1) In all the cases below, assume that the random processes X(t) and Y(t) are all...
,Two random processes are defined by Y(t)-X(t) cos(wot) where X(t) and Y(t) are jointly wSs. a) If θ is a constant (non-random), is there any value of θ that will make Yl(t) and Y(t) orthogonal? b) if θ is a uniform r.v., statistically independent of x(t) and Y(t), are there any conditions on θ that will make Yı(t) and Y2(t) orthogonal? ,Two random processes are defined by Y(t)-X(t) cos(wot) where X(t) and Y(t) are jointly wSs. a) If θ is...
Three random variables A, B, and C and 1. The random processes X(t) and Y (t) answer the questions below. (24 points) independent identically distributed (id) uniformly between are defined by the given equations. Use this information to are X(t) = At + B Y(t) = At + C (a) Find the autocorrelation function between X(t) and Y(t) (b) Find the autocovariance function between X (t) and Y(t). (c) Are X(t) and Y(t) correlated random processes? Three random variables A,...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is...
Let (t) and (t) be two WSS orthogonal random processes. a. Further define: u(t) = x(t)-2y(t) and v(t)=3x(t)+y(t) b. Find Ru(tau), Rv(tau), Ruv(tau) and Rvu(tau) in terms of Rx(tau) and Ry(tau).
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
2. (30 points) Let X(t) be a wide-sense stationary (WSS) random signal with power spectral density S(f) = 1011(f/200), and let y(t) be a random process defined by Y(t) = 10 cos(2000nt + 1) where is a uniformly distributed random variable in the interval [ 027]. Assume that X(t) and Y(t) are independent. (a) Derive the mean and autocorrelation function of Y(t). Is Y(t) a WSS process? Why? (b) Define a random signal Z(t) = X(t)Y(t). Determine and sketch the...
3.21. Problem. (Section 11.2) In each of the following cases below, assume that X and Y are independent random variables then use the Convolution Theorem to derive the proba- bility density function of X +Y. (a) The random variable X is uniform distribution on 0, 1) and the random variable Y is an exponential distribution with = 0.2. (b) The random variable X is a uniform distribution on (0, 2) and the random variable Y is a uniform distribution on...
Please answer #2 A and B for the Lightbulb problem "dy", etc. (a). The marginal density, fr (y), of Y. (Be explicit about all cases.) (b). P(X > 0.1 IY 0.5) (c), E(X | Y 0.5) 2x +2y ) dy 3y: if 0 y < 1, and 0 otherwise 0.1 r2x +2 (0.5) (3) 0.5 dx 64/75 2x +2(0.5) (3)0.52 dx- 5/18 2. Let Y be the lifetime, in minutes, of a lightbulb. Assume that the lightbulb has an expected...
1. Assume that X and Y are both binary random variables. Assume that there are constants, Bo and B such that Y-Ao + AX + t. Assume Elu 1 X-0. (a) Express EY | X-0nters of Bo and B1. (b) Express EY | X = 1] in terms of A, and A. (c)Assume that the joint pdf for (X, Y) is 1/4 f(,y) (0,0) 1/8 if(x, y) = (1,0) 3/8 if (r, y) (0,1) 1/4 if (x,y) - (1, 1)....