(* Content-type: application/vnd.wolfram.cdf.text *) (*** Wolfram CDF File ***) (* http://www.wolfram.com/cdf *) (* CreatedBy='Mathematica 9.0' *) (*************************************************************************) (* *) (* The Mathematica License under which this file was created prohibits *) (* restricting third parties in receipt of this file from republishing *) (* or redistributing it by any means, including but not limited to *) (* rights management or terms of use, without the express consent of *) (* Wolfram Research, Inc. 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Shaw y J. Tigg. Originalmente este fichero se hizo con ", StyleBox["Mathematica", FontSlant->"Italic"], " 4, se han realizado los cambios imprescindibles para adaptarlo a ", StyleBox["Mathematica", FontSlant->"Italic"], " 9 pero no est\[AAcute] optimizado para esta versi\[OAcute]n. De hecho ", StyleBox["Mathematica", FontSlant->"Italic"], " 9 dispone de funciones que permitirian desarrollar lo mismo de forma mas \ compacta, pero la ideas ideas fundamentales se mantienen. 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" }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Ejemplo", "Section"], Cell[TextData[{ "Sea una funci\[OAcute]n periodica dada por un tren de pulsos de la forma :\n\ f(t) = ", Cell[BoxData[ TagBox[ StyleBox[ RowBox[{"{", StyleBox[GridBox[{ { RowBox[{ RowBox[{ RowBox[{"A", " ", "para"}], " ", "-", RowBox[{"d", "/", "2"}]}], " ", "<", "t", "<", " ", RowBox[{"d", "/", "2"}], " "}]}, { RowBox[{ RowBox[{ RowBox[{ RowBox[{"0", "para"}], " ", "-", RowBox[{"T", "/", "2"}]}], " ", "<", "t", "<", " ", RowBox[{ RowBox[{"-", " ", "d"}], "/", "2"}]}], ",", " ", RowBox[{ RowBox[{"d", "/", "2"}], " ", "<", "t", "<", RowBox[{"T", "/", "2"}], " "}]}]} }], ShowAutoStyles->True]}], ShowAutoStyles->False], #& ]]], "\n", "Sustituyendo en (3)" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Coef1", "=", RowBox[{ FractionBox["A", "T"], RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{ RowBox[{"-", "d"}], "/", "2"}], RowBox[{"d", "/", "2"}]], " ", RowBox[{ SuperscriptBox["\[ExponentialE]", 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De hecho se puede interpretar como que \ una funci\[OAcute]n no periodica puede representarse por una serie de \ exponenciales con la frecuencia funcamental tendiendo a cero.\nAsimismo puede \ concluirse que cualquier funci\[OAcute]n tiene dos modos equivalentes de \ representaci\[OAcute]n: una en el dominio del tiempo f(t) y otra en el \ dominio de la frecuencia F(", Cell[BoxData["w"]], ") y ambas pueden relacionarse." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Aplicaci\[OAcute]n de la trasformada de Fourier en la eliminaci\[OAcute]n del \ ruido\ \>", "Section"], Cell["\<\ Una de las aplicaciones mas interesantes de la trasformadas de Fourier es \ para reducir el ruido de una se\[NTilde]al. 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altas que corresponden al ruido, se trata de eliminar \ estas interferencias. Vemos que el ruido esta aproximadamente localicado en: \ \nLocalizaci\[OAcute]n se\[NTilde]al A: X : {35, 45}, Y:{35, 45}\nLocalizaci\ \[OAcute]n se\[NTilde]al B: X : {35, 45}, Y:{35, 45}\nObviamente cada vez que \ generemos la se\[NTilde]al aleatorias ", StyleBox["unknownfreqx", FontWeight->"Bold"], " y ", StyleBox["unknownfreqy", FontWeight->"Bold"], " estos rangos variar\[AAcute]n" }], "Text"], Cell["\<\ Pondemos observar la se\[NTilde]al A, seleccionando el rango apropiado\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"ListDensityPlot", "[", RowBox[{ RowBox[{"Abs", "[", RowBox[{"fouriersinedata", "[", RowBox[{"[", " ", RowBox[{ RowBox[{"Range", "[", RowBox[{"35", ",", "45"}], "]"}], ",", " ", RowBox[{"Range", "[", RowBox[{"35", ",", "45"}], "]"}]}], " ", "]"}], "]"}], " ", "]"}], ",", " ", RowBox[{"Mesh", "\[Rule]", " ", "False"}]}], " ", "]"}], " "}]], "Input"], Cell[BoxData[ GraphicsBox[GraphicsComplexBox[CompressedData[" 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