随机信号处理考试5

《随机信号分析与处理》期末自我测评试题（五）

考试形式：闭卷考试时间： 150 分钟满分： 100 分

考试对象：学员队别：大队学号：

学员姓名：各专业必修

(1) A random process may be viewed as a _______________________, with time t as a parameter.

(2)When the autocorrelation function of the random process X(t) varies only with time difference , and the mean

is a constant, X(t) is said to be ____________________.

(3)A white noise is applied to a linear time-invariant system; the output process is __________________.

(4) The autocorrelation function defines how much a signal is _________ a time-shift version of itself. White noise is known to correlate only with an exact replica of itself.

(5) If X(t) has a periodic component, then __________________ will have a periodic component with the same period.

(6) A random process X(t) is ergodic if all of its statistics can be determined from _______________of the process.

(7) According to Wiener-Khinchin Theorem, the autocorrelation function of a wss process and its _________________ constitute a Fourier transform pair.

(8) For a Gaussian process X(t), If it is stationary in the wide-sense, it is also __________.

(9) For a detection problem, the observation is ___________ which is generated according to some probability law.

(10) X(t) is called ____________ process if its PSD is concentrated a small frequency band and the frequency band is much less than center frequency.

(11)The decision problem in the case of two hypotheses essentially consists in partitioning _______________ Z into two regions Z0 and Z1.

(12) The estimate to minimize the mean square error is called _________________.

(13) Decision tests based on several optimum criteria fall into the general class of________________. But thresholds will , in general, be different for the different criterion

(14)For nonrandom parameter estimation problem, if an efficient estimate exists, it must be ________________.

(15) For a linear mean square error estimate, __________ is orthogonal to the observation.

(1) Consider a detection problem. Assume the decision rule can be expressed as

Then, the false alarm probability can be written as

(a) ;

(b) ;

(c) ;

(d) ;

( )

(2) For an estimation problem, the posteriori density can be expressed as

Then, the maximum a posteriori (MAP) estimate of is

(a) (b)

(c) (d)

( )

(3) The autocorrelation function of the random process X(t) is given by

Then, the mean and the variance of X(t) are

(a) 5, 9 (b) 25, 3

(c) 25, ±3 (d) 25, 9

( )

(4) Suppose that X(t) is a Gaussian random process with zero mean and autocorrelation function

. Then the third order PDF at time is , where the covariance matrix is

(a) (b)

(c) (d)

( )

(5) The state transition diagram of Markov chain is shown as following figure. Then, the state transition matrix of this Markov chain is given by