本次加拿大代考主要为信号系统相关的限时测试

3 Questions

Question 1.

Using the graphical method (i.e., the method used during the lectures), compute x h(t), where x and h are as shown in the

ﬁgures. (You must compute x h, not h x.) For each separate case in your solution, you must state the convolution result and

the corresponding range of t as well as show the fully-labelled graph from which this result is derived. Each curve in these

plots must be labelled with its formula (e.g., 3t +1, e t

, t

2 +3, etc.). Each convolution result may be stated in the form of

an integral, but the integral must be simpliﬁed as much as possible without integrating. The unit-step function must not appear

anywhere in your answer. [8 marks]

Question 2.

A LTI system H has the impulse response h(t) = t[u(t 1) u(t 2)]. Determine whether H has each of the following

properties:

(a) memoryless [1 mark]

(b) causal [1 mark]

(c) BIBO stable [3 marks]

In your answer to each of parts (a) to (c), you must explicitly state any conditions that you are testing in order to arrive at

your answer. Show all of your work and do not skip any steps in your solution.

Question 3.

Consider the systemH with input x and output y that consists of three interconnected LTI subsystems as shown in the diagram,

where each subsystem is labelled with its impulse response.

(a) Find the impulse response h of the system H in terms of h1, h2, and h3. Show all of your work and do not skip any steps

in your solution. [4 marks]

(b) Suppose now that h1(t) = d(t 2), h2(t) = 5d(t), and h3(t) = d(t). Find a fully simpliﬁed formula for h. [2 marks]

h1

h2

h3 +

x y

Question 4.

A LTI system H has the system function H(s) = a+bs, where a and b are complex constants. The input x(t) = 3et

+2 yields

the output y(t) = H x(t), where y(t) = 3et

+6. Find a and b. Show all of your work and do not skip any steps in your

solution. [5 marks]