ag-gipp/GoUldI

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data/mathematical/211.mml

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<math xmlns='http://www.w3.org/1998/Math/MathML' display='inline'><semantics><mrow><mo stretchy="false">(</mo><mi>f</mi><mo>*</mo><mi>g</mi><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mover><mo>=</mo><mrow><mi mathvariant="normal">def</mi></mrow></mover><msubsup><mo>∫</mo> <mrow><mo lspace="verythinmathspace" rspace="0em">−</mo><mn>∞</mn></mrow> <mn>∞</mn></msubsup><mi>f</mi><mo stretchy="false">(</mo><mi>τ</mi><mo stretchy="false">)</mo><mi>g</mi><mo stretchy="false">(</mo><mi>t</mi><mo>−</mo><mi>τ</mi><mo stretchy="false">)</mo><mi>d</mi><mi>τ</mi></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>