6. (20 points) The sample function X(t) of a stationary random process Y(t) is given by: X(t) = …………) where w is a constant, Y(t) and 0 are statistically independent, and 0 is uniformly distributed between 0 and 2n. Find ...
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5.(20 Points) In an optical communications system, the photodetector output is a poisson random variable K. either with an expected value of 10,000 photons (hypothesis H0) or with an expected value of 1,000,000 photons (hypothesis H1) Given that both hypotheses ...
4. (15 points) Transmit 100 bits. The probability of transmitting bit “I”, P[I]=p. Let Xi denote the number of bit “1” is transmitted. (a) What is Px33(x)? Are X1 and X2 independent? (b) Define Y= X1 +X2 +.••+X100. (c) Describe ...
3. (15 points) X and Y have the joint PDF (a) find out B. (b) what’s the minimum mean square error estimation of X given X>1/2?
2. (13 points) If X has an exponential (A.) PDF. what is the PDF of W = X3?
1. (15 points) Two random variables X and Y have the joint PDF given by (a) the value of the constant k that makes fxy (x, y) a true joint PDF (b) the marginal PDF’s of X and Y
4. A discrete-time (DT) waveform originally sampled at 16 KHz is to be added to a music track sampled at 44.1 KHz. Assume resampling system shown below for up-sampling to 441 KHz. (a) Determine the minimum integer value of M and ...
3. Consider the following discrete system (sketched below). (a) Find the Impulse response h[n] of the overall system. (b) Calculate H(e”) in the most compact form. (c) Specify the corresponding difference equation between y[n] and x[n].
2. Let’s consider the IIR filter expressed by (where `b’ is positive) y[n]= 0.9 y[n]-11+ `b’ (a) Decide the proper value of ‘b’ to have [H(0)]=1. Once done, decide the discrete frequency of 3 dB bandwidth, Waft. (5) (b) Based on ...
1. A causal LTI system is described by H(z)= 1 1— —4 Z_i —6 1-i- 1 Z _2 1— — Z— (a) Draw the block diagram for this system In Direct Form II. (3) (b) Draw the corresponding Signal Flow ...