Digital Representation of Analog Signals

254 Pages·2015·1.37 MB·English

SamplingTheorem PulseCodeModulation DifferentialPulseCodeModulation DeltaModulation Summary
6: Digital Representation of Analog Signals
Y.Yoganandam,RunaKumari,andS.R.Zinka
DepartmentofElectrical&ElectronicsEngineering
BITSPilani,HyderbadCampus
Sep16–Sep24,2015
6:DigitalRepresentationofAnalogSignals CommunicationSystems,Dept.ofEEE,BITSHyderabad
SamplingTheorem PulseCodeModulation DifferentialPulseCodeModulation DeltaModulation Summary
Outline
1 SamplingTheorem
2 PulseCodeModulation
3 DifferentialPulseCodeModulation
4 DeltaModulation
5 Summary
6:DigitalRepresentationofAnalogSignals CommunicationSystems,Dept.ofEEE,BITSHyderabad
SamplingTheorem PulseCodeModulation DifferentialPulseCodeModulation DeltaModulation Summary
Outline
1 SamplingTheorem
2 PulseCodeModulation
3 DifferentialPulseCodeModulation
4 DeltaModulation
5 Summary
6:DigitalRepresentationofAnalogSignals CommunicationSystems,Dept.ofEEE,BITSHyderabad
g(t)
t
0
SamplingTheorem PulseCodeModulation DifferentialPulseCodeModulation DeltaModulation Summary
Sampling Theorem
6:DigitalRepresentationofAnalogSignals CommunicationSystems,Dept.ofEEE,BITSHyderabad
SamplingTheorem PulseCodeModulation DifferentialPulseCodeModulation DeltaModulation Summary
Sampling Theorem
g(t)
t
0
6:DigitalRepresentationofAnalogSignals CommunicationSystems,Dept.ofEEE,BITSHyderabad
SamplingTheorem PulseCodeModulation DifferentialPulseCodeModulation DeltaModulation Summary
Sampling Theorem
g(t)
t
0
G(f)
f
0
6:DigitalRepresentationofAnalogSignals CommunicationSystems,Dept.ofEEE,BITSHyderabad
SamplingTheorem PulseCodeModulation DifferentialPulseCodeModulation DeltaModulation Summary
Sampling Theorem
g(t)
t
0
T
S
G(f)
f
0
6:DigitalRepresentationofAnalogSignals CommunicationSystems,Dept.ofEEE,BITSHyderabad
SamplingTheorem PulseCodeModulation DifferentialPulseCodeModulation DeltaModulation Summary
Sampling Theorem
g(t)
t
0
T
S
G(f)
f
0
6:DigitalRepresentationofAnalogSignals CommunicationSystems,Dept.ofEEE,BITSHyderabad
SamplingTheorem PulseCodeModulation DifferentialPulseCodeModulation DeltaModulation Summary
Sampling Theorem
g(t)
t
0
T
S
G(f)
f
-2/TS -1/TS 0 1/TS 2/TS
6:DigitalRepresentationofAnalogSignals CommunicationSystems,Dept.ofEEE,BITSHyderabad
Weobtainsampledsignalg¯(t)bymultiplyingg(t)withimpulsetrainδ (t).
Ts
ImpulsetraincanbeexpressedasaFourierseriesasshownbelow:
1 2π
δTs(t)= Ts [1+2cosωst+2cos2ωst+2cos3ωst+···], ωs = Ts
Therefore
g¯(t)=g(t)δ (t)
Ts
1
= [g(t)+2g(t)cosωst+2g(t)cos2ωst+2g(t)cos3ωst+···].
Ts
ApplyingFouriertransformonbothsidesoftheaboveequationgives
∞
G¯ (ω)= 1 ∑ G(ω−nωs). (1)
Ts n=−∞
SamplingTheorem PulseCodeModulation DifferentialPulseCodeModulation DeltaModulation Summary
Sampling Theorem
6:DigitalRepresentationofAnalogSignals CommunicationSystems,Dept.ofEEE,BITSHyderabad