3-(10 points) Consider a C-T. LTI system given below X(t) - h(t) y(t) The impulse response...
(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)
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)...
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...
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?
1. (20 p) Compute and sketch the output y(t) of the continuous-time LTI system with impulse response h(t) = el-tuſt - 1)for an input signal x(t) = u(t) - ut - 3). 2. (20p) Consider an input x[n] and an unit impulse response h[n] given by n-2 x[n] = (4)”- u[n – 2] h[n] = u(n + 2] Determine and plot the output y[n] = x[n] *h[n].
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
In each step to follow, the signals h(t), a(t), and y(t) denote respectively the impulse response, input, and output of a continuous-time LTI system. Accordingly, H(w), X(w) and Y(w) denote their Fourier transforms. Hint: Carefully consider for each step whether to work in the time domain or frequency domain. (b) (25 points) On the axes below, provide a clearly labeled sketch of y(t) for all t given Σ H(w)-( ) sine? (w/8) j2Tt r(t)-e δ(t-n/2) and with sinc(t) = sin(t)/t...
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,...
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x) = sin(πx)/πx ): h(t) = 8/π sinc(8t/π) where input x(t) of the LTI system is the following continuous-time signal x(t) = cos(t) cos(8t) a) find the Fourier transform of x(t) b) find the Fourier transform of h(t) c) Is this LTI system BIBO stable? Prove d) find the output y(t) of the LTI system