ENG201: Linear Systems Analysis and Design Assignment, SUSS, Singapore Determine whether the following signals are periodic. If a signal is periodic, then calculate its fundamental period
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] = πΏ[π β 1].
(ii) Determine π¦[π] when π₯[π] = πΏ[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 βπ [π].
(b) Analyse the above systemβs frequency response by computing the Discrete
Fourier Transform of its impulse response.
(c) An input signal π₯[π] = 2 cos ( 2π6 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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