chapter 6. sampling and pulse modulation husheng li the university of tennessee
Post on 15-Dec-2015
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Nyquist CriterionThe sampling rate
should be at least twice the bandwidth of the signal, in order to fully reconstruct the signal.
Otherwise, there will be aliasing effect.
Ideal Sampling and ReconstructionWe consider the ideal sampling function:
The spectrum of the sampled signal is given by
Reconstruction of SignalWhen the Nyquist criterion is satisfied, the
signal can be reconstructed by using interpolation filter:
Sampling in PracticeWe need to consider three factors of sampling
in practice:
The sampled wave consists of pulses having finite amplitude and duration, rather than impulses.
Practical reconstruction filters are not ideal filters.
The message to be sampled are timelimited signals whose spectra are not and cannot be strictly bandlimited.
Aliasing
The signal is filteredusing a RC LPF antialiasingfilter with bandwidthB>>W.
The shaded area representsthe aliased componentsthat have spilled over the filter’spassband.
Pulse-Amplitude Modulation If a message waveform is adequately described
by periodic sample values, it can be transmitted using analog pulse modulation wherein the sample values modulate the amplitude of a pulse train. The process is called pulse-amplitude modulation (PAM).
Flat-top Sampling and PAMMore popular than the chopper circuit, we can
use a sample-and-hold technique for PAM.
Spectrum of Flat-top SamplingThe spectrum of the flat-top sampling is the
convolution of the ideal sampling spectrum and the spectrum of pulse:
Aperture EffectThe loss of high-frequency content is called
aperture effect. The larger the pulse duration is, the larger the effect is.
The aperture effect can be corrected in the signal reconstruction:
Unipolar Flat-Top PAMWe define the unipolar flat-top PAM as
The resulting constant pulse rate f_s is particularly important for synchronization in time-division multiplexing.
The spectrum of the unipolar PAM is obtained by replace X(f) with
Pulse-Time ModulationThe time parameters of a pulse train can also
be modulated:
PDM: pulse-duration modulation
PPM: pulse-position modulation
Properties of PDM/PPMPDM and PPM need very sharp rising time t_r.
Then, the required bandwidth satisfies
which could be much larger than PAM.
The PDM and PPM have the potential for wideband noise reduction, since the information resides in the time location of the pulse edges, not the pulses themselves.
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