信号与系统课后答案

12111222112211122231(1)()cos4sin6()()2(),22().3323.22(2)(),8,212(),.5ftAtBtXtXtXtTwXtTwTTTTTXtTwXtTw对为周期信号,对也为周期信号,因是有理数,则X(t)是周期信号,3-3.解：由题易知11w2T210aa132ab故210cc132cc其单边幅度谱如图3-3-120F11F22jF213FnnFF故双边幅度谱如图3-3-2所示)33cos()42cos()4cos(22ttttf故有414233其相位谱如图3-3-3所示3-4.(b)21)1(100dtTtTaT0)cos()1(20dtnwtTtTaTndtnwtTtbTn)sin()1(0=n1故])sin(1)2sin(5.0)[sin(15.0)(2nwtnwtwttf210FnjjbaFnnn1)(21)2,1(n3-6.(a)由于f(t)为偶函数，只含有直流分量和偶次谐波余弦分量。0F图3-3-2双边幅度谱-31w-21w-1w01w21w31ww10.5nF031w12w31ww图3-3-3相位谱44n022c1w12w31wwnc0c1c13c图3-3-1单边幅度谱(f)由于f(t)为偶函数，只含有直流分量和偶次谐波余弦分量。02101210212210002022312()cos()21{()}(){()}{cos()}22()()24{()}()224{cos()}[()()]()(){[]44wjwjfftwtftFwftwtEwFwSaEwftSaewt解:由频域卷积定理有FFF由由时移性质可得F而F即0202()[]]}4wjwwSae3-11.解：（1）∵()()2wGttSa∴000()2()2wwtwSaGw令04w有4sin242()2tGwt∴4sin2(1)()(1)jwtGwet3-25.(3)2121212121ssfT，带宽为(4)2222121ssfT，带宽为(7)2222121ssfT，带宽为(8)22222121221212121ssfT，带宽为3-39.解：（1）由图可知：jRcjRcjcjFUHc4410101111（2）把周期电压源信号tf展开为傅里叶级数0sin22cos2cos211222222220nTTnTTTTbTnnEdttTnETdttntfTaTEEdtTdttfTa则2Ttf展开为：tTnnnEEtTnaatfnnn2cos2sin222cos110有展开式可以得出：直流分量为：2E1n时，基波分量为：tTEtTE2cos22cos2sin23n时，三次谐波分量为：tTEtTE6cos326cos23sin325n时，五次谐波分量为：tTEtTE10cos5210cos25sin523-42.解：此电路的系统函数为CJRLJRCJRLJRIVH112121代入L和C的数值，其幅频特性为：22122221222111RRRRRRH要求无失真传输，即为KH，代入得22122221222111RRRRRRH=k42212221242222221212211RRRRKRRRR令两边对应项系数相等，得222212221222212212211RkRRRRkRRkR解方程组得121RR3-47.解（1）)()()(2wGtsatf)(*)()(11thtftf)().()(11wHwFwF又)(3)(41wGwH故)(3)(21wGwF其频谱如图)2cos()()(12wttftf)]2()2([*)(21)(12)]2()2([2322wGwG其频谱如图)(*)()(22thtftywjewGwGwHwFwY21122)]5.2()5.2([23)()()(H1(w)-4-3-2–101234w3F1(w)-4-3-2–101234w3F2(w)-4-3-2–101234w2/3-4-3-2–101234wY(w)2/3)]5.2()5.2([23)(11wGwGwY（2）)]2()2([*)(21)2cos()()(2)]2()2([2)(22wGwGwF)()()(11wHwFwF)]5.1()5.1([2311wGwG)]2()2([)].5.1()5.1([23)(11)]()5.3()5.3([232112wGwGwG)()()(22wHwFwYwjewGwGwG22112)]()5.3()5.3([23)]5.1()5.1([23)(11wGwGwY112121351211()(2)22(2)[]24[()]2()1()()()4000[()][(1000)(100)]1()()()2SintftSatSattftG解:所以F11F由22222()11[()][(1000)(1000)]221[(1000)(1000)]41[()][(1000)(1000)]4wytGwGwGwGwytGwGw所以F滤波后FF(w)-4-3-2–101234w2/H1(w)-4-3-2–101234w3F1(w)-4-3-2–101234w2/3F2(w)-4-3-2–101234wY(w)-4-3-2–101234w-8-6-4–202468w2/