信号分析与处理_杨西侠_课后答案二三五章精选.doc

PAGE 2-1 画出下列各时间函数的波形图，注意它们的区别 1）x1(t) = sin ? t·u(t) 1 1 -1 π 2π 3π t x1(t) 0 4π 2）x2(t) = sin[ ? ( t – t0 ) ]·u(t) 01 0 1 t0 t x2(t) -1 3）x3(t) = sin ? t·u ( t – t0 ) 0 0 1 t0 t x3(t) 4）x2(t) = sin[ ? ( t – t0 ) ]·u ( t – t0 ) 0 0 1 t0 t x4(t) -1 2-2 已知波形图如图2-76所示，试画出经下列各种运算后的波形图 0 0 1 t x(t) -1 1 2 3 图 2-76 （1）x ( t-2 ) 0 0 1 t x ( t-2 ) -1 1 2 3 4 （2）x ( t+2 ) -3 -3 1 t x ( t+2 ) -4 -2 -1 0 1 （3）x (2t) 0 0 1 t x(2t) -1 1 2 3 （4）x ( t/2 ) 0 0 1 t x ( t/2 ) -1 1 2 3 4 -2 （5）x (-t) -3 -3 1 t x (-t) 2 -2 -1 0 1 （6）x (-t-2) x ( x (-t-2) -5 1 t 0 -4 -3 -2 -1 1 （7）x ( -t/2-2 ) -5 -5 1 t 0 -4 -3 -2 -1 1 x ( -t/2-2 ) -7 -6 -8 （8）dx/dt 0 0 1 t dx/dt -1 1 2 3 -2 -δ (t-2) 2-3 应用脉冲函数的抽样特性，求下列表达式的函数值 (1)δ(t) dt = x(-t0) (2)δ(t) dt = x(t0) (3) u(t -) dt = u() (4) u(t – 2t0) dt = u(-t0) (5)δ(t+2) dt = e2-2 (6)δ(t-) dt = + (7) =– = 1- = 1 – cosΩt0 + jsinΩt0 2-4 求下列各函数x1(t)与x2(t) 之卷积，x1(t)* x2(t) (1) x1(t) = u(t), x2(t) = e-at · u(t) ( a0 ) x1(t)* x2(t) = = = (2) x1(t) =δ(t+1) -δ(t-1) , x2(t) = cos(Ωt + ) · u(t) x1(t)* x2(t) = = cos[Ω(t+1)+]u(t+1) – cos[Ω(t-1)+]u(t-1) (3) x1(t) = u(t) – u(t-1) , x2(t) = u(t) – u(t-2) x1(t)* x2(t) = 当 t 0时，x1(t)* x2(t) = 0 当 0t 1时，x1(t)* x2(t) = = t 当 1t 2时，x1(t)* x2(t) = = 1 当 2t3时，x1(t)* x2(t) = =3-t 当 3t时，x1(t)* x2(t) = 0 x1 x1(t)* x2(t) 0 1 t 1 2 3 (4) x1(t) = u(t-1) , x2(t) = sin t · u(t) x1(t)* x2(t) = = = 1- cos(t-1) 2-5 已知周期函数x(t)前1/4周期的波形如图2-77所示，根据下列各种情况的要求画出x(t)在一个周期( 0tT )的波形 (1) x(t)是偶函数，只含有偶次谐波分量 f(t) = f(-t), f(t) = f(t±T/2) t t T/2 0 3T/4 T/4 T -T/4 -T/2 f(t) (2) x(t)是偶函数，只含有奇次谐波分量 f(t) = f(-t), f(t) = -f(t±T/2) t t T/2 0 3T/4 T/4 T -T/4 -T/2 f(t) (3) x(t)是偶函数，含有偶次和奇次谐波分量 f(t) = f(-t) t t T/2 0 3T/4 T/4 T -T/4 -T/2 f(t) (4) x(t)是奇函数，只含有奇次谐波分量 f(t) = -f(-t), f(t) = -f(t±T/2) t t T/2 0 3T/4 T/4 T -T/4 -T/2 f(t) (5) x(t)是奇函数，只含有偶次谐波分量 f(t) = -f(-t), f(t) = f(t±T/2) t t T/2 0 3T/4 T/4 T -T/4 -T/2 f(t) (6) x(t)是奇函数，含有偶次和奇次谐波分量 f(t) = -f(-t) t t T/2 0 3T/4 T/4 T -T/4 -T/2 f(t) t t T/2 0 3T/4 T/4 T -T/4 -T/2 f(t) 2-