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]