# Engineering Exam代考：ELEN30012 Signals and Systems

## 信号与系统的代写高分代写案例

Question 1

• I am a non-zero continuous-time signal x. When you use me as an input signal to a stable linear time-invariant system then the output signal will be myself times a constant complex number. Who am I? Explain your answer-but no proofs are needed.
• Consider a continuous-time system given by the equation

y ⑴=sin(tXt),

where v denotes the input signal and y denotes the output signal.

1. Is this system linear time-invariant? If “no”, which property is miss­ing: “linearity” or “time-invariance”, or both——explain your answers. If “yes”, give a proof.
2. Consider the response y to the input signal v given by v(t) = cost Show that y can be expressed as = 6cos(u；of — </>), where b, and <p are positive real numbers and where (p < 2兀；be sure to give the numerical values of b, and 0.
4. Consider an ideal filter with frequency response

1        0 < |cu| <

0 otherwise ‘

where 3c is a positive real number. Consider the output signal y that is the response of this filter to the periodic input signal v from part (b). For S =开/3 it can be shown that the signal y can be written as

y(t) = & + K2cos(δ)，

where K? and a are real numbers. Determine K]，K2 and a.

• Repeat (c) for = tt/8.
• Repeat (c) for ljc = 2tt/3.
• [Consider the wave w given by

oo

w(t) = g[t — 81) for all i G R,

1——OQ

with g defined for alU 6 R as

W = J        4             -2 < t < 0

0         [    0            otherwise.

Repeat part (b) for this wave w.

• Which of the following discrete lime signals are periodic? No explanations are needed; there can be zero, one or more than one answer.
• x[n) = cos(7rn)
• x(n) – cos(n\/5)
• x(n) — cos(n\/5) + cos(7T7i)
• x(n) — cos(n\/5) + cos(2n\/5)
• Which of the following continuous time signals are periodic? No expla­nations are needed; there can be zero, one or more than one answer.
• x(t) = C0S(7Tf)
• x(t) = cos(t\/5)
• x(t) = cos(t\/5) + cos(7rt)
• x(t) = cos(t\/5) + cos(2t\/5)

Question 2

In this question 6 denotes the discrete-time unit pulse signal:

J(n) = |                       [0 otherwise.

• 11 mark] Consider the discrete-time signal x, defined for all n e Z, given by

x(n\ = J 1                 九=123

[0         otherwise.

Further define the discrete-time signal y by

y(n) = x(n) + x(—n) + d(n).

Sketch y and make sure that you indicate relevant values in your plot.

• Plot the signal where denotes discrete-time convolution and x and y are as in (a). Make sure that you indicate relevant values in your plot.
• Let x be as in part (a). Consider the system that has x as its unit pulse response. Compute the system’s step response.

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