2. 设 是窄带信号，定义 是在 区间上均匀分布的随机相位。 是寬带信号，它是一个零均值、方差为1的白噪音信号e(n)激励一个线性滤波器而产生，其差分方程为 。

1）　　计算 和 各自的自相关函数，并画出其函数图形。根据此选择合适的延时，以实现谱线增强。

2）　　产生一个 序列。选择合适的 值。让 通过谱线增强器。画出输出信号 和误差信号e(n)的波形，并分别与 和 比较。

-Computer Experiments:　



1. Consider an AR process x(n) defined by the difference equation



where v(n) is an additive white noise of zero mean and variance　.The AR parameters　and　 are both real valued:



a)　　Calculate the noise variance　 such that the AR process x(n) has unit variance .Hence , generate different realization of the process x (n).

b)　　Given the input x (n), an LMS filter of length M = 2 is used to estimate the unknown　AR parameters　 and　 . The step size　 is assigned the value 0.05. Compute and plot the ensemble average curve of　and　 by averaging the value of parameters　and　 over an ensemble of 100 different realization of the filter. Calculate the time constant according to the experiment results and compare with the corresponded theoretical value.

c)　　For one realization of the LMS filter, compute the prediction error

　　　　　　　　

And the two tap-weight errors

　　　　　　　　

and　　　　　　　



Using power spectral plots of　, show that