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