习题课一
例9.设随机过程 X (t ) sin(2 At ) ,A 是在 (0.1) 上均匀分 布的随机变量，t 只能取整数，证明X (t ) 是平稳过程。证明： mX (t ) E ( X (t )) E[sin(2 At )] sin(2 at) p A (a)da0 1
sin(2 at )da =00
1
R X (t1 , t 2 ) R X (t , t ) E ( X (t ) X (t ))
sin(2 at )sin(2 a(t ))da0
1
0.5, 1 1 [cos(2 a ) cos(2 a(2t ))]da 2 0 0
0 0
E[ X 2 (t )] E[sin 2 (2 At )] 所以，X(t)是平稳过程。随机信号分析 物理学与电子技术学院12