Table of formulas
Convolutions:
Continuous-time first and second order lowpass
systems in standard form:
1
H ( j )
1 j
y (t ) x(t ) * h(t ) x( )h(t )d
yn xn* hn
xk hn k
n 2
H ( j )
2
( j ) 2 2n ( j ) n
k
Continuous-time Fourier Series:
x(t )
ak e

Fall 2002
ELG3120A Midterm Solutions
Question 1
(a) y (t ) = (t + 5) cos(
1
)
x (t )
1.
Since the output depends on the present value of the input, the system is causal.
2.
t
y (t ) = (t + 5) cos(
1
)
x (t )
Bounded input generate unbounded output, the sy

10 INTRODUCTION
Under certain conditions, a continuous-time signal can be completely represented by and
recoverable from knowledge of its values, or samples. at points equally spaced in time.
This somewhat surprising property follows from a basic result t

Solution for Midterm
Question 1
(a) y ( t ) = x ( t 1) + x ( 2 t )
Noncausal since the output also depends on the future input
Stable. If the input is bounded as x ( t ) M x < ,
y ( t ) x ( t 1) + x ( 2 t ) 2 M x < , so the system is stable.
Time-invarian