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© 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)
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© 2010 The McGraw-Hill Companies Chapter 6: Sampling and pulse modulation Sampling theory and practice Pulse-amplitude modulation Pulse-time modulation
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© 2010 The McGraw-Hill Companies Sampling theory and practice
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© 2010 The McGraw-Hill Companies Chopper sampling
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© 2010 The McGraw-Hill Companies Switching sampler (a) functional (b) waveforms (c) circuit
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© 2010 The McGraw-Hill Companies Chopper sampler equations
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© 2010 The McGraw-Hill Companies
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Spectra for switching sampling (a) message (b) sampled message (c) sampled message aliasing caused by undersampling
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© 2010 The McGraw-Hill Companies Accurate reconstruction
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© 2010 The McGraw-Hill Companies
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Ideal sampling
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© 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
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© 2010 The McGraw-Hill Companies Ideal reconstruction To reconstruct the sampled signal, we use a LPF
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© 2010 The McGraw-Hill Companies Ideal LPF for reconstruction
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© 2010 The McGraw-Hill Companies Reconstruction by interpolation From the time/sequence domain perspective, we can reconstruct via interpolation
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© 2010 The McGraw-Hill Companies Ideal reconstruction via interpolation
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© 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
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© 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
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© 2010 The McGraw-Hill Companies Practical reconstruction filter
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© 2010 The McGraw-Hill Companies Reconstruction using a zero order hold (ZOH) interpolation
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© 2010 The McGraw-Hill Companies Reconstruction using a first order hold (FOH) interpolation
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© 2010 The McGraw-Hill Companies Signal reconstruction from sampled signal (a) ZOH (b) FOH
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© 2010 The McGraw-Hill Companies
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RC anti-alias filter oversample the message signal
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© 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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© 2010 The McGraw-Hill Companies
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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.
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© 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
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© 2010 The McGraw-Hill Companies Upsampling via linear interpolation (a) (b) (a) Original signal sampled, (b) signal upsampled by factor of 2
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© 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
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© 2010 The McGraw-Hill Companies Upsampling does not add information
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© 2010 The McGraw-Hill Companies 6.2, 6.3 Pulse Modulation
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© 2010 The McGraw-Hill Companies 6.2 Pulse-Amplitude Modulation (PAM)
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© 2010 The McGraw-Hill Companies
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Analog signal and corresponding PAM signal
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© 2010 The McGraw-Hill Companies Flat-top sampling (a) sample & hold circuit (b) waveform
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© 2010 The McGraw-Hill Companies PAM signals
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© 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
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© 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
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© 2010 The McGraw-Hill Companies Types of pulse-time modulation
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© 2010 The McGraw-Hill Companies (a) Generation of PDM and PM signals, (b) waveforms
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© 2010 The McGraw-Hill Companies Conversion of PDM or PPM into PAM
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© 2010 The McGraw-Hill Companies
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