tag:blogger.com,1999:blog-79607206336481703742024-03-19T03:50:18.387-07:00SISTEMAS Y SEÑALESJonathan Mantillahttp://www.blogger.com/profile/17040185264536385686noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-7960720633648170374.post-24403864457437944952013-03-05T21:24:00.000-08:002013-03-05T21:24:11.311-08:00EJEMPLOS DE SISTEMAS LINEALES Y NO LINEALES VARIABLES Y NO VARIABLES EN EL TIEMPOEJEMPLO PARA UN SISTEMA LINEAL VARIABLE EN EL TIEMPO:<br />
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<span style="font-family: 'Times New Roman', serif; font-size: 12pt; position: relative; top: -0.5pt;">Si<span style="letter-spacing: .6pt;"> </span>y</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 1pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; position: relative; top: -0.5pt;">(t)<span style="letter-spacing: -1.35pt;"> </span>=<span style="letter-spacing: 1.25pt;"> </span>x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 1pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; position: relative; top: -0.5pt;">(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt; position: relative; top: -0.5pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; position: relative; top: -0.5pt;">t)<span style="letter-spacing: .1pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; position: relative; top: -0.5pt;">y<span style="letter-spacing: 1.1pt;"> </span>y</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 1pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: -1.5pt; position: relative; top: 1pt;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; position: relative; top: -0.5pt;">(t)<span style="letter-spacing: -.5pt;">
</span>=<span style="letter-spacing: .75pt;"> </span>x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; top: 1pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; position: relative; top: -0.5pt;">(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt; position: relative; top: -0.5pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; position: relative; top: -0.5pt;">t)<span style="letter-spacing: -1.55pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; position: relative; top: -0.5pt;">e<span style="letter-spacing: -.3pt;">n</span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; position: relative; top: -0.5pt;">tonces</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">y</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.45pt;"> </span>+<span style="letter-spacing: .8pt;"> </span>α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">y</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -.8pt;"> </span>=<span style="letter-spacing: 1.45pt;"> </span>α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t)<span style="letter-spacing: -.45pt;"> </span>+<span style="letter-spacing: .8pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">2<span style="letter-spacing: -.15pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.5pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-family: 'Times New Roman', serif; font-size: 12pt; letter-spacing: -0.3pt;">P</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">or<span style="letter-spacing: 2.55pt;"> </span>otro<span style="letter-spacing: 2.25pt;"> </span>lado,<span style="letter-spacing: 1.85pt;"> </span>si<span style="letter-spacing: .75pt;"> </span>x(t)<span style="letter-spacing: -1.85pt;"> </span>=<span style="letter-spacing: .35pt;"> </span>α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">1<span style="letter-spacing: -.15pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.6pt;"> </span>+<span style="letter-spacing: .4pt;"> </span>α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -.75pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">y<span style="letter-spacing: 1.1pt;"> </span>se<span style="letter-spacing: .7pt;"> </span>calcula<span style="letter-spacing: 1.9pt;"> </span><span style="letter-spacing: .5pt; mso-font-width: 114%;">y</span>(t)<span style="letter-spacing: -.95pt;"> </span>=<span style="letter-spacing: 1.25pt;"> </span></span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">T<span style="letter-spacing: 1.9pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">[</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">)]</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; letter-spacing: 0.9pt;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">e<span style="letter-spacing: -.3pt;">n</span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">tonces</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-family: 'Times New Roman', serif; font-size: 12pt; letter-spacing: 0.5pt;">y</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -.95pt;"> </span>=<span style="letter-spacing: 1.25pt;"> </span>x(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t)<span style="letter-spacing: -.1pt;"> </span>=<span style="letter-spacing: 1.25pt;"> </span>α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t)<span style="letter-spacing: -1.35pt;"> </span>+<span style="letter-spacing: .6pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.5pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.5pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">)</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
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<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">lo<span style="letter-spacing: .6pt;"> </span>que<span style="letter-spacing: 1.4pt;"> </span>indica<span style="letter-spacing: 2.05pt;"> </span>que<span style="letter-spacing: 1.4pt;"> </span>el<span style="letter-spacing: .65pt;"> </span>sistema<span style="letter-spacing: 2.7pt;">
</span>es<span style="letter-spacing: .7pt;"> </span>lineal.<o:p></o:p></span></div>
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<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Si<span style="letter-spacing: 2.55pt;"> </span><span style="letter-spacing: .5pt; mso-font-width: 114%;">y</span>(t)<span style="letter-spacing: 2.4pt;"> </span>= <span style="letter-spacing: 1.15pt;"> </span>x(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t)<span style="letter-spacing: 2.45pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">e<span style="letter-spacing: -.35pt;">n</span>tonces <span style="letter-spacing: 1.4pt;"> </span>la <span style="letter-spacing: .3pt;"> </span>respuesta <span style="letter-spacing: 2.55pt;"> </span>a <span style="letter-spacing: .4pt;"> </span>la <span style="letter-spacing: .3pt;"> </span>se<span style="letter-spacing: -6.2pt; mso-font-width: 108%;">n</span><span style="letter-spacing: .3pt; mso-font-width: 146%;">˜</span>al <span style="letter-spacing: -.15pt;"> </span>x(t)<span style="letter-spacing: 2.55pt;"> </span>desplazada <span style="letter-spacing: 2.5pt;"> </span>en <span style="letter-spacing: .2pt;"> </span>el<span style="letter-spacing: 2.6pt;"> </span>tiem<span style="letter-spacing: .3pt;">p</span>o <span style="letter-spacing: 1.6pt;"> </span>es x(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t<span style="letter-spacing: .25pt;"> </span></span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−<span style="letter-spacing: 1.4pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">0</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: -1.5pt; position: relative; top: 2pt;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">)) <span style="letter-spacing: .85pt;"> </span>=<span style="letter-spacing: 2.95pt;"> </span>x(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t<span style="letter-spacing: -1.65pt;"> </span>+<span style="letter-spacing: .8pt;"> </span>t</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; top: 2pt;">0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">). <span style="letter-spacing: .9pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; letter-spacing: -0.3pt;">P</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">or <span style="letter-spacing: 1.0pt;"> </span>otro
<span style="letter-spacing: .7pt;"> </span>lado,
<span style="letter-spacing: .65pt;"> </span>si<span style="letter-spacing: 2.2pt;"> </span>se<span style="letter-spacing: 2.15pt;"> </span>desplaza
<span style="letter-spacing: 1.0pt;"> </span>la<span style="letter-spacing: 2.8pt;"> </span>salida <span style="letter-spacing: .45pt;"> </span>corres<span style="letter-spacing: .3pt;">p</span>ondie<span style="letter-spacing: -.35pt;">n</span>te a<span style="letter-spacing: 2.0pt;"> </span>x(t)<span style="letter-spacing: 1.15pt;"> </span>e<span style="letter-spacing: -.3pt;">n</span>tonces
<span style="letter-spacing: .5pt; mso-font-width: 108%;">y</span>(t<span style="letter-spacing: -.2pt;"> </span></span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−<span style="letter-spacing: .8pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; top: 2pt;">0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">)<span style="letter-spacing: .05pt;"> </span>=<span style="letter-spacing: 1.7pt;"> </span>x(</span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t<span style="letter-spacing: -1.6pt;"> </span></span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">−<span style="letter-spacing: .8pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">0</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: -1.5pt; position: relative; top: 2pt;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">). <span style="letter-spacing: 1.55pt;"> </span>Esto<span style="letter-spacing: 2.95pt;"> </span>implica<span style="letter-spacing: 2.55pt;">
</span>que<span style="letter-spacing: 1.95pt;"> </span>el<span style="letter-spacing: 1.2pt;"> </span>sistema <span style="letter-spacing: .25pt;"> </span>es<span style="letter-spacing: 1.25pt;"> </span><span style="letter-spacing: -.65pt;">v</span>aria<span style="letter-spacing: -.35pt;">n</span>te
<span style="letter-spacing: 1.6pt;"> </span>en<span style="letter-spacing: 1.8pt;"> </span>el tiem<span style="letter-spacing: .3pt;">p</span>o.<o:p></o:p></span></div>
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EJEMPLO PARA UN SISTEMA NO LINEAL INVARIABLE EN EL TIEMPO:<br />
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<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">Si<span style="letter-spacing: .6pt;"> </span>y</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: -1.5pt; position: relative; top: 2pt;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -.05pt;"> </span>=<span style="letter-spacing: 1.05pt;"> </span>x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.6pt;"> </span>+<span style="letter-spacing: .4pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">1<span style="letter-spacing: .7pt;"> </span>y<span style="letter-spacing: 1.1pt;"> </span>y</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.35pt;"> </span>=<span style="letter-spacing: 1.25pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">2<span style="letter-spacing: -.7pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.85pt;"> </span>+<span style="letter-spacing: -.4pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">1<span style="letter-spacing: .7pt;"> </span>e<span style="letter-spacing: -.3pt;">n</span>tonces<o:p></o:p></span></div>
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<span style="font-family: 'Times New Roman', serif; font-size: 12pt;">α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">1<span style="letter-spacing: -.15pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">y</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: -1.5pt; position: relative; top: 2pt;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -.4pt;"> </span>+<span style="letter-spacing: .6pt;"> </span>α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">y</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.5pt;"> </span>=<span style="letter-spacing: 1.25pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">1<span style="letter-spacing: -.15pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.6pt;"> </span>+<span style="letter-spacing: .4pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">2<span style="letter-spacing: -.15pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.6pt;"> </span>+<span style="letter-spacing: .4pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">1 <span style="letter-spacing: .5pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">+<span style="letter-spacing: -1.35pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 8pt; margin: 0.4pt 0cm 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="line-height: normal; margin: 0cm 0cm 0.0001pt 34.95pt;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; letter-spacing: -0.3pt;">P</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">or<span style="letter-spacing: 2.55pt;"> </span>otro<span style="letter-spacing: 2.25pt;"> </span>lado,<span style="letter-spacing: 1.85pt;"> </span>si<span style="letter-spacing: .75pt;"> </span>x(t)<span style="letter-spacing: -1.85pt;"> </span>=<span style="letter-spacing: .35pt;"> </span>α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">1<span style="letter-spacing: -.15pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.6pt;"> </span>+<span style="letter-spacing: .4pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; top: 2pt;">2<span style="letter-spacing: -.15pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: .65pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">y<span style="letter-spacing: 1.1pt;"> </span>se<span style="letter-spacing: .7pt;"> </span>calcula<span style="letter-spacing: 1.9pt;"> </span><span style="letter-spacing: .5pt; mso-font-width: 114%;">y</span>(t)<span style="letter-spacing: -.95pt;"> </span>=<span style="letter-spacing: 1.25pt;"> </span></span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt;">T<span style="letter-spacing: 1.9pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">[</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">t</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">)]</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; letter-spacing: 0.9pt;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">e<span style="letter-spacing: -.3pt;">n</span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">tonces</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 24pt; margin: 1.1pt 123.05pt 0.0001pt 34.95pt; text-indent: 119.25pt;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; letter-spacing: 0.5pt;">y</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -.95pt;"> </span>=<span style="letter-spacing: 1.25pt;"> </span>x(t)<span style="letter-spacing: -.65pt;"> </span>+<span style="letter-spacing: .6pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">1<span style="letter-spacing: .1pt;"> </span>=<span style="letter-spacing: 1.15pt;"> </span>α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.6pt;"> </span>+<span style="letter-spacing: .5pt;"> </span>α</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">(t)<span style="letter-spacing: -1.6pt;"> </span>+<span style="letter-spacing: .5pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt;">1 lo<span style="letter-spacing: .6pt;"> </span>que<span style="letter-spacing: 1.4pt;"> </span>indica<span style="letter-spacing: 2.05pt;"> </span>que<span style="letter-spacing: 1.4pt;"> </span>el<span style="letter-spacing: .65pt;"> </span>sistema<span style="letter-spacing: 2.7pt;">
</span>no<span style="letter-spacing: 1.25pt;"> </span>es<span style="letter-spacing: .7pt;"> </span>lineal.</span></div>
<div class="MsoNormal" style="line-height: 24pt; margin: 1.1pt 123.05pt 0.0001pt 34.95pt; text-indent: 119.25pt;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 15.7pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">Si<span style="letter-spacing: .65pt;"> </span><span style="letter-spacing: .5pt; mso-font-width: 114%;">y</span>(t)<span style="letter-spacing: -.9pt;"> </span>=<span style="letter-spacing: 1.3pt;"> </span>x(t)<span style="letter-spacing: -.6pt;"> </span>+<span style="letter-spacing: .6pt;"> </span>1<span style="letter-spacing: .75pt;">
</span>la<span style="letter-spacing: 1.4pt;"> </span>respuesta <span style="letter-spacing: .65pt;"> </span>a<span style="letter-spacing: 1.5pt;"> </span>la<span style="letter-spacing: 1.4pt;"> </span>e<span style="letter-spacing: -.35pt;">n</span>trada<span style="letter-spacing: .8pt;"> </span>desplazada <span style="letter-spacing: .6pt;"> </span>es<span style="letter-spacing: .75pt;"> </span>x(t<span style="letter-spacing: -.8pt;"> </span></span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt; line-height: 15.7pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">−<span style="letter-spacing: .45pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 15.7pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">t</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; line-height: 15.7pt; position: relative; text-indent: 119.25pt; top: 1pt;">0</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 15.7pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">)<span style="letter-spacing: -1.8pt;"> </span>+<span style="letter-spacing: -.1pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 15.7pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">1,<span style="letter-spacing: 1.05pt;"> </span>y<span style="letter-spacing: 1.15pt;"> </span>la<span style="letter-spacing: 1.4pt;"> </span>respuesta</span></div>
<div class="MsoNormal" style="margin: 1.1pt 123.05pt 0.0001pt 34.95pt; text-indent: 119.25pt;">
</div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 20.2pt;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: -0.5pt;"></span></div>
<div style="text-align: left;">
<span style="font-size: 12pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">desplazada <span style="letter-spacing: 1.2pt;"> </span>corres<span style="letter-spacing: .3pt;">p</span>ondie<span style="letter-spacing: -.35pt;">n</span>te
<span style="letter-spacing: 1.65pt;"> </span>a<span style="letter-spacing: 2.1pt;"> </span>x(t)<span style="letter-spacing: 1.25pt;"> </span>ta<span style="letter-spacing: -.35pt;">m</span>b<span style="letter-spacing: -.3pt;">i</span><span style="letter-spacing: -5.55pt; mso-font-width: 146%;">´</span>en <span style="letter-spacing: -1.45pt;"> </span>es<span style="letter-spacing: 1.35pt;"> </span><span style="letter-spacing: .5pt; mso-font-width: 108%;">y</span>(t<span style="letter-spacing: -.1pt;"> </span></span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">−<span style="letter-spacing: .9pt;"> </span></span><span style="font-size: 12pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">t</span><span style="font-size: 8pt; letter-spacing: 0.6pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: 1pt;">0</span><span style="font-size: 12pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">)<span style="letter-spacing: .1pt;"> </span>=<span style="letter-spacing: 1.8pt;"> </span>x(t<span style="letter-spacing: -1.15pt;"> </span></span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">−<span style="letter-spacing: .9pt;"> </span></span><span style="font-size: 12pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">t</span><span style="font-size: 8pt; letter-spacing: 0.6pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: 1pt;">0</span><span style="font-size: 12pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">)<span style="letter-spacing: -1.7pt;"> </span>+<span style="letter-spacing: .15pt;"> </span></span><span style="font-size: 12pt; line-height: 15.9pt; position: relative; text-indent: 119.25pt; top: -0.5pt;">1<span style="letter-spacing: 1.35pt;"> </span><span style="letter-spacing: .3pt;">p</span>or<span style="letter-spacing: 2.45pt;"> </span>lo<span style="letter-spacing: 1.25pt;"> </span>que<span style="letter-spacing: 2.05pt;"> </span>el</span></div>
<span style="text-indent: 119.25pt;"><div style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: normal; text-align: left;">
<span style="font-size: 12pt; text-indent: 119.25pt;">sistema</span><span style="font-size: 12pt; letter-spacing: 2.7pt; text-indent: 119.25pt;"> </span><span style="font-size: 12pt; text-indent: 119.25pt;">es</span><span style="font-size: 12pt; letter-spacing: 0.7pt; text-indent: 119.25pt;"> </span><span style="font-size: 12pt; text-indent: 119.25pt;">i</span><span style="font-size: 12pt; letter-spacing: -0.35pt; text-indent: 119.25pt;">n</span><span style="font-size: 12pt; letter-spacing: -0.65pt; text-indent: 119.25pt;">v</span><span style="font-size: 12pt; text-indent: 119.25pt;">aria</span><span style="font-size: 12pt; letter-spacing: -0.35pt; text-indent: 119.25pt;">n</span><span style="font-size: 12pt; text-indent: 119.25pt;">te </span><span style="font-size: 12pt; letter-spacing: 1.4pt; text-indent: 119.25pt;"> </span><span style="font-size: 12pt; text-indent: 119.25pt;">en</span><span style="font-size: 12pt; letter-spacing: 1.25pt; text-indent: 119.25pt;"> </span><span style="font-size: 12pt; text-indent: 119.25pt;">el</span><span style="font-size: 12pt; letter-spacing: 0.65pt; text-indent: 119.25pt;"> </span><span style="font-size: 12pt; text-indent: 119.25pt;">tiem</span><span style="font-size: 12pt; letter-spacing: 0.3pt; text-indent: 119.25pt;">p</span><span style="font-size: 12pt; text-indent: 119.25pt;">o.</span></div>
<div style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: normal; text-align: left;">
<span style="font-size: 12pt; text-indent: 119.25pt;"><br /></span></div>
<br />EJEMPLO PARA SISTEMA LINEAL INVARIABLE EN EL TIEMPO</span><br />
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 20.2pt; text-align: left;">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-indent: 0px;"> y</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; text-indent: 0px; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: -1.5pt; position: relative; text-indent: 0px; top: 2pt;"> </span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-indent: 0px;">(t)<span style="letter-spacing: -0.05pt;"> </span>=<span style="letter-spacing: 1.05pt;"> d/dt </span>x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.6pt; position: relative; text-indent: 0px; top: 2pt;">1</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-indent: 0px;">(t)<span style="letter-spacing: -1.6pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-indent: 0px;"><span style="letter-spacing: 0.7pt;"> </span>y<span style="letter-spacing: 1.1pt;"> </span>y</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; letter-spacing: 0.55pt; position: relative; text-indent: 0px; top: 2pt;">2</span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-indent: 0px;">(t)<span style="letter-spacing: -1.35pt;"> </span>=<span style="letter-spacing: 1.25pt;"> d/dt </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-indent: 0px;">x</span><span style="font-family: 'Times New Roman', serif; font-size: 8pt; position: relative; text-indent: 0px; top: 2pt;">2<span style="letter-spacing: -0.7pt;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 12pt; text-indent: 0px;">(t)</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 20.2pt; text-align: left;">
<span style="letter-spacing: -2px; text-indent: 0px;"><span style="font-family: Times New Roman, serif;"></span></span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 20.2pt;">
</div>
<div class="MsoNormal" style="line-height: 19.55pt; margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 146.4pt; margin-right: 0cm; margin-top: 0cm; mso-layout-grid-align: none; mso-line-height-rule: exactly; mso-pagination: none; text-autospace: none;">
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</div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 146.4pt;">
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style='position:absolute;left:0;text-align:left;margin-left:407.8pt;
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coordsize="206,0" o:allowincell="f" path="m,hhl206,e" filled="f"
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</v:shape><![endif]--><!--[if !vml]--><span style="height: 2px; left: 0px; margin-left: 543px; margin-top: 7px; position: absolute; width: 15px; z-index: 251453437;"><img height="2" src="file:///C:/Users/JONATH~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png" v:shapes="_x0000_s1027" width="15" /></span><!--[endif]-->α1y1(t) + α2 y2 (t) = α1 d/dtx1(t) + α2 d/dt x2(t)<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0.0001pt 146.4pt;">
Por otro lado, si x(t) = α1x1(t) + α2x2(t) y se calcula y(t) = T [x(t)] entonces y(t) = d/dt x(t) = d/dt[α1x1 (t) + α2x2 (t)] = α1 d/dtx1 (t) + α2 d /dt x2 (t) por lo que el sistema es lineal.</div>
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<span style="font-family: 'Times New Roman', serif; position: relative; top: -6.5pt;"></span></div>
<div class="MsoNormal" style="font-size: 12pt; line-height: 11.1pt; margin: 0cm 0cm 0.0001pt 20pt;">
<span style="font-size: 12pt; position: relative; top: 4pt;"><span style="letter-spacing: 2.95pt;"><br /></span></span></div>
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<span style="font-size: 12pt; position: relative; top: 4pt;"><span style="letter-spacing: 2.95pt;"> </span>Si<span style="letter-spacing: -.3pt;"> </span><span style="letter-spacing: .5pt; mso-font-width: 114%;">y</span>(t)<span style="letter-spacing: -.95pt;"> </span>= d/dt <span style="letter-spacing: .5pt;"> </span></span><span style="font-size: 8pt; letter-spacing: -3.35pt; position: relative; top: -0.5pt;"> </span><span style="font-size: 12pt; position: relative; top: 4pt;">x(t)<span style="letter-spacing: -.3pt;"> </span></span><span style="font-size: 12pt; position: relative; top: 4pt;">e<span style="letter-spacing: -.35pt;">n</span>tonces<span style="letter-spacing: 1.55pt;">
</span>la<span style="letter-spacing: .45pt;"> </span>respuesta<span style="letter-spacing: 2.7pt;"> </span>a<span style="letter-spacing: .55pt;"> </span>x(t<span style="letter-spacing: -2.2pt;"> </span></span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt; letter-spacing: 0.9pt; position: relative; top: 4pt;">−</span><span style="font-size: 12pt; position: relative; top: 4pt;">t</span><span style="font-size: 8pt; letter-spacing: 0.55pt; position: relative; top: 6pt;">0</span><span style="font-size: 12pt; position: relative; top: 4pt;">)<span style="letter-spacing: -.15pt;"> </span></span><span style="font-size: 12pt; position: relative; top: 4pt;">es<span style="letter-spacing: 3px;"> d/dt </span></span><span style="font-size: 12pt; position: relative; top: 4pt;">x</span><span style="font-size: 12pt; position: relative; top: 4pt;">(</span><span style="font-size: 12pt; position: relative; top: 4pt;">t</span><span style="font-size: 12pt; letter-spacing: -2.2pt; position: relative; top: 4pt;"> </span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt; letter-spacing: 0.8pt; position: relative; top: 4pt;">−</span><span style="font-size: 12pt; position: relative; top: 4pt;">t</span><span style="font-size: 8pt; position: relative; top: 6pt;">0</span><span style="font-size: 8pt; letter-spacing: -1.5pt; position: relative; top: 6pt;"> </span><span style="font-size: 12pt; position: relative; top: 4pt;">).<span style="letter-spacing: 2.65pt;"> </span>La<span style="letter-spacing: .45pt;"> </span>salida<span style="letter-spacing: 1.1pt;"> </span><span style="letter-spacing: .5pt; mso-font-width: 109%;">y</span>(t)<span style="letter-spacing: -.25pt;"> </span>desplazada</span><span style="font-size: 12pt;"><o:p></o:p></span></div>
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</span><!--[endif]--><span style="position: relative; top: -1pt;"><span style="font-size: small;">en</span><span style="font-size: 12pt; letter-spacing: 1.25pt;"> </span><span style="font-size: small;">el</span><span style="font-size: 12pt; letter-spacing: 0.65pt;"> </span><span style="font-size: small;">tiem</span><span style="font-size: 12pt; letter-spacing: 0.3pt;">p</span><span style="font-size: small;">o</span><span style="font-size: 12pt; letter-spacing: 2.65pt;"> </span><span style="font-size: small;">es</span><span style="font-size: 12pt; letter-spacing: 0.7pt;"> </span><span style="font-size: small;">ta</span><span style="font-size: 12pt; letter-spacing: -0.35pt;">m</span><span style="font-size: small;">b</span><span style="font-size: 12pt; letter-spacing: -0.3pt;">i</span><span style="font-size: 12pt; letter-spacing: -5.5pt;">´</span><span style="font-size: small;">en</span> d/dt</span><span style="font-size: 12pt; position: relative; top: -1pt;">x(t<span style="letter-spacing: -.8pt;"> </span></span><span style="font-family: 'Segoe UI Symbol', sans-serif; font-size: 12pt; position: relative; top: -1pt;">−<span style="letter-spacing: .45pt;"> </span></span><span style="font-size: 12pt; position: relative; top: -1pt;">t</span><span style="font-size: 8pt; position: relative; top: 1pt;">0</span><span style="font-size: 8pt; letter-spacing: -1.5pt; position: relative; top: 1pt;"> </span><span style="font-size: 12pt; position: relative; top: -1pt;">)<span style="letter-spacing: 1.4pt;"> </span><span style="letter-spacing: .35pt;">p</span>or<span style="letter-spacing: 1.7pt;"> </span>lo<span style="letter-spacing: .6pt;"> </span>que<span style="letter-spacing: 1.4pt;"> </span>el<span style="letter-spacing: .65pt;"> </span>sistema<span style="letter-spacing: 2.7pt;">
</span>es<span style="letter-spacing: .7pt;"> </span>i<span style="letter-spacing: -.35pt;">n</span><span style="letter-spacing: -.65pt;">v</span>aria<span style="letter-spacing: -.35pt;">n</span>te <span style="letter-spacing: 1.4pt;"> </span>en<span style="letter-spacing: 1.25pt;"> </span>el<span style="letter-spacing: .65pt;"> </span>tiem<span style="letter-spacing: .3pt;">p</span>o.</span><span style="font-size: 12pt;"><o:p></o:p></span></div>
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Jonathan Mantillahttp://www.blogger.com/profile/17040185264536385686noreply@blogger.com1tag:blogger.com,1999:blog-7960720633648170374.post-19029630464606493232013-02-06T19:19:00.000-08:002013-02-06T20:00:30.890-08:00EJEMPLOS DE SEÑALESHola a todos en este primer post hablaremos de las señales continuas, discretas análogas y digitales y algunos ejemplo de estas señales.<br />
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<b>SEÑALES CONTINUAS:</b><br />
<span style="background-color: white; font-family: arial, helvetica, clean, sans-serif; font-size: 13px; line-height: 16px;">Una señal contínua es una señal "suave" que está definida para todos los puntos de un intervalo determinado del conjunto de los números reales. Por ejemplo, la función seno es un ejemplo continuo, como la función exponencial o la función constante. Una parte de la función seno en el rango de tiempos de 0 a 6 segundos también es contínua. Si deseamos ejemplos de la naturaleza tenemos la corriente, el voltaje, el sonido, la luz, etc.</span><br />
<span style="background-color: white; color: #333333; font-family: arial, helvetica, clean, sans-serif; font-size: 13px; line-height: 16px;"><br /></span>
<b>SEÑALES DISCRETAS:</b><br />
<span style="background-color: white; font-family: arial, helvetica, clean, sans-serif; font-size: 13px; line-height: 16px;">Una señal discreta es una señal discontinua que está definida para todos los puntos de un intervalo determinado del conjunto de los números enteros. Su importancia en la tecnología es que, los computadores y microchips que son utilizados en este nuevo mundo "Digital" en el que vivimos, solo manejan señales discretas. Una señal discreta en la naturaleza podria ser el pulso cardiaco, el rebotar de una pelota al caer libremente, etc.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2mR5h-t1zSadw_VMKTZOkS4a1jBuS9UxepBxMRGeXySYGYsStxK-3NJ23kT52buOnHou_NnmLUMS2BnRuzwVeqAAhTJNcIv5CGRAlbT-X9fkO79f1aWsXhBImqeEzHPR9Iomrxvsz/s1600/muestreo.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2mR5h-t1zSadw_VMKTZOkS4a1jBuS9UxepBxMRGeXySYGYsStxK-3NJ23kT52buOnHou_NnmLUMS2BnRuzwVeqAAhTJNcIv5CGRAlbT-X9fkO79f1aWsXhBImqeEzHPR9Iomrxvsz/s320/muestreo.png" height="320" width="256" /></a></div>
<b>SEÑALES ANALOGAS:</b><br />
<br />
Son variables eléctricas que evolucionan en el tiempo en forma análoga a alguna<br />
variable física. Estas variables pueden presentarse en la forma de una corriente, una<br />
tensión o una carga eléctrica. Varían en forma continua entre un límite inferior y un<br />
límite superior. Cuando estos límites coinciden con los límites que admite un determinado dispositivo, se dice que la señal está normalizada. La ventaja de trabajar con se-<br />
señales normalizadas es que se aprovecha mejor la relación señal/ruido del dispositivo.<br />
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<b>SEÑALES DIGITALES:</b><br />
<br />
Son variables eléctricas con dos niveles bien diferenciados que se alternan en el<br />
tiempo transmitiendo información según un código previamente acordado. Cada nivel<br />
eléctrico representa uno de dos símbolos: 0 ó 1, V o F, etc. Los niveles específicos dependen del tipo de dispositivos utilizado. Por ejemplo si se emplean componentes de la<br />
familia lógica TTL (transistor-transistor-logic) los niveles son 0 V y 5 V, aunque cualquier valor por debajo de 0,8 V es correctamente interpretado como un 0 y cualquier<br />
valor por encima de 2 V es interpretado como un 1 (los niveles de salida están por debajo de 0,4 V y por encima de 2,4 V respectivamente). En el caso de la familia CMOS<br />
(complementary metal-oxide-semiconductor), los valores dependen de la alimentación.<br />
Para alimentación de +5 V, los valores ideales son también 0 V y 5 V, pero se reconoce<br />
un 0 hasta 2,25 V y un 1 a partir de 2,75 V.<br />
Estos ejemplos muestran uno de los principales atractivos de las señales digitales:<br />
su gran inmunidad al ruido.<br />
Las señales digitales descriptas tienen la particularidad de tener sólo dos estados y<br />
por lo tanto permiten representar, transmitir o almacenar información binaria. Para<br />
transmitir más información se requiere mayor cantidad de estados, que pueden lograrse<br />
combinando varias señales en paralelo (simultáneas), cada una de las cuales transmite<br />
una información binaria.<br />
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<b>EJEMPLOS:</b><br />
<b><br /></b>
<b>SEÑALES DIGITALES :</b><br />
gran parte de los equipos electrónicos que utilizamos habitualmente y que son la manifestación mas extendida de la revolución tecnológica, trabajan con señales digitales:<br />
<br />
<ul>
<li>el ordenador</li>
<li>el cdrom y los equipos de música </li>
<li>el teléfono y otros equipos de comunicaciones</li>
</ul>
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la voz es una señal analógica y por tanto el que habla produce una señal analógica y el que escucha solo es capaz de interpretar señales también analógicas. sin embargo el canal de comunicación transmite señales digitales. se hace preciso transformar en algún punto la señal analógica en digital y posteriormente la digital en analógica.</div>
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<b><br /></b>
si conectamos un instrumento de medida (osciloscopio, analizador digital,..) a cualquiera de estos equipos nos mostraría señales eléctricas que exclusivamente tienen dos niveles de tensión:<br />
0 voltios y 5 voltios<br />
asi, el teclado intercambia con la cpu información digital exclusivamente.<br />
al pulsar una tecla se genera una serie de pulsos de tensión que son interpretados por la CPU.<br />
cuando hablamos por un teléfono conectado a la red digital, el proceso es mas complejo porque en este sistema coexisten las señales analógicas y digitales.<br />
<b><br /></b>
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<b>SEÑALES ANÁLOGAS:</b><br />
<b><br /></b>
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Ejemplos de aquellos sistemas analógicos que ahora se han vuelto digitales:<br />
<br />
Grabaciones de video: Un disco versátil digital de múltiples usos (DVD por las siglas de digital versatile disc) almacena video en un formato digital altamente comprimido denominado MPEG-2. Este estándar codifica una pequeña fracción de los cuadros individuales de video en un formato comprimido semejante al JPEG y codifica cada uno de los otros cuadros como la diferencia entre éste y el anterior. La capacidad de un DVD de una sola capa y un solo lado es de aproximadamente 35 mil millones de bits suficiente para grabar casi 2 horas de video de alta calidad y un disco de doble capa y doble lado tiene cuatro veces esta capacidad.<br />
Grabaciones de audio: Alguna vez se fabricaron exclusivamente mediante la impresión de formas de onda analógicas sobre cinta magnética o un acetato (LP), las grabaciones de audio utilizan en la actualidad de manera ordinaria discos compactos digitales (CD. Compact Discs). Un CD almacena la música como una serie de números de 16 bits que corresponden a muestras de la forma de onda analógica original se realiza una muestra por canal estereofónico cada 22.7 microsegundos. Una grabación en CD a toda su capacidad (73 minutos) contiene hasta seis mil millones de bits de información.<br />
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Jonathan Mantillahttp://www.blogger.com/profile/17040185264536385686noreply@blogger.com5tag:blogger.com,1999:blog-7960720633648170374.post-85208073616679763362013-02-06T17:44:00.002-08:002013-02-06T17:57:08.395-08:00EJEMPLOS DE SEÑALESJonathan Mantillahttp://www.blogger.com/profile/17040185264536385686noreply@blogger.com0