Please show work and please do not use AI Problem 4:Let X(t) be a random process as: X(t) = cos(2лft+),where is a random variable distributed uniformly over (0, 2). This means that its PDF is1for Є[0,2]fo()=2π0otherwise(a) Determine the expectation of X(t), mx(t).(b) Determine the autocorrelation function of X(t), Rx(t,t+t).(c) Is X(t) a wide sense stationary (WSS) process? Explain why.(d) Determine the power spectral density (PSD) of X(t), Sx(f).

(a) **Expectation of \( X(t) \) (Mean):**The expectation, denoted as \( m_X(t) \), represents the…

Answered: Problem 4: Let X(t) be a random process…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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2. The function F is represented by the following sum-of-product form with d as the don't care conditions. I F(A, B, C, D, E) = (0,5,6, 8, 9, 10, 11, 16) + d(20, 24, 25, 26, 27) a) Use the Karnaugh map to obtain the simplified Boolean expression for the function F.
y(t) = e-1u(t) The above equation defines a continuous time signal y(t) from a pressure sensor at a plant. a.Determine the power & energy of this system. b.What are the 3 areas of application of i.Signals ii.Systems c.Briefly summarise with explanation the difference between discrete & continuous time signal and also write an expression that describes each signal type.
Use Karnaugh maps to find all possible minimum sum-of-products expressions for each function. (b) g(d, e, f) = Em(1, 4, 6) + Ed(0, 2,7) (c) F(p, q, r) = (p+q' + r)(p' + q + r)
F(A, B,C, D) =) (3,6, 7, 10, 11, 12, 14) How many equal alternative minimizations this function has?
The signal x(t) is band-limited to 40 Hz and is modulated with a 320 Hz carrier, which generates y(t). This signal is then processed by a quadratic-law device that produces the output g(t) = y²(t). a) What is the minimum sampling rate for x(t) that avoids aliasing?b) What is the minimum sampling rate for y(t) that avoids aliasing?c) What is the minimum sampling rate for g(t) that avoids aliasing?
Let xo and x1 be continuous-time signals. Suppose that xo is an even signal. a) Show that (xo * x1)(0) = S, co(t)¤1(t)dt. b) By using part a) show that 1 | To(t)#1(t)dt - Xo(w)X1 (w)dw 27
2. Find the minimum product of sums for: F(A,B,C,D,E)= m(0, 1, 2, 6, 7, 9, 10, 15, 16, 18, 20, 21, 27, 30)+E d(3, 4, 11, 12, 19)
2) A joint pdf is described below. A new random variable is formed as shown: W=Y+X. Determine an expression for the CDF for W. Please solve all integrals -4 y 4 -4 4 X 1 128 0 fxy(x, y) 2-1 = −4 < y < 4, −4 < x < 4 y<-x otherwsie
let us say we are given ZA and Z'B and those two are prime implicants of a specific function. The Z standing for a variable, while the A and B are both two product terms. Consider A*B does not equal to zero, Is their consensus AB an implicant? Also is it a prime implicant? If the answer is yes a prime implicant then prove it. If the anwer is no not a prime implicant give a counterexample to show the opposite.
For the function f(a,b,c,d)= Em(0,1,3,5,6,7,8,10,14,15), find all minimum sum-of-products solution, using the Quine-McCluskey method.
DIGITAL COMMUNICATION
a) The dynamics of a discrete-time system are determined by the difference equation;8yk+2 –6y+1 +yk=9Determine the response of the system given thaty0=1 and y1=1.5 b) Find the state transition matrix for the digital system given byX (k+1) = [ -1 0] x (k) [ 1 3] c) Obtain Z-transform of (1-e-Ts )/s(1/s+1) d) The z-transform X (z) of a function X (k), is given by;X (z) =z(0.1065z +0.09021)/(z-1)(z2-1.5z+0.6967) Determine an expression for X (k), by finding the inverse z-transform function of X(z)

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