# ENG201: Determine whether the following signals are periodic. If a

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Question 1

(a) Determine whether the following signals are periodic. If a signal is periodic, then calculate its fundamental period.

(b) A linear system, L, has the following relationship,

between its input π₯[π] and its output, π¦[π], where β[π] = π’[π] β π’[π β 4] and
π’[π] is the discrete unit step.

(i) Determine π¦[π] when π₯[π] = πΏ[π β 1].

(ii) Determine π¦[π] when π₯[π] = πΏ[π β 2].

(iii) Is the system linear time-invariant (LTI)?

(iv) Determine and sketch π¦[π] when π₯[π] = π’[π].

(c) Which of the following impulse responses corresponds to a stable LTI system? Justify your answer.

Question 2

Consider the following three linear time-invariant (LTI) systems connected as shown in Figure Q2 below:

(a) The impulse response of each block is given by:

Describe the overall system impulse response βπ  [π].

(b) Analyse the above systemβs frequency response by computing the Discrete
Fourier Transform of its impulse response.

(c) An input signal π₯[π] = 2 cos ( 2π6 π) is fed into the above system. From the
frequency response obtained in Question 2(b), calculate the output signal, π¦[π].

(d) Discuss the stability of the above-given system.

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