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.
The impulse response h(t) of a linear time-invariant system is 2*pi[(t-2)/2]. Find and plot the output...
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
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
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.
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...
2. Let y(t)(e')u(t) represent the output of a causal, linear and time-invariant continuous-time system with unit impulse response h[nu(t) for some input signal z(t). Find r(t) Hint: Use the Laplace transform of y(t) and h(t) to first find the Laplace transform of r(t), and then find r(t) using inverse Laplace transform. 25 points
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 ?
4. Consider the magnitude and phase of the frequency response Hi(2) of a linear and time-invariant (LTI) discrete-time System 1, given for-r < Ω-T, as: H, (12)| 10 phase H1(Ω)--0 for all Ω (a) Suppose an 5cos(n s input to System 1. Find the output ya[n] (b) Suppose ancos(is input to System 1. Find the output ybn] (c) Suppose I take the discrete-time signal from part (a): xa[n] 5cos(n), but I remove half of the values: to arrive at a...
4. Let S be a linear, time-invariant, and causal system whose input x(t) and corresponding output y(t) are shown below: r(t) Page 1 of 2 Please go to next page... y(t) ? (a) Find the impulse response function h(t) of ? (b) Find the output of S when its input is e*, t<0, t2, t20
(c) If the impulse response function of a linear time invariant (LTI) system is h0)-Se u(), compute the output of this system due to an input ) which is a 4 second pulse of height 3, as shown in Fig.1 below. x(t) t(sec) 0 Fig.1 Input signal 10 marks/
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...