A stationary, Guassian process X (t) with mean ?X and variance ?2X is passed through two linear

Question:

A stationary, Guassian process X (t) with mean ?X and variance ?2X is passed through two linear filters with impulse responses b1 (t) and b2 (t) yielding processes y (t) and Z (t), as shown in Figure.

(a) Determine the joint probability density function of the random variables Y (t1) and Z (t2).

(b) What conditions are necessary and sufficient to ensure that Y (t1) and Z (t2) are statistically independent?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Communication Systems

ISBN: 978-0471178699

4th Edition

Authors: Simon Haykin

See More Books

Question Posted: Feb 09, 2011 05:30 AM

See More Questions

The joint probability density function of the random variables X, Y, and Z is find (a) The joint marginal density functions of Y and Z: (b) The marginal density of Y; (c) P (1/4 < X < 2 , Y > , KZ <...
The joint probability density function of the random variables X, Y , and Z is Find (a) the joint marginal density function of Y and Z; (b) the marginal density of Y; (c) (d) 4ryz? 4ryz, 0 < x, y <...
The joint density function of the random variables X and Y is (a) Show that X and V are not independent. (b) Find P(X > 0.3 | Y = 0.5).
Types of audit procedures Audit procedures are used to gatherevidence to support the auditors conclusions on the fairpresentation of a companys financial statements. Procedures can beperformed...
A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?
Again, consider an analysis of the quantitative variable, length of time in practice (i.e., years of experience). a. Access the data file and find the range, variance, and standard deviation for the...
With reference to Exercise 10.3, what can we say with $95 \%$ confidence about the maximum error if we use the sample proportion to estimate the corresponding true proportion? Data From Exercise...
1. In light of the foregoing payoffs, why did Airbus go ahead with the A380 Superjumbo even though its $10.7 billion development cost required as many as 250 planes to break even by 2010? 2. In 2004,...
Jesse and Tim form a partnership by combining the assets of their separate businesses. Jesse contributes accounts receivable with a face amount of $45,000 and equipment with a cost of $179,000 and...
The vectors span R3. Pare down the set {x1, x2, x3, x4, x5} to form a basis for R3. X2 X2 = X3 = X4 = 274
Let X (t) is zero-mean, stationary, Guassian process with autocorrelation function RX (). This process is applied to a square-law device, which is obtained by the input-output relation Y (t) = X2...
A stationary, Guassian process X (t) with zero and power spectral density Sx (f) is applied to a linear filter whose impulse response b (t) is shown in Figure. A sample Y is taken if the random...
When a large evacuated flask is filled with argon gas, its mass increases by 3.224 g when the same flask is again evacuated and then filled with a gas of unknown molar mass, the mass increase is...
A cross-section of a beam is shown in Figure Q2. If the shear force in this section is V determine the value and the location of the maximum shear stress in the section. In Figure Q2, a = 68 mm and...
Buy the stock, buy the MAR K =25 put and sell all the MAR K =40 calls that are necessary to finance the put purchase. Graph the P/L at expiration of the strategy in the first part. t = FEB 26 St...
Littletown Theater has a monopoly over the performing arts market in Littletown since there is only space for one theater. Marginal cost is constant at $30. The following graph shows the demand and...
Sally would like to salary sacrifice some of her salary into superannuation. Her employer contributions are $15,000 each year. What is the maximum amount of her salary that she can salary sacrifice...
Disney Co. has an exciting project and seek your advice. The project has an initial outlay of $10 million and is expected to generate $2 million each year for the next 10 years. You decide to...
A sample of 24 older homes are randomly divided into four groups and retrofitted with different types of insulation. The response variable is the relative decrease in energy usage. The data is...
Determine by direct integration the values of x for the two volumes obtained by passing a vertical cutting plane through the given shape of Fig. 5.21. The cutting plane is parallel to the base of the...
Explain the different ways to represent compounds. Why are there so many?
What is attenuation?
What is white noise and how does it affect a signal?
What is intermodulation noise?
The veterinarian suspects a bleeding disorder in a young mixed breed dog. He requests that you perform a BMBT test on the dog. What other piece of information is necessary with any coagulation test?
.. Evaluate the following integrals: a) / b) c) d) x4 dx x-1 5x+1 dx (2x+1)(x-1) x3+4x+x-1 .3 x3 + x2 x+4x+3 x4 +5x +4 dx dx e) / 1 x3 - 1 dx
4. Evalute the following: (a) The region bounded by y = (3-2)' y = 0, x = 1, and x = 2 is revolved about the x-axis. (b) The region bounded by y = 1-x2, x = 0, x = 1,is revolved about the line x = 1....

A stationary, Guassian process X (t) with mean ?X and variance ?2X is passed through two linear

Question:

Y() хо

Step by Step Answer:

a The random variable Yt obtained by observing the filter output of impul se response ht at time t i...View the full answer

Communication Systems

Students also viewed these Telecommunication Engineering questions