Unpolarized and polarized elementary kaon electroproduction at MAMI
Elementary CT Signalsfaculty.citadel.edu/potisuk/elec309/ppt/2018/ct_esig.pdf · 1 Elementary CT...
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1 Elementary CT Signals Prof. Siripong Potisuk CT Sinusoidal Signal Expressed with the sine or cosine function Three intrinsic parameters: A = amplitude = angular frequency (rad/s) ϕ = phase angle (rad) ) cos( ) ( ) sin( ) ( t A t v t A t i
Transcript of Elementary CT Signalsfaculty.citadel.edu/potisuk/elec309/ppt/2018/ct_esig.pdf · 1 Elementary CT...
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Elementary CT Signals
Prof. Siripong Potisuk
CT Sinusoidal Signal
Expressed with the sine or cosine function
Three intrinsic parameters:
A = amplitude
= angular frequency (rad/s)
ϕ = phase angle (rad)
)cos()(
)sin()(
tAtv
tAti
2
Derived Parameters
Sinusoidal Metrics
Average or DC value of zero
A power signal with
RMS value =
Bounded between -A and A
2
2APavg
2
APavg
3
Example: Determine the parameters of the periodic
signal 1)3/8.0(cos2)(~ 2 ttw
Why Sinusoidal Function
Occur naturally : pendulum motion, bouncing
ball, string vibration, ocean surface ripples, etc.
Easy to handle mathematically
Easy to generate and transmit dominant
form of signal in the communications and power
industries
A set of harmonically related sinusoids is used
in Fourier series representation of well-defined
periodic signals
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CT Real Exponential Signals
aBu(t)Betx at ,for )(
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CT Complex Exponential Signals
Can be expressed analytically as
Periodic with a period of
Average Power:
)sin()cos(
)(~
00
00
tAjtA
eeAAetxtjjtj
0
20 T
2~ APx
CT Unit Impulse
Continuous-time impulse function
Also known Dirac Delta Function
Defined as a result of the limiting operation
on the width of a rectangular pulse while
keeping the unity area constant
constant area = strength
1)( and 0 ,0)( dtttt
6
)(lim)(
otherwise
2/2/
,0
,/1)(
0
tdt
ttd
Properties of CT Unit Impulse
. and at continuous is )(:
)( )()(:Sifting )4
)()()()(:Sampling)3
)()(:Even)2
)(||
1)(:scalingTime)1
00
00
000
btatttxNote
txdttttx
tttxtttx
tt
ta
at
a
b
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Example: Evaluate the following integrals:
tdte
tdttt
t )22( (b)
)1()cos( (a) 2
Example: Graph the following signal:
)()(~0
n
nTttp
This is a periodic signal called an impulse train and
obtained by adding versions of the delta function
that are time-shifted by integer multiples of T0.
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CT Unit Step Signal
A causal CT function defined by
A common test signal for feedback control system
and
0
0
,0
,1)(
t
ttu
dt
tdut
)()(
0
)()()( dtdtut
CT Unit Ramp Signal
A causal CT function defined by
A common test signal for feedback control system
0
0
,0
,1)(
t
ttr
t
tutdutr )()()(
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CT Rectangular Pulse
A even CT function defined by
A common signal in communications system
21
21
2121
||
||
,0
,1)(rect
tutut
tt
General Rectangular Function
22
22
otherwise
)()(
,0
,1rect
TtuTtu
TtTTt
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Waveform Synthesis
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Example: Express the waveforms shown in terms of unit-
step and/or ramp functions.
