Problem 1 Find the input-output differential equation relating the input signal f(t) to the output signal y(t).
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- Consider a system whose input x (t) and output y (t) satisfy the differential equation of the first order dy(t)/dt + 2y(t) = x(t) The system also satisfies the initial rest condition. Determine the output of the system y (t) when the input is x (t) = e ^3t u(t)Find the time-domain expression(A) ? = 18.6 ∠ − 54° ?(B) ? = (20 ∠45° - 50 ∠ − 30° ) mA(C) ? = (20 + ?80 − 30 ∠15° ) �a) Y(ω) = 1/(5+jω) The expression above defines the frequency domain signal Y(ω) from a time domain signal y(t) i) Determine the imaginary & real parts of Y(ω). ii.Determine the signal y(t) that produced the signal Y(ω). b)What are the 3 areas of application of i.Signals ii.Systems c) Briefly summarise with explanation the difference between discrete & continuous time signal and also write an expression that describes each signal type.
- Input output relationship of a continuous time linear time invariant system is representedby a differential equation given asWhen the unit step function is applied to the input of the system whose block diagram is given below, the output response takes the value c (0.2) = 0.11 for t = 0.2 s and c (infinity) = 0.333 for t = infinity. What is the steady-state error of the system? calculate.How do you determine if a differential equation is linear and time invariant for the class signals and systems? For instance, how do you accomplish this for T1{x(t)} = y(t) s.t. D^2(y(t)) + (t^2)*y(t) = x(t) (please note the star I am using as multiplication here not anything else).