1. (a) Given function 0t2 x(t) = - - 0, otherwise plot function x(-^t + 2)...
Section 2.1 I. Suppose 2(t) if 4<t 5 otherwise Determine the absolute time duration of this signal and plot it. 2. Suppose rn]-1 if n 23 otherwise Classify this signal as left-sided, right-sided, two-sided, or time-limited and plot it. Section 2.2 3. Suppose r(t) is as given in Problem 1. Plot and give an expression for y(t) - (^ + ^t). Also determine the turn-on and turn-off times for y(t) 4. Suppose a[n] is as given in Problem 2. Plot...
Determine and plot the autocorrelation function rxx[l] of the
signal 1, 0≤n≤N−1
x[n] = 0, otherwise .
Determine and plot the autocorrelation function r] of the signal x[n] = 0, otherwise
3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t).
3. Consider the periodic signal x(t) = 0 otherwise (a) Plot r(t). (b) What is the period T of x(t)? (c) Find the CTFS coefficients ak for (t).
Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...
Consider a signal x(t) which is given as 1 x(t) - 2 <t<2 2 0, otherwise a) Sketch x(t) b) Sketch 3x(t – 1) c) Sketch – 2x(-t - 1) Identify all labels and amplitudes to get the whole score.
1. Suppose x(t)-1f 4<t<5 otherwise 0 Determine the absolute time duration of this signal and plot it. 2. Suppose lnlf n 2 otherwise Classify this signal as left-sided, right-sided, two-sided, or time-limited and plot it.
(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
х 0<I< 3. The tent function is defined by T(x) = 1 - < x < 1 2 otherwise (a) Express T(2) in terms of the Heaviside function. (b) Find the Laplace transform of T(x). (c) Solve the differential equation y" – y=T(x), y(0) = y'(0) = 0
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0