© 2010 The McGraw-Hill Companies Communication Systems, 5e Chapter 6: Sampling and pulse modulation A. Bruce Carlson Paul B. Crilly (modified by J. H. Cho using Prof. W.J. Song’s lecture note)

© 2010 The McGraw-Hill Companies Chapter 6: Sampling and pulse modulation  Sampling theory and practice  Pulse-amplitude modulation  Pulse-time modulation

© 2010 The McGraw-Hill Companies Sampling theory and practice

© 2010 The McGraw-Hill Companies Chopper sampling

© 2010 The McGraw-Hill Companies Switching sampler (a) functional (b) waveforms (c) circuit

© 2010 The McGraw-Hill Companies Chopper sampler equations

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Spectra for switching sampling (a) message (b) sampled message (c) sampled message aliasing caused by undersampling

© 2010 The McGraw-Hill Companies Accurate reconstruction

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Ideal sampling

© 2010 The McGraw-Hill Companies In the frequency domain The spectrum is: Note: with this and chopper sampling, the message spectrum is periodic with period

© 2010 The McGraw-Hill Companies Ideal reconstruction To reconstruct the sampled signal, we use a LPF

© 2010 The McGraw-Hill Companies Ideal LPF for reconstruction

© 2010 The McGraw-Hill Companies Reconstruction by interpolation From the time/sequence domain perspective, we can reconstruct via interpolation

© 2010 The McGraw-Hill Companies Ideal reconstruction via interpolation

© 2010 The McGraw-Hill Companies Practical sampling and reconstruction  Real samplers have finite durations pulses (e.g. chopper sampling)  Practical reconstruction filters are not ideal  Sampled signals are time limited  not bandlimited  cannot avoid some aliasing

© 2010 The McGraw-Hill Companies Non-ideal sampling  As seen earlier, no loss of info with non-impulse sampling  Non-ideal LPF reconstruction can be overcome by prefiltering the original message  equalization  We can minimize aliasing by band limiting the input signal  anti-alias LPF

© 2010 The McGraw-Hill Companies Practical reconstruction filter

© 2010 The McGraw-Hill Companies Reconstruction using a zero order hold (ZOH) interpolation

© 2010 The McGraw-Hill Companies Reconstruction using a first order hold (FOH) interpolation

© 2010 The McGraw-Hill Companies Signal reconstruction from sampled signal (a) ZOH (b) FOH

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RC anti-alias filter  oversample the message signal

© 2010 The McGraw-Hill Companies Message spectrum (a) output of RC filter, (b) after sampling (a) Original message spectrum, (b) spectrum after sampling

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If a signal has been over-sampled but with an acceptable amount of aliasing, we then  Feed it to our DSP for digital filtering to remove the components above W.  Down-sample the signal to some desired rate.

© 2010 The McGraw-Hill Companies Upsampling  Some cases we can only sample a signal at the Nyquist rate; but need more samples  upsample the data.  Upsampling  insert correct samples between the original set  Time domain: interpolation  Frequency domain: zero padding

© 2010 The McGraw-Hill Companies Upsampling via linear interpolation (a) (b) (a) Original signal sampled, (b) signal upsampled by factor of 2

© 2010 The McGraw-Hill Companies Why upsampling?  Upsampling  greater time resolution  Adaptive filtering methods may require more samples than obtained by the Nyquist rate  Other DSP algorithms that depend on time resolution may require more than the minimum number of samples

© 2010 The McGraw-Hill Companies Upsampling does not add information

© 2010 The McGraw-Hill Companies 6.2, 6.3 Pulse Modulation

© 2010 The McGraw-Hill Companies 6.2 Pulse-Amplitude Modulation (PAM)

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Analog signal and corresponding PAM signal

© 2010 The McGraw-Hill Companies Flat-top sampling (a) sample & hold circuit (b) waveform

© 2010 The McGraw-Hill Companies PAM signals

© 2010 The McGraw-Hill Companies PAM  Rarely used for single channel communication systems, but  used in conjunction with instrumentation, data telemetry, and instrumentation systems  Time-division multiplexing (TDM) systems  Basis for other digital modulation systems

© 2010 The McGraw-Hill Companies 6.3 Pulse time modulation  Pulse duration modulation (PDM). Also called pulse width modulation (PWM)  Pulse position modulation (PPM)  Info in zero crossings  potential for wideband noise reduction

© 2010 The McGraw-Hill Companies Types of pulse-time modulation

© 2010 The McGraw-Hill Companies (a) Generation of PDM and PM signals, (b) waveforms

© 2010 The McGraw-Hill Companies Conversion of PDM or PPM into PAM

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