SherbyNet - /page/wikibook/entry.mu

<!DOCTYPE html>

<title>Signal transfer function</title>

</head>

<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Signal transfer function</span></span>

</h1>

</header>

<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>The <b>signal transfer function</b> (<b>SiTF</b>) is a measure of the <a href="Signal_(electrical_engineering)" class="mw-redirect" title="Signal (electrical engineering)">signal output</a> versus the <a href="Signal_(electrical_engineering)" class="mw-redirect" title="Signal (electrical engineering)">signal input</a> of a system such as an <a href="Infrared" title="Infrared">infrared</a> system or <a href="Sensor" title="Sensor">sensor</a>. There are many general applications of the SiTF. Specifically, in the field of image analysis, it gives a measure of the <a href="Noise" title="Noise">noise</a> of an imaging system, and thus yields one assessment of its performance.<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>

<div class="mw-heading mw-heading2"><h2 id="SiTF_evaluation">SiTF evaluation</h2></div>

<p>In evaluating the SiTF curve, the signal input and signal output are measured <a href="Differential_(infinitesimal)" class="mw-redirect" title="Differential (infinitesimal)">differentially</a>; meaning, the differential of the input signal and differential of the output signal are calculated and plotted against each other. An operator, using computer software, defines an arbitrary area, with a given set of data points, within the signal and <a href="Background_radiation" title="Background radiation">background</a> regions of the output image of the infrared sensor, i.e. of the unit under test (UUT), (see "Half Moon" image below). The average signal and background are calculated by averaging the data of each arbitrarily defined region. A <a href="Polynomial" title="Polynomial">second order polynomial</a> curve is <a href="Curve_fitting" title="Curve fitting">fitted</a> to the data of each <a href="Line_(video)" class="mw-redirect" title="Line (video)">line</a>. Then, the polynomial is subtracted from the average signal and background data to yield the new signal and background. The difference of the new signal and background data is taken to yield the net signal. Finally, the net signal is plotted versus the signal input. The signal input of the UUT is within its own spectral response. (e.g. <a href="Color_temperature" title="Color temperature">color-correlated temperature</a>, <a href="Pixel" title="Pixel">pixel</a> intensity, etc.). The slope of the linear portion of this curve is then found using <a href="Least_squares" title="Least squares">the method of least squares</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="SiTF_curve">SiTF curve</h2></div>

<p>The net signal is calculated from the average signal and background, as in <a href="Signal_to_noise_ratio_(imaging)" class="mw-redirect" title="Signal to noise ratio (imaging)">signal to noise ratio (imaging)#Calculations</a>.

The SiTF curve is then given by the signal output data, (net signal data), plotted against the signal input data (see graph of SiTF to the right). All the data points in the linear region of the SiTF curve can be used in the method of <a href="Least_squares" title="Least squares">least squares</a> to find a linear approximation. Given <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\,}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n\,}</annotation>

</semantics>

</math></span><img src="./205e33e6845813cc72ca346b896a7945f90ca373.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.782ex; height:1.676ex;" alt="{\displaystyle n\,}" loading="lazy"></span> data points <span class="mwe-math-element mwe-math-element-inline"><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_{i}\,,y_{i}\,)}">

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle (x_{i}\,,y_{i}\,)}</annotation>

</semantics>

</math></span><img src="./be30494b11a6d4aa07ddc75948ce72ecd91729ff.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.686ex; height:2.843ex;" alt="{\displaystyle (x_{i}\,,y_{i}\,)}" loading="lazy"></span> a best fit line parameterized as <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=mx+b\,}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle y=mx+b\,}</annotation>

</semantics>

</math></span><img src="./47b2eec92c8434787099970aaba86e3b676b0b2e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.849ex; height:2.509ex;" alt="{\displaystyle y=mx+b\,}" loading="lazy"></span> is given by:<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>

</p>

<mfrac>

<mrow>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

<mrow>

<mfrac>

<mrow>

</mrow>

</mrow>

</msubsup>

</mrow>

</mfrac>

</mrow>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

<msup>

</mrow>

</msup>

</mrow>

</mfrac>

</mrow>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle m={\frac {{\frac {\sum x_{i}y_{i}}{n}}-{\frac {\sum x_{i}}{n}}{\frac {\sum y_{i}}{n}}}{{\frac {\sum x_{i}^{2}}{n}}-({\frac {\sum x_{i}}{n}})^{2}}}\qquad \qquad b={\frac {\sum y_{i}}{n}}-m{\frac {\sum x_{i}}{n}}}</annotation>

</semantics>

</math></span><img src="./9bcb7723b5bd027f947a8eb4fd8fce62627dd94a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.171ex; width:53.371ex; height:9.176ex;" alt="{\displaystyle m={\frac {{\frac {\sum x_{i}y_{i}}{n}}-{\frac {\sum x_{i}}{n}}{\frac {\sum y_{i}}{n}}}{{\frac {\sum x_{i}^{2}}{n}}-({\frac {\sum x_{i}}{n}})^{2}}}\qquad \qquad b={\frac {\sum y_{i}}{n}}-m{\frac {\sum x_{i}}{n}}}" loading="lazy"></span></dd></dl>

<ul><li><a href="Optical_transfer_function" title="Optical transfer function">Optical transfer function</a></li>

<li><a href="Distortion" title="Distortion">Distortion</a></li>

<li><a href="Minimum_resolvable_temperature_difference" title="Minimum resolvable temperature difference">Minimum resolvable temperature difference</a></li>

<li><a href="Noise_equivalent_temperature_difference" class="mw-redirect" title="Noise equivalent temperature difference">Noise equivalent temperature difference</a></li>

<li><a href="Power_spectral_density" class="mw-redirect" title="Power spectral density">Power spectral density</a></li>

<li><a href="Minimum_resolvable_contrast" title="Minimum resolvable contrast">Minimum resolvable contrast</a></li>

<li><a href="Signal_to_noise_ratio_(imaging)" class="mw-redirect" title="Signal to noise ratio (imaging)">Signal to noise ratio (imaging)</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

/* start https://en.wikipedia.org/ */

.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("./mw/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("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/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}}

/* end https://en.wikipedia.org/ */

</style><cite id="CITEREFTom_L._Williams1998" class="citation book cs1">Tom L. Williams (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-luzt97NKLEC&q=SiTF+signal-transfer-function+input-and-output&pg=PA247"><i>The Optical Transfer Function of Imaging Systems</i></a>. CRC Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-7503-0599-1</bdi>.</cite></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"><a rel="nofollow" class="external text" href="http://www.electro-optical.com/eoi_page.asp?h=Education">Electro Optical Industries, Inc.(2005). EO TestLab Methodology. In <i>Education</i>.</a></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a href="Edward_Aboufadel" title="Edward Aboufadel">Aboufadel, E. F.</a>, Goldberg, J. L., Potter, M. C. (2005).<i>Advanced Engineering Mathematics (3rd ed.).</i>New York, New York: Oxford University Press</span>

</li>

</ol></div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external free" href="http://www.electro-optical.com">http://www.electro-optical.com</a></li></ul></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2021-05-22" href="https://en.wikipedia.org/wiki/?title=Signal_transfer_function&oldid=1024444289">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

</div>

</div></div>

</div>

</main>

</div>

</body></html>