A CT LTI system with impulse response h(t) = u(t)−u(t−1) is given the input x(t) = (1 − |t|)(u(t ...
The unit impulse response and the input to an LTI system are given by: h(t) u(t) - u(t - 4) x(t) e2[u(t)-u(t - 4)] x(t) 1 y(t) h(t) 1. Determine the output signal, i.e.y(t), you may use any method. 2. Is this system memoryless? Why? 3. Is this system causal? Why? 4. Is this system BIBO stable? Why?
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
(1) For the impulse response (h(t)) and input signal (x(t)) of an LTI system shown below, find and plot the output response (y(t)) by integrating the convolution analytically h(t) x(t) t (s)
Consider an LTI system with the impulse response h(t) = e- . Is the system casual? Explain. Find and plot the output s(t) given that the system input is x(t) = u(t). Note that s(t) in this case is commonly known as the step response of the system. If the input is x(t) = u(t)-u(t-T). Express the output y(t) as a function of s(t). Also, explicitly write the output y(t) as a function of t. a) b) c)
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
(Frequency response of CT LTI systems): You want to design a system whose unit impulse response has the form: h(t) =u(t) - u(t - N). Find all possible values of N >0 such that when the input signal x(t) = cos(πt), the output signal y(t) = 0 for all t.
A causal LTI system yields the following input output relationship. Find h(t), the impulse response of the system. (Hint: Try first to determine the output when the input is u(t)) a(t) y(t) LTT →t 2 2 Figure 1: An input-output pair
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
Consider the LTI system with input ??(??) = ?? ?????(??) and the
impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine
??(??) and ??(??) and the ROCs B. (3 points) Using the
convolutional property of the Laplace transform, determine ??(??),
the Laplace transform of the output, ??(??) C. (3 points) From the
answer of part B, find ??(??)
9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...