Review
Zybooks
examples
Ch 1
how one parameter changes
depending on another parameter
Signal
information about
visuallyrepresented through waveforms
System process that creates an output signal in response
signal
to
Vi
o
R2
I
R
yo
r
Vi
voltage divider rule
realsystems
for too
Noncasualsignal D xnetsto for t co
Anti casual xact o for t o
Physicallyrealizable systems
Casualsignal D xcts o
Analogsignal similaritybetween the measured
signal andphysicalquantity a b b
Discrete time
signal dependentvariable v continues
to enjoy infinite resolution in terms ofits own
t
magnit.de but not along independent variable
LD Ven
digitalsignals are moreimmune tonoise
interference thananalog counterparts
digital
disc
g
to
an
input
1 2 Signal Transformations
yet
x Ct
T
T 0
is delayed by seconds relative to xD
yet
TCO yet is advanced
T seconds
by
peak occurs earlier
Timeshift transformation
Sliding the waveform to the
when T is positive and
the
along
light
time axis
sliding left when negative
scaling transformation
Time
y Lt
yz
t
Zt
X
yet
compressed
2
x
x
expanded
at
slopes have doubled
Slope has reduced
Time reversal transformation
yet
Écoites
XC E
negative
Combined transformation
yet
Z t
2C t
x Cat
b
T
x Ca t
bla
bad
x
act D
time scale
x Cat
T
x Cat
or
TD
vise versa
yet
timeshift
Ex
Fanfare
It log Ct
log
lot
EX
Shiftright by 0.5
COS
CTX rect x
cosctcxto.gg
rectato s
costing rect x to s
sina.rectcxto.es
1 3 Waveform Properties
even symmetry waveform is symmetrical
with respect to vertical axis
XC
XC t
Odd symmetry shape
side
of the
minor image
right
y Ct
the
on
left
hand
vertical axis is inverted
the waveform on
hand side
of
yet
even x even
even x odd
odd
Et
x
X CE XzCE
even
odd
x odd
Periodic Us Non periodic
Ct
xCt
n
the
even
Period
repeats itselfevery
To seconds
Examples
of Ct
periodXCETT
cos
COS CUT Ht T
X
xCt
Cos Cat
Curt
Tls
1 4 Non periodic
t
XCE
0.5
cos
fog
waveforms
COSCUTS
CUTE
o
za
2
COSCUT'D
12
1
1
Singularityfunction not finite everywhere
derivative
Unitramp function ret T
re
ret D
are
EYE
E
or has
defined
O
FIEF
as
infinite
1.5
pct
E
Power
Signal
Ect
and
Energy
R
It
Set pct
t
The instantaneous
of any signal
E
x et
c
t c ta
and
power
x CER
pct
t
de
Emo fix
Ital energy
L
00
total
energy
t
Excelled
L
to od
average power Pav
Pav
liftoff
III
500
Pau lying
Pav
O
CE
Epee
at
Xcel
at
finite
foot
Ix card
t
Pensifnal
Delaying
does
not
alter
the
energy
CHECK OUT THE EXAMPLE
Pav
Af
in
a
sinusoid