4. Analysis of Digital Pulses
21
CSN 08704 D ata,A udio,Video and Im ages http://asecuritysite.com/comm s Telecomm unications P rofBill Buchanan 4.Analysis ofD igitalP ulses
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Transcript of 4. Analysis of Digital Pulses
CSN08704
Data, Audio, Video and Imageshttp://asecuritysite.com/comms
Telecommunications
Prof Bill Buchanan
4. Analysis of Digital Pulses
CSN08704
Data, Audio, Video and Imageshttp://asecuritysite.com/comms
Telecommunications
Prof Bill Buchanan
4. Analysis of Digital Pulses: Frequency and Time Domain
Signals
V t V ft( ) sin( ) 2 Time domain Frequency domain
Vmax
f
T (1/f)
(1/T)
-V max
0
Vmax
AmplitudeAmplitude
Repetitive Signals
ω1 = 2.π.f1 where f1 is the fundamental frequency.
tNBtBtBtNAtAtAAtf
N
N
11211
112110
sin...2sinsin cos...2coscos)(
Repetitive Signals• 1 1st, 0.4 2nd, 0.2 3rd.• 0.4 4th, 0.05 5th.• Link.
Repetitive Signals
Example
1
0.3
0.2
1/T 3/T 5/T f
T
0.9
-0.9
0
Time domain Frequency domain
V
f t t t t( ) sin( ) . sin( ) . sin( ) 1 1 10 3 3 0 2 5
Even Symmetry
t
f t A A t A t A N tN( ) cos cos ... cos 0 1 1 2 1 12
Odd Symmetry
t
f t B t B t B N tN( ) sin sin ... sin 1 1 2 1 12
Half Symmetry• No even harmonics ... just odd harmonics.
Time
CSN08704
Data, Audio, Video and Imageshttp://asecuritysite.com/comms
Telecommunications
Prof Bill Buchanan
4. Analysis of Digital Pulses: Pulse Analysis
Repetitive Pulse Stream
t
+V
T
Duty Cycle tT
v t VT
V n f tnn
n
( ) cos( )
2 11
V VT
Nxxn
2 . sinx
T
Sin(x)/x
0 10 20 30 40 50 60 70 80 90
10.90.80.70.60.50.40.30.20.1
0-0.1-0.2-0.3
V VT
Nxxn
2 . sin xT
04 8 12 16 20 24 28
Harmonic
Amplitude0.4
0.350.3
0.250.2
0.150.1
0.050
-0.05-0.1
Worked Example5 V
0 V
25 s
5 sv t
VtT
VtT
N tT
N tT
N tN
( ) .sin( )
cos( )
2
11
V VtT
VDC pk 5525
1.
Worked Example
fT
kHz
f kHzf kHzf kHzf kHz
1 6
2
3
4
5
1 125 10
40
80120160200
5 V
0 V
25 s
5 s
Worked Example5 V
0 V
25 s
5 s
VVtT
N tT
N tT
N 2
.sin( )
V NN
NN
N
2 5 525
0 20 2
318 0 63
. sin( . ).
. .sin( . )
V
N f (kHz) V amplitude (Volts) 1 2 3 4 5
40 80 120 160 200
1.87 1.51 1.01 0.47 0
5 V
0 V
25 s
5 s
v t t t tt
i ( ) . sin( ) . sin( ) . sin( ). sin( ) ... . . .
1 187 151 2 101 30 47 4
1 1 1
1
+
t ( ) V0 V1 V2 V3 1 1.77 cost 1.51 cos2t 1.01 cos3t 45 1 1.32 0 –0.71 1.61 90 1 0 –1.51 0 –0.51 135 1 –1.32 0 0.71 0.39 180 1 –1.87 1.51 –1.01 –0.37 225 1 –1.32 0 0.71 0.39 270 1 0 –1.51 0 –0.51 315 1 1.32 0 –0.71 1.61 0,360 1 1.87 1.51 1.01 5.39
Worked Example
-1
0
1
2
3
4
5
6
0 45 90 135
180
225
270
315
360
Angle (deg.)Vo
ltage
(V)
t ( ) V0 V1 V2 V3 1 1.77 cost 1.51 cos2t 1.01 cos3t 45 1 1.32 0 –0.71 1.61 90 1 0 –1.51 0 –0.51 135 1 –1.32 0 0.71 0.39 180 1 –1.87 1.51 –1.01 –0.37 225 1 –1.32 0 0.71 0.39 270 1 0 –1.51 0 –0.51 315 1 1.32 0 –0.71 1.61 0,360 1 1.87 1.51 1.01 5.39
5 V
0 V
25 s
5 s
CSN08704
Data, Audio, Video and Imageshttp://asecuritysite.com/comms
Telecommunications
Prof Bill Buchanan
4. Analysis of Digital Pulses
