1. Question 1 [25 marks] Consider the impulse responses of the two discrete-time transfer functions 1 G(z) = z(z-0.8) G2

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1 Question 1 25 Marks Consider The Impulse Responses Of The Two Discrete Time Transfer Functions 1 G Z Z Z 0 8 G2 1 (112.24 KiB) Viewed 52 times

1. Question 1 [25 marks] Consider the impulse responses of the two discrete-time transfer functions 1 G(z) = z(z-0.8) G2(2) 0.54z 22 - 1.12 +0.59 (a) Determine the initial delay and the value of the first non-zero element of each re- sponse [4 marks] (b) Determine a discrete-time index after which the response of G1(z) can be reasonably approximated to be null [5 marks] (c) Determine the number of samples per period of the response of G2(z), and a discrete- time index after which the response of G2(z) can be reasonably approximated to be null (8 marks] (d) Use the results of (a-c) to draw a sketch of each response. The sketches shall be approximate, but the features of the responses determined in (a-c) should be clearly identifiable. Hint: In the case of G2(z), the response is a sinusoidal sequence with null phase shift. [8 marks]