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# 信号系统代考 | ECE 260 Continuous-Time Signals and Systems

### 信号系统代考 | ECE 260 Continuous-Time Signals and Systems

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

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

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
(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] 