Determine if the linear time-invariant continuous-time system with impulse response t 1 h(t) 0. t 1...
Please dont use Laplace or Fourier A linear time-invariant continuous-time system has the impulse response h(t) = (sin(t) + e-t) u(t) (a) Compute the step response s(t) for all 20. (b) Compute the output response y(t) for all t > 0 when the input is u(t)-(t-2) with no initial energy in the system.
3. Design a stable Continuous-time Linear time-invariant system H with all of the following three properties: . The impulse response h(t) has the form h(t) = A8(t) + Be-2 u(t) where A and B are real-valued constants, The angle of H(jw) has the following straight-line approximation ZH(jw) (rad) -7/2 -71 mtmw log scale] 10 100 1000 If the input o(t) is 1 for all time, then the output y(t) is 1 for all time. Determine the system function H(s) that...
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system 2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system
The impulse response h(t) of a linear time-invariant system is 2*pi[(t-2)/2]. Find and plot the output when the system is driven by an input signal that is identical to the impulse response.
4. A linear time invariant system has the following impulse response: h(t) =2e-at u(t) Use convolution to find the response y(t) to the following input: x(t) = u(t)-u(t-4) Sketch y(t) for the case when a = 1
Problem 1 (Marks: 2+1.5+1.5+4) A linear time-invariant system has following impulse response -(よ 0otherwise 1. Determine if the system is stable or not. (Marks: 2) 2. Determine if the system is causal or non-causal. (Marks: 2) 3. Determine if the system is finite impulse response (FIR) or infinite impulse response (IIR). (Marks: 2) 4. If the system has input 2(n) = δ(n)-6(n-1) + δ(n-2), determine output y(n) = h(n)*2(n) for n=-1, 0, 1, 2, 3, 4, 5, 6, (Marks: 4)
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input 1(1) and output y(t) is specified by the differential equation D(D? + 1)y(t) = Df(t). a. Find the characteristic polynomial, characteristic equation, characteristic root(s), and characteristic mode(s) of this system. b. Is this system asymptotically stable, marginally stable, or unstable? Justify your answer.
For a continuous time linear time-invariant system, the input-output relation is the following (x(t) the input, y(t) the output): , where h(t) is the impulse response function of the system. Please explain why a signal like e/“* is always an eigenvector of this linear map for any w. Also, if ¥(w),X(w),and H(w) are the Fourier transforms of y(t),x(t),and h(t), respectively. Please derive in detail the relation between Y(w),X(w),and H(w), which means to reproduce the proof of the basic convolution property...
Consider an linear time invariant system whose impulse response is shown in the figure below. If the input x(t) = u(t) then what will be the output at t=1.5 seconds ?
Consider a linear time-invariant system with impulse response hin (-1, n o 2, n 1 h[n]--1, n=2 0, otherwise (a) Determine the system frequency response H(e"). Then compute the magnitude and (b) Does the system have a linear phase? Briefly explain your answer. (2 marks) (c) Compute the system output yin] for all values of n if the input r[n] has the form of: phase of H(e (6 marks) 1,n=1 2, n 2 n3, n 3 4, n-4 0, otherwise...