I only need help with part E, please. I posted the whole problem in case you want it. SOLVE ONLY PART E
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Given a LTI system with the following input signal x(t), The impulse response of the system is defined as, h(t) = 2u(t - 2). (a) Find the expression of x(t). (b) Sketch the impulse response h(t). (c) Find the output of the system y(t) = x(t) * h(t). (Show all the necessary intermediate steps.) B. Consider an input x[n] and a unit impulse response h[n] given by x[n] = (1/3)^{n-2} u[n - 2], h[n] = u[n + 2]. (a) Sketch the signal x[n] and the impulse response h[n]. (b) Determine the output y[n] = x[n] * h[n]. (Show all the necessary intermediate steps.)
Sri K.
Problem 3. (LTI systems, impulse response) Recall that any signal can be decomposed into a sum of scaled unit impulses and recall that a unit impulse can be constructed from a linear combination of unit step functions. Now consider ̳[n] = a^n u[n], 0 < a < 1 a. Show that any signal x[n] can be decomposed as x[n] = ∑_{k=-∐}^∐ c_k ̳(n - k) and express c_k in terms of x[n]. Hint: recall that ̴[n] = u[n] - u[n - 1]. Show that ̴[n] = ̳[n] - a̳[n - 1] and use this to answer part a. b. Use the properties of linearity and time invariance to express the output y[n] = A(x[n]) in terms of the input x[n] and the signal g[n] = A(̳[n]), where A(·) is an LTI system. c. Express the impulse response h[n] = A(̴[n]) in terms of g[n] = A(̳[n]).
Evaluate the following integral: 1- Evaluate the following integral: ∫[0 to π] 1 / (1.25 + cos w) dw 2- If the input to a LTI system is x(n) and the system time impulse response is h(n). Find output y(n) if: x[n]= e^(-j0.5πn) H(e^jw) = 2+jW 3- The unit impulse response for a Linear Time Invariant Discrete Time System is h[n] and its output is discrete time unit impulse function δ(n). Find its input x[n] if the DTFT of h[n] defined as: H(e^iw) = (1 + 0.7e^-jw) / e^+jw 4- Let x(n) is a real discrete signal and has DTFT X(e^jw). Then, find y(n) if Y(e^jw)=X(e^j3w)
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