omega _{m}+\omega _{c}\right)t\right)+\cos \left(\left(\omega _{m}-\omega _{c}\right)t\right)\right]} ^{\mbox{Modulated Signal}}\times \overbrace {V'_{c}\cos \left(\omega _{c}t\right)} ^{\mbox{Carrier}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/10be70e8c2bd5a09722075f8cb9d8dff864915c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.028ex; width:57.309ex; height:9.343ex;" alt="{\displaystyle \overbrace {{\frac {V_{m}V_{c}}{2}}\left[\cos \left(\left(\omega _{m}+\omega _{c}\right)t\right)+\cos \left(\left(\omega _{m}-\omega _{c}\right)t\right)\right]} ^{\mbox{Modulated Signal}}\times \overbrace {V'_{c}\cos \left(\omega _{c}t\right)} ^{\mbox{Carrier}}}"></span> <dl><dd><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 =\left({\frac {1}{2}}V_{c}V'_{c}\right)\underbrace {V_{m}\cos(\omega _{m}t)} _{\text{original message}}+{\frac {1}{4}}V_{c}V'_{c}V_{m}\left[\cos((\omega _{m}+2\omega _{c})t)+\cos((\omega _{m}-2\omega _{c})t)\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mo>′</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <munder> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>original message</mtext> </mrow> </munder> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mo>′</mo> </msubsup> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mrow> <mo>[</mo> <mrow> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>−</mo> <mn>2</mn> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle =\left({\frac {1}{2}}V_{c}V'_{c}\right)\underbrace {V_{m}\cos(\omega _{m}t)} _{\text{original message}}+{\frac {1}{4}}V_{c}V'_{c}V_{m}\left[\cos((\omega _{m}+2\omega _{c})t)+\cos((\omega _{m}-2\omega _{c})t)\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c094a8f49326dd035e8fd8d0d8519b627f2d371" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:76.917ex; height:8.343ex;" alt="{\displaystyle =\left({\frac {1}{2}}V_{c}V'_{c}\right)\underbrace {V_{m}\cos(\omega _{m}t)} _{\text{original message}}+{\frac {1}{4}}V_{c}V'_{c}V_{m}\left[\cos((\omega _{m}+2\omega _{c})t)+\cos((\omega _{m}-2\omega _{c})t)\right]}"></span></dd></dl></dd></dl> <p>The equation above shows that by multiplying the modulated signal by the carrier signal, the result is a scaled version of the original message signal plus a second term. Since <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 \omega _{c}\gg \omega _{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>≫</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{c}\gg \omega _{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a39c058a7e4f4ed3ff9a8b35d1dc52fbdd40a7f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.125ex; height:2.176ex;" alt="{\displaystyle \omega _{c}\gg \omega _{m}}"></span>, this second term is much higher in frequency than the original message. Once this signal passes through a low pass filter, the higher frequency component is removed, leaving just the original message. </p> <div class="mw-heading mw-heading3"><h3 id="Distortion_and_attenuation">Distortion and attenuation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-sideband_suppressed-carrier_transmission&action=edit&section=4" title="Edit section: Distortion and attenuation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>For demodulation, the demodulation oscillator's frequency and phase must be exactly the same as the modulation oscillator's, otherwise, distortion and/or attenuation will occur. </p><p>To see this effect, take the following conditions: </p> <ul><li>Message signal to be transmitted: <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 f(t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bf044fe2fbfc4bd8d6d7230f4108430263f9fd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.927ex; height:2.843ex;" alt="{\displaystyle f(t)}"></span></li> <li>Modulation (carrier) signal: <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 V_{c}\cos(\omega _{c}t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V_{c}\cos(\omega _{c}t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41c2a98213c92a8033c73bc0a2e95feac40df357" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.837ex; height:2.843ex;" alt="{\displaystyle V_{c}\cos(\omega _{c}t)}"></span></li> <li>Demodulation signal (with small frequency and phase deviations from the modulation signal): <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 V'_{c}\cos \left[(\omega _{c}+\Delta \omega )t+\theta \right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mo>′</mo> </msubsup> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>[</mo> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <mi>ω</mi> <mo stretchy="false">)</mo> <mi>t</mi> <mo>+</mo> <mi>θ</mi> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V'_{c}\cos \left[(\omega _{c}+\Delta \omega )t+\theta \right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12d890390bf7ee207d27ce00328ec2150468c1ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.585ex; height:2.843ex;" alt="{\displaystyle V'_{c}\cos \left[(\omega _{c}+\Delta \omega )t+\theta \right]}"></span></li></ul> <p>The resultant signal can then be given by </p> <dl><dd><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 f(t)\times V_{c}\cos(\omega _{c}t)\times V'_{c}\cos \left[(\omega _{c}+\Delta \omega )t+\theta \right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>×</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mi>t</mi> <mo stretchy="false">)</mo> <mo>×</mo> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mo>′</mo> </msubsup> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>[</mo> <mrow> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <mi>ω</mi> <mo stretchy="false">)</mo> <mi>t</mi> <mo>+</mo> <mi>θ</mi> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(t)\times V_{c}\cos(\omega _{c}t)\times V'_{c}\cos \left[(\omega _{c}+\Delta \omega )t+\theta \right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3c390fda8004f4fa5683a61c7ad3d5e2e202532" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.03ex; height:2.843ex;" alt="{\displaystyle f(t)\times V_{c}\cos(\omega _{c}t)\times V'_{c}\cos \left[(\omega _{c}+\Delta \omega )t+\theta \right]}"></span> <dl><dd><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 ={\frac {1}{2}}V_{c}V'_{c}f(t)\cos \left(\Delta \omega \cdot t+\theta \right)+{\frac {1}{2}}V_{c}V'_{c}f(t)\cos \left[(2\omega _{c}+\Delta \omega )t+\theta \right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mo>′</mo> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">Δ</mi> <mi>ω</mi> <mo>⋅</mo> <mi>t</mi> <mo>+</mo> <mi>θ</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mo>′</mo> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>[</mo> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>+</mo> <mi mathvariant="normal">Δ</mi> <mi>ω</mi> <mo stretchy="false">)</mo> <mi>t</mi> <mo>+</mo> <mi>θ</mi> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ={\frac {1}{2}}V_{c}V'_{c}f(t)\cos \left(\Delta \omega \cdot t+\theta \right)+{\frac {1}{2}}V_{c}V'_{c}f(t)\cos \left[(2\omega _{c}+\Delta \omega )t+\theta \right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a68b86960df0e291487bbfb0350006a07bb212c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:63.233ex; height:5.176ex;" alt="{\displaystyle ={\frac {1}{2}}V_{c}V'_{c}f(t)\cos \left(\Delta \omega \cdot t+\theta \right)+{\frac {1}{2}}V_{c}V'_{c}f(t)\cos \left[(2\omega _{c}+\Delta \omega )t+\theta \right]}"></span></dd> <dd><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 {\xrightarrow {\text{After low pass filter}}}{\frac {1}{2}}V_{c}V'_{c}f(t)\cos \left(\Delta \omega \cdot t+\theta \right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>→</mo> <mpadded width="+0.611em" lspace="0.278em" voffset=".15em"> <mtext>After low pass filter</mtext> </mpadded> </mover> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <msubsup> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mo>′</mo> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">Δ</mi> <mi>ω</mi> <mo>⋅</mo> <mi>t</mi> <mo>+</mo> <mi>θ</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\xrightarrow {\text{After low pass filter}}}{\frac {1}{2}}V_{c}V'_{c}f(t)\cos \left(\Delta \omega \cdot t+\theta \right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe91346f478e167200ac0ce87c5c659ea8a56c46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-top: -0.327ex; width:41.712ex; height:5.343ex;" alt="{\displaystyle {\xrightarrow {\text{After low pass filter}}}{\frac {1}{2}}V_{c}V'_{c}f(t)\cos \left(\Delta \omega \cdot t+\theta \right)}"></span></dd></dl></dd></dl> <p>The <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 \cos \left(\Delta \omega \cdot t+\theta \right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mi mathvariant="normal">Δ</mi> <mi>ω</mi> <mo>⋅</mo> <mi>t</mi> <mo>+</mo> <mi>θ</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cos \left(\Delta \omega \cdot t+\theta \right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b3d42244b3bf8654010c3696b9569852a3df5e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.752ex; height:2.843ex;" alt="{\displaystyle \cos \left(\Delta \omega \cdot t+\theta \right)}"></span> terms results in distortion and attenuation of the original message signal. In particular, if the frequencies are correct, but the phase is wrong, contribution from <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 \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> is a constant attenuation factor, also <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 \Delta \omega \cdot t}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ω</mi> <mo>⋅</mo> <mi>t</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \omega \cdot t}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12542ccbb73d375f689bd8a25e88dbb574922850" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.9ex; height:2.176ex;" alt="{\displaystyle \Delta \omega \cdot t}"></span> represents a cyclic inversion of the recovered signal, which is a serious form of distortion. </p><p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:Demodulation_distortion_diagram.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/3/32/Demodulation_distortion_diagram.png" decoding="async" width="532" height="286" class="mw-file-element" data-file-width="532" data-file-height="286" /></a></span> </p> <div class="mw-heading mw-heading2"><h2 id="How_it_works">How it works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-sideband_suppressed-carrier_transmission&action=edit&section=5" title="Edit section: How it works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This is best shown graphically. Below is a message signal that one may wish to modulate onto a carrier, consisting of a couple of sinusoidal components with frequencies respectively 800 Hz and 1200 Hz. </p><p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DSBSC_Message_Signal.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/22/DSBSC_Message_Signal.png" decoding="async" width="491" height="369" class="mw-file-element" data-file-width="491" data-file-height="369" /></a></span> </p><p>The equation for this message signal is <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 s(t)={\frac {1}{2}}\cos \left(2\pi 800t\right)-{\frac {1}{2}}\cos \left(2\pi 1200t\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>π</mi> <mn>800</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>π</mi> <mn>1200</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s(t)={\frac {1}{2}}\cos \left(2\pi 800t\right)-{\frac {1}{2}}\cos \left(2\pi 1200t\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa137509b781c52458d20130d65827c1470b2c4b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:39.096ex; height:5.176ex;" alt="{\displaystyle s(t)={\frac {1}{2}}\cos \left(2\pi 800t\right)-{\frac {1}{2}}\cos \left(2\pi 1200t\right)}"></span>. </p><p>The carrier, in this case, is a plain 5 kHz (<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 c(t)=\cos \left(2\pi 5000t\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>π</mi> <mn>5000</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c(t)=\cos \left(2\pi 5000t\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ed6f9dda3f932501c5549e9c88f2b9538fdd13f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.659ex; height:2.843ex;" alt="{\displaystyle c(t)=\cos \left(2\pi 5000t\right)}"></span>) sinusoid—pictured below. </p><p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DSBSC_Carrier_Signal.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/a/a1/DSBSC_Carrier_Signal.png" decoding="async" width="491" height="369" class="mw-file-element" data-file-width="491" data-file-height="369" /></a></span> </p><p>The modulation is performed by multiplication in the time domain, which yields a 5 kHz carrier signal, whose amplitude varies in the same manner as the message signal. </p><p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DSBSC_Modulated_Output.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/DSBSC_Modulated_Output.png" decoding="async" width="491" height="369" class="mw-file-element" data-file-width="491" data-file-height="369" /></a></span> </p><p><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 x(t)=\underbrace {\cos \left(2\pi 5000t\right)} _{\mbox{Carrier}}\times \underbrace {\left[{\frac {1}{2}}\cos \left(2\pi 800t\right)-{\frac {1}{2}}\cos \left(2\pi 1200t\right)\right]} _{\mbox{Message Signal}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>π</mi> <mn>5000</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Carrier</mtext> </mstyle> </mrow> </munder> <mo>×</mo> <munder> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <munder> <mrow> <mo>[</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>π</mi> <mn>800</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mi>π</mi> <mn>1200</mn> <mi>t</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> <mo>⏟</mo> </munder> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Message Signal</mtext> </mstyle> </mrow> </munder> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x(t)=\underbrace {\cos \left(2\pi 5000t\right)} _{\mbox{Carrier}}\times \underbrace {\left[{\frac {1}{2}}\cos \left(2\pi 800t\right)-{\frac {1}{2}}\cos \left(2\pi 1200t\right)\right]} _{\mbox{Message Signal}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c908bd48c94a484e5cb06c3bf2fa72a3c3e473f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.838ex; margin-right: -0.028ex; width:57.563ex; height:10.509ex;" alt="{\displaystyle x(t)=\underbrace {\cos \left(2\pi 5000t\right)} _{\mbox{Carrier}}\times \underbrace {\left[{\frac {1}{2}}\cos \left(2\pi 800t\right)-{\frac {1}{2}}\cos \left(2\pi 1200t\right)\right]} _{\mbox{Message Signal}}}"></span> </p><p>The name "suppressed carrier" comes about because the carrier signal component is suppressed—it does not appear in the output signal. This is apparent when the spectrum of the output signal is viewed. In the picture shown below we see four peaks, the two peaks below 5000 Hz are the lower sideband (LSB) and the two peaks above 5000 Hz are the upper sideband (USB), but there is no peak at the 5000 Hz mark, which is the frequency of the suppressed carrier. </p><p><span class="mw-default-size" typeof="mw:File"><a href="/wiki/File:DSBSC_Spectrum.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/f/fb/DSBSC_Spectrum.png" decoding="async" width="491" height="369" class="mw-file-element" data-file-width="491" data-file-height="369" /></a></span> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-sideband_suppressed-carrier_transmission&action=edit&section=6" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background: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.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20130306024554/http://www.its.bldrdoc.gov/fs-1037/dir-012/_1791.htm">"double-sideband suppressed-carrier (DSB-SC) transmission"</a>. <i>Federal Standard 1037C</i>. <a href="/wiki/General_Services_Administration" title="General Services Administration">General Services Administration</a>. Archived from <a rel="nofollow" class="external text" href="http://www.its.bldrdoc.gov/fs-1037/dir-012/_1791.htm">the original</a> on 2013-03-06.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Federal+Standard+1037C&rft.atitle=double-sideband+suppressed-carrier+%28DSB-SC%29+transmission&rft_id=http%3A%2F%2Fwww.its.bldrdoc.gov%2Ffs-1037%2Fdir-012%2F_1791.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-sideband+suppressed-carrier+transmission" class="Z3988"></span></span> </li> </ol></div> <p><style data-mw-deduplicate="TemplateStyles:r1041539562">.mw-parser-output .citation{word-wrap:break-word}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}</style><span class="citation FS1037C MS188"><span class="noviewer" typeof="mw:File"><span><img alt="Public Domain" src="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/12px-PD-icon.svg.png" decoding="async" width="12" height="12" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/18px-PD-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/24px-PD-icon.svg.png 2x" data-file-width="196" data-file-height="196" /></span></span> This article incorporates <a href="/wiki/Copyright_status_of_works_by_the_federal_government_of_the_United_States" title="Copyright status of works by the federal government of the United States">public domain material</a> from <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20220122224547/https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm"><i>Federal Standard 1037C</i></a>. <a href="/wiki/General_Services_Administration" title="General Services Administration">General Services Administration</a>. Archived from <a rel="nofollow" class="external text" href="https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm">the original</a> on 2022-01-22.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Federal+Standard+1037C&rft.pub=General+Services+Administration&rft_id=https%3A%2F%2Fwww.its.bldrdoc.gov%2Ffs-1037%2Ffs-1037c.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADouble-sideband+suppressed-carrier+transmission" class="Z3988"></span> (in support of <a href="/wiki/MIL-STD-188" title="MIL-STD-188">MIL-STD-188</a>).</span> </p> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Double-sideband_suppressed-carrier_transmission&action=edit&section=7" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>A DSBSC generation and demodulation instrument is described as side application of a commercial lock-in amplifier in <a rel="nofollow" class="external text" href="http://www.zhinst.com/blogs/sadik/2013/08/dsb-sc/">Double-sideband Suppressed-carrier Modulation</a>.</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Double-sideband_suppressed-carrier_transmission&oldid=1179098221">https://en.wikipedia.org/w/index.php?title=Double-sideband_suppressed-carrier_transmission&oldid=1179098221</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Radio_modulation_modes" title="Category:Radio modulation modes">Radio modulation modes</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Articles_needing_additional_references_from_September_2019" title="Category:Articles needing additional references from September 2019">Articles needing additional references from September 2019</a></li><li><a href="/wiki/Category:All_articles_needing_additional_references" title="Category:All articles needing additional references">All articles needing additional references</a></li><li><a href="/wiki/Category:Wikipedia_articles_incorporating_text_from_the_Federal_Standard_1037C" title="Category:Wikipedia articles incorporating text from the Federal Standard 1037C">Wikipedia articles incorporating text from the Federal Standard 1037C</a></li><li><a href="/wiki/Category:Wikipedia_articles_incorporating_text_from_MIL-STD-188" title="Category:Wikipedia articles incorporating text from MIL-STD-188">Wikipedia articles incorporating text from MIL-STD-188</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 7 October 2023, at 21:37<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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Double-sideband suppressed-carrier transmission - Wikipedia