posted 10 months ago

a. What is the PDF, mean and covariance matrix of the vector g = U z where U is a deterministic(constant) unitary matrix. Unitary matrix is a matrix that has the property U"U = I

b. In part (a), did you find out that the two vectors q and z have the same PDF? If Yes, we call zisotropic vector. Read through the Summary Box (Summary A1) in Appendix A

posted 10 months ago

\text { a. What is the mean vector and covariance matrix of the vector } z=\left[\begin{array}{l} z_{1} \\ z_{2} \end{array}\right]

С.In part (b), you calculated E(y). Which one of the following is correct:

\text { i. } E(v)=e^{j \theta} E(z)

\text { ii. } E(y) \neq e^{j \theta} E(z)

d. In part (c), if the correct answer is (i) then the vector z is called circular symmetric vector. If the correct answer is (ii) then the vector z is not circular symmetric vector. Read through the Appendix A to learn more about this statement.

posted 10 months ago

b. Write the PDF of the random variable y = a x + b where a and b are two deterministic real values.

a. Write the probability density function (PDF) of the x

posted 10 months ago

Now assume two independent real random variables x, and x2. Each one of them is Gaussian with zero mean and variance o² = 1

b. What is the mean vector and covariance matrix of the vector z = Ax + b where A is a 2x2deterministic (constant) matrix and b is a 2x1 deterministic (constant) vector.

posted 10 months ago

The bandpass filter has a bandwidth of 2W centered at fo, and the lowpass filter has a bandwidth of W. Plot the spectra of the signals x (t), yı (t), y2(t), y3 (t), and y4 (1).What are the bandwidths of these signals?

posted 10 months ago

1. Plot Y (f), the Fourier transform of y(t).

2. Show that if y(t) is transmitted, the receiver can pass it through a replica of the system shown in Figure P-3.11 (b) to obtain m(t) back. This means that this system can be used as a simple scrambler to enhance communication privacy.

posted 10 months ago

posted 10 months ago

posted 10 months ago

m(t)=2 \cos 2000 \pi t+\cos 6000 \pi t .

The modulated signal is

u(t)=100 m(t) \cos 2 \pi f_{c} t

\text { where } f_{c}=1 \mathrm{MHz}

1. Determine and sketch the spectrum of the AM signal.

2. Determine the average power in the frequency components.

posted 10 months ago

\text { a. What is the mean vector and covariance matrix of the vector } x=\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]

b. What is the mean vector and covariance matrix of the vector z = Ax + b where A is a 2x2deterministic (constant) matrix and b is a 2x1 deterministic (constant) vector.