OBAFEMI AWOLOWO UNIVERSITY
ILE-IFE
DEPARTMENT OF ELECTRONIC AND ELECTRICAL ENGINEERING
EEE 309 Mid Semester Test (2018/ 2019 Academic Session)
INSTRUCTION: Answer ALL questions
TIME ALLOWED: 100 minutes
Name:
Reg. No.:
Signature:
1. TRUE or FALSE,
. Prove you answer. TRUE
(
)
Therefore,
.
2. The image called Albers consists of an eight-inch yellow square in the center of a white twelve-inch square
background. Express Albers as a function.
[
] [
]
) [
]
(
) (
(
) {
(
)
) are the RGB values for white.
where (
) are the RGB values for color yellow, and (
3. Each one of Figures Q3a and Q3b implements a 1100 CodeRecognizer. Show that they are equivalent.
Figure Q3a
Figure Q3b
To show that they are equivalent, we must show that they simulate each other. Q3b simulates Q3a with the
simulation relation
(
)( )(
)(
)(
)
Q3a simulates Q3b with the simulation relation
(
)( )(
)(
)(
)
4. An elevator connects two floors, 1 and 2. It can go up (if it is on floor 1), down (if it is on floor 2) and stop
on either floor. Passengers at any floor may press a button requesting service. Using a FSM, design a
controller that manages the elevator’s basic movements. Note that detectors exist at each floor to inform the
FSM of the elevator’s position.
Note that this solution is not unique.
5. TRUE or FALSE, it is possible for a machine without state-determined outputs to be placed in a wellformed feedback composition. TRUE
6. Define the composite state machine in Figure Q6 in terms of the component machines.
Figure Q6
Assumptions:
(
)
(( ( )
(
where
( )) ( ( ) (
( )
( )))))
(( (
)
(
))
( ))
( ) is a unique solution of
( )
( ( )(
( )
( )))
7. Find a state space representation of the system shown in Figure Q7. You can assume that the initial voltage
across the capacitor is zero. (Hint: let charge be the output of the system)
Figure Q7
( )
( )
( )
∫ ( )
( )
(
( )
)
( )
( )
( )
( )
(
( )
)
̇( )
From the question (hint), ( )
̇( )
(
( )
(
) ( )
) ( )
( )
( ) (but ( )
̇( )
(
̇ ( )
)
̇ ( )
( )
( ) ( )
(
( )
)
̇( )
)
̈( )
(
( )
( )
( )
( )
( )
( )
( )
)
8. Show that if the initial state of a one-dimensional discrete-time SISO system is zero, then
( )
∑ (
) ( )
where y(n), x(n) and h(n) are the output, input and impulse response, respectively.
(
)
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( )
( ) {
( )
( )
, ( )
, ( )
, ( )
, …, Therefore,
the state response and output
( )
,…
response are given by
( )
, ( )
, ( )
, ( )
,
( )
( )
∑
…, ( )
,…
( )
{
( )
{∑
( )}
( )
Suppose the input sequence is ( ) ( )
( )
Combining y(n) and h(n), we have
( )
( )
( )
( )
( )
( )
( ) ∑ (
) ( )
( )
( )( )
( )
( )
( )
( )
9. Construct a hybrid 30-minute parking meter that indicates “safe” or “expired”. The inputs are coin5, coin25
and tick. When coin5 occurs, time is incremented by 5 minutes, and when coin25 occurs, it is incremented
by 25, up to a maximum of 30 minutes. When tick occurs, the time is decremented by 1.
10. From Question 9, draw the state trajectories (both the mode and the clock state) and the output signal when
coin5 occurs at time 0, coin25 occurs at time 3, and then there is no input event for the next 35 minutes.
11. Find the period p and the coefficients
discrete-time signal x where
,
,
,
( )
( )
( ⁄
,
,
, and all other
⁄
)
, while all other
are arbitrary.
.
and
,
,
(
of the Fourier series expansion for the
⁄ )