Husheng Li The University of Tennessee Chopper Sampling We introduce a switching function such that xs txtst where Nyquist Criterion The sampling rate should be at least twice the bandwidth of the signal in order to fully reconstruct the signal ID: 165374
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Slide1
Chapter 6. Sampling and Pulse Modulation
Husheng Li
The University of TennesseeSlide2
Chopper Sampling
We introduce a switching function such that
x_s
(t)=x(t)s(t), whereSlide3
Nyquist Criterion
The 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.Slide4
Ideal Sampling and Reconstruction
We consider the ideal sampling function:
The spectrum of the sampled signal is given bySlide5
Reconstruction of Signal
When the
Nyquist
criterion is satisfied, the signal can be reconstructed by using interpolation filter:Slide6
Homework
Deadline: Nov. 11, 2013Slide7
Sampling in Practice
We 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
.Slide8
Reconstruction MethodsSlide9
Aliasing
The signal is filtered
u
sing a RC LPF antialiasing
f
ilter with bandwidthB>>W.The shaded area representsthe aliased componentsthat have spilled over the filter’s
p
assband
. Slide10
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).Slide11
Flat-top Sampling and PAM
More popular than the chopper circuit, we can use a sample-and-hold technique for PAM.Slide12
Spectrum of Flat-top Sampling
The spectrum of the flat-top sampling is the convolution of the ideal sampling spectrum and the spectrum of pulse:Slide13
Aperture Effect
The 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:Slide14
Unipolar Flat-Top PAM
We 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 Slide15
Pulse-Time Modulation
The time parameters of a pulse train can also be modulated:
PDM: pulse-duration modulation
PPM: pulse-position modulationSlide16
Generation of PDM or PPMSlide17
Signal ReconstructionSlide18
Properties of PDM/PPM
PDM 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.Slide19
Spectrum of PPM
Using the distribution theory of impulses, we have
PPM with
nonuniform
sampling is a combination of linear and exponential carrier modulation.