AMAT 415 — Weeks 10-11 problems

54) Find a signal with z-transform \displaystyle{\frac{2z-1}{z^2+4}}.

55) Find the z-transform of x=\{\sin(\pi n/3)\}. Find the transfer function and impluse response of a filter F such that F(x)=\delta_0.

56) Find the impulse response, transfer function, and frequency response of the following filters. Then plot their amplitude and phase responses. (Feel free to use Matlab for the plots.)

  • y_n=x_n + 2x_{n-1} + x_{n-2}
  • y_n=x_{n+2} + x_{n-2}

57) Find the amplitude response of the filter with transfer function \displaystyle{B(z)=\frac{2}{2-z}}. (Your answer should be evidently real.) Sketch the graph.

58) Find the transfer function of a filter F such that F kills the 400 Hz component of a signal sampled at 1000 Hz. Find such an F whose frequency response is real and even.

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