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mathmlben

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Visualization for goldstandard

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="left-parenthesis f asterisk g right-parenthesis left-parenthesis t right-parenthesis equals Overscript normal d normal e normal f Endscripts integral Subscript negative normal infinity Superscript normal infinity Baseline f left-parenthesis tau right-parenthesis g left-parenthesis t minus tau right-parenthesis d tau"> <semantics> <mrow data-semantic-type="relseq" data-semantic-role="equality" data-semantic-id="50" data-semantic-children="49,47" data-semantic-content="15"> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="49" data-semantic-children="35,36" data-semantic-content="48" data-semantic-parent="50"> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="35" data-semantic-children="34" data-semantic-content="0,4" data-semantic-parent="49"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="0" data-semantic-parent="35" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="multiplication" data-semantic-id="34" data-semantic-children="1,3" data-semantic-content="2" data-semantic-parent="35"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="1" data-semantic-parent="34">f</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="2" data-semantic-parent="34" data-semantic-operator="infixop,∗"><!-- ∗ --> </mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="3" data-semantic-parent="34">g</mi> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="4" data-semantic-parent="35" data-semantic-operator="fenced">)</mo> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="48" data-semantic-parent="49" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="36" data-semantic-children="6" data-semantic-content="5,7" data-semantic-parent="49"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="5" data-semantic-parent="36" data-semantic-operator="fenced">(</mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="6" data-semantic-parent="36">t</mi> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="7" data-semantic-parent="36" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-REL"> <mover data-semantic-type="overscore" data-semantic-role="equality" data-semantic-id="15" data-semantic-children="8,14" data-semantic-parent="50" data-semantic-embellished="relation" data-semantic-operator="relseq,="> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="8" data-semantic-parent="15">=</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="14" data-semantic-children="9,10,11" data-semantic-content="12,13" data-semantic-parent="15"> <mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="9" data-semantic-parent="14">d</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="12" data-semantic-parent="14" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="10" data-semantic-parent="14">e</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="13" data-semantic-parent="14" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="normal" data-semantic-id="11" data-semantic-parent="14">f</mi> </mrow> </mrow> </mover> </mrow> </mrow> <mrow data-semantic-type="integral" data-semantic-role="integral" data-semantic-id="47" data-semantic-children="21,46,43" data-semantic-content="16" data-semantic-parent="50"> <msubsup data-semantic-type="limboth" data-semantic-role="integral" data-semantic-id="21" data-semantic-children="16,19,20" data-semantic-parent="47"> <mo data-semantic-type="largeop" data-semantic-role="integral" data-semantic-id="16" data-semantic-parent="21" data-semantic-operator="integral"><!-- ∫ --> </mo> <mrow class="MJX-TeXAtom-ORD" data-semantic-type="prefixop" data-semantic-role="negative" data-semantic-id="19" data-semantic-children="18" data-semantic-content="17" data-semantic-parent="21"> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="17" data-semantic-parent="19" data-semantic-operator="prefixop,−"><!-- − --> </mo> <mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-id="18" data-semantic-parent="19"><!-- ∞ --> </mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal" data-semantic-type="identifier" data-semantic-role="unknown" data-semantic-font="normal" data-semantic-id="20" data-semantic-parent="21"><!-- ∞ --> </mi> </mrow> </msubsup> <mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="46" data-semantic-children="41,26,39" data-semantic-content="44,45" data-semantic-parent="47"> <mrow data-semantic-type="appl" data-semantic-role="simple function" data-semantic-id="41" data-semantic-children="22,37" data-semantic-content="40,22" data-semantic-parent="46"> <mi data-semantic-type="identifier" data-semantic-role="simple function" data-semantic-font="italic" data-semantic-id="22" data-semantic-parent="41" data-semantic-operator="appl">f</mi> <mo data-semantic-type="punctuation" data-semantic-role="application" data-semantic-id="40" data-semantic-parent="41" data-semantic-added="true" data-semantic-operator="appl"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="37" data-semantic-children="24" data-semantic-content="23,25" data-semantic-parent="41"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="23" data-semantic-parent="37" data-semantic-operator="fenced">(</mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="24" data-semantic-parent="37">τ <!-- τ --> </mi> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="25" data-semantic-parent="37" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="44" data-semantic-parent="46" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="26" data-semantic-parent="46">g</mi> <mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="45" data-semantic-parent="46" data-semantic-added="true" data-semantic-operator="infixop,⁢"></mo> <mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="39" data-semantic-children="38" data-semantic-content="27,31" data-semantic-parent="46"> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="27" data-semantic-parent="39" data-semantic-operator="fenced">(</mo> <mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="38" data-semantic-children="28,30" data-semantic-content="29" data-semantic-parent="39"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="28" data-semantic-parent="38">t</mi> <mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="29" data-semantic-parent="38" data-semantic-operator="infixop,−"><!-- − --> </mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="30" data-semantic-parent="38">τ <!-- τ --> </mi> </mrow> <mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="31" data-semantic-parent="39" data-semantic-operator="fenced">)</mo> </mrow> </mrow> <mrow data-semantic-type="punctuated" data-semantic-role="integral" data-semantic-id="43" data-semantic-children="32,42,33" data-semantic-content="42" data-semantic-parent="47"> <mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="32" data-semantic-parent="43">d</mi> <mo data-semantic-type="punctuation" data-semantic-role="comma" data-semantic-id="42" data-semantic-parent="43" data-semantic-added="true" data-semantic-operator="punctuated"></mo> <mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="33" data-semantic-parent="43">τ <!-- τ --> </mi> </mrow> </mrow> </mrow> <annotation encoding="application/x-tex">(f*g)(t){\stackrel {\mathrm {def} }{=}}\int _{-\infty }^{\infty }f(\tau )g(t-\tau )d\tau</annotation> </semantics> </math>