Question: Birthday is 0709 Consider a first-order system with input x(t) and output y(t). Let the time constant be the part of your birth date in

Birthday is 0709

Consider a first-order system with input x(t) and output y(t). Let the time constant be the part of your birth date in the format of day, month (ddmm) in microseconds. Complete the following steps:

  1. Write the differential equation representing the system.
  2. Derive the transfer function H(s).

Note: Label all graphs appropriately.

  1. Use H(s) with MATLAB to complete the following actions:
  • Find the poles are zeros.
  • Find the step response.
  • Find the impulse response.
  • The system output when the input is x(t) = sin (21ddmmt) What do you notice? Do you need to change the ddmm value? Why or why not? Change it if you have to.
  • Find the Laplace transform of x(t) = sin (21ddmmt) using MATLAB.
  • Find Y(s)=X(s)H(s) using MATLAB.
  • Find y(t) using the ilaplace function in MATLAB.
  1. Find H(w) analytically.
  • Find the Fourier transform of x(t) = sin(21ddmmt) using MATLAB.
  • Find Y(w)=X(w)H(w) using MATLAB.
  • Find y(t) using ifourier function in MATLAB.
  1. Comment on the results and compare the Laplace and Fourier transform results.

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