1. Solve the following for y(oO-xOho 2. Convolve the following (t) x(t) b) ふ(t) c) e...
Please don't use the Laplace Transform Method. Thank you! 2. Convolve the following: ふ(t) a) 초지 x(t) he) (七) c) e 上 xlt) 仕)
Problem 1: Find the Laplace transform X(s) of x(0)-6cos(Sr-3)u(t-3). 10 Problem 2: (a) Find the inverse Laplace transform h() of H(s)-10s+34 (Hint: use the Laplace transform pair for Decaying Sine or Generic Oscillatory Decay.) (b) Draw the corresponding direct form II block diagram of the system described by H(s) and (c) determine the corresponding differential equation. Problem 3: Using the unilateral Laplace transform, solve the following differential equation with the given initial condition: y)+5y(0) 2u), y(0)1 Problem 4: For the...
use Fourier Transforms to convolve f(t) = e-2t u(t-2) and h (t) = e-4t u(t-3). Check your answer by performing the time-domain convolution. use Fourier Transforms to convolve f(t) = e-2t u(t-2) and h (t) = e-4t u(t-3). Check your answer by performing the time-domain convolution.
Problem 4. Convolve the following input X(t) with the system impulse response h(t) and plot the system output y(t). h(t) Problem 5. Construct a Bode plot of the input impedance DMM 100nF zin - 300F CM 500 ohms
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...
4. Let h(t), (t), and y(t), for -oo < oo, be the impulse response function, the input, and the output of a linear time-invariant system, respectively. Give the following spectra: Input magnitude spectrum: Input phase spectrum: ex(2) T/2 Output magnitude spectrum: tY() Output phase spectrum: ey (2) / 2 Find H() from the above spectra and from the fact that H() 0 for not belonging to the interval (-2,2). Find the impulse response function h(t) from H() found above. Is...
5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F, C2-1F. Identify the natural and forced response of the system a) Find the zero input response. b) Unit impulse response. c) zero state response. d) The total response. e Identify the natural and forced response of the system. 5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F,...
Using parsevals theorem and FT to find y(t) and its power (b) (4 pts) Fourier Series The input signal r(t) and impulse response h(t) of an LTI system are as follows: z(t) = sin(2t)cos(t)-e131 + 2 and h(t) = sin(21) Use the Fourier Series method to find the output y(t) (c) (4 pts) Parseval's Identity and Theorem. Consider the system in the previous problem. Use Parseval's Identity to compute the power P of the output y(t). Use Parseval's Theorem to...
2. Consider the system: CD +2)y (t) 2x (t) a. b. c. d. Find the ZIR if y(0)-2. Find the magnitude of the frequency response. Find the phase of the frequency response. Find the steady-state solution to an input x(t)-10 cos(2t + 300)
If the input to the system described by the difference equation y(n+1) (1/2)x(n+) -x(n) is a) Does it matter what are the initial conditions for nc0 in order to find y(n) for n20? Explain your b) x(n) -u(n) answer. (3 points). Determine the transfer function H(z) and the Frequency Response (H(est) (10 points). Find the amplitude lH(epT)I and the phase He*') as a function of co. Evaluate both for normalized frequency ω T=z/4. ( 10 points) c) Find the steady...