# 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.
3. Explain how your answer in (ii) can be used to answer (i).
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.

## Recent Case

### 盘点留学生常用5 种最佳笔记方法，哪一种适合您

SCI期刊论文的发表过程是一项复杂而细致的工作，涉

### 轻松掌握万能Essay模板，撰写一篇合格的英文论文

Python可谓是当下最火的编程语言，同时，Pyt