) Consider the signal x(t) shown below. Sketch the following: -1 2 x(t) 1 2 Hint:...

 

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) Consider the signal x(t) shown below. Sketch the following: -1 2 x(t) 1 2 Hint: what function is "delta-like"? 3 i. y(t) = x(t) [1 − u(t − 1) + u(t − 2)] ii. y(t) = f[§(7 + 1) − 8(7 − 1) + 8(7 — 2)]x(T)dt iii. y(t) = x(t) + r(t + 1) − u(t) − 3r(t) + 3r(t − 1) – r(t − 3) (b) (9 points) Evaluate these integrals: i. So f(t+1)8(t+1)dt -∞ 4 8(bt) == 8(t) a ii. fe2Tu(T-1)dT iii. ff(t) (8(t-1) + 8(t + 1))dt (c) (4 points) Let a be a positive constant. Show the following property for the delta function: t ) Consider the signal x(t) shown below. Sketch the following: -1 2 x(t) 1 2 Hint: what function is "delta-like"? 3 i. y(t) = x(t) [1 − u(t − 1) + u(t − 2)] ii. y(t) = f[§(7 + 1) − 8(7 − 1) + 8(7 — 2)]x(T)dt iii. y(t) = x(t) + r(t + 1) − u(t) − 3r(t) + 3r(t − 1) – r(t − 3) (b) (9 points) Evaluate these integrals: i. So f(t+1)8(t+1)dt -∞ 4 8(bt) == 8(t) a ii. fe2Tu(T-1)dT iii. ff(t) (8(t-1) + 8(t + 1))dt (c) (4 points) Let a be a positive constant. Show the following property for the delta function: t