1). Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, y(t) denotes the system output and x(t) is the system input. (1) Memoryless (2) Time invariant (3) Linear (4) Causal (S) Stable (A) y(t) = [cos(3t)]x(t)] (B) y(t)= 0, x(t)< 0; = x(t)+x(t-2), x(t)>_0;
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### System A: \( y(t) = [\cos(3t)]x(t) \) ** Show more…
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1.27. In this chapter, we introduced a number of general properties of systems. In partic- ular, a system may or may not be (1) Memoryless (2) Time invariant (3) Linear (4) Causal (5) Stable Determine which of these properties hold and which do not hold for each of the following continuous-time systems. Justify your answers. In each example, y(t) de- notes the system output and x(t) is the system input. (a) y(t) = x(t - 2) + x(2 - t) (b) y(t)=[cos(3t)]x(t) (c) y(t)=∫_{-∞}^{2t} x(τ)dτ (d) y(t) = {0, t < 0; x(t) + x(t - 2), t ≥ 0 (e) y(t) = {0, x(t) < 0; x(t) + x(t - 2), x(t) ≥ 0 (f) y(t) = x(t/3) (g) y(t)=dx(t)/dt
Sri K.
Which of the following systems is both time-invariant and causal? A. y(t) = x(2t) B. y(t) = x(t + 1) * x(t) C. y(t) = (t + 3) * cos(x(t - 3)) D. y(t) = x(t/4) E. y(t) = x(t) * x(t - 5)
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Q1/ (A) In the following equations make a test and (proof) weather the system is linear or non-linear. 1- y(t) = sin t x(t). 2- y(n) = x(n²). 3- y(t) = t³ x(t) + 10. 4- y(t) = e ^x(t) 5- y(t) = 10 cos 100 π t x(t). Q 2/ Classify and (proof) whether the systems are Time Varying (TV) or Time Invariant (TIV) as below. 1- y(n) = 2 x (n) - y (n - 1). 2- y(t) = x (t+10) + x²(t). 3- y(n) = x (2n+2) - x (n). 4- y'(t) + t y(t) = x (t) 5- y''(t) + 3 y'(t) = x'(t) +2 x (t)
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