Post on 04-Apr-2018
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Lecture 1Sampling of Signals
by
Graham C. GoodwinUniversity of Newcastle
Australia
Lecture 1
Presented at the Zaborszky Distinguished Lecture Series
December 3rd, 4th and 5th, 2007
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Recall Basic Idea of Sampling
and Quantization
Quantization
Sampling
t1 t3t2 t4t
0
1
2
3
4
5
6
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In this lecture we will ignore quantizationissues and focus on the impact of differentsampling patterns for scalar and
multidimensional signals
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Outline
1. One Dimensional Sampling
2. Multidimensional Sampling
3. Sampling and Reciprocal Lattices
4. Undersampled Signals5. Filter Banks
6. Generalized Sampling Expansion (GSE)
7. Recurrent Sampling
8. Application: Video Compression at Source9. Conclusions
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Sampling: Assume amplitude quantizationsufficiently fine to be negligible.
Question: Say we are given
Under what conditions can we recover
from the samples?
( );f t t
( );if t i Z
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A Well Known Result (Shannons
Reconstruction Theorem for Uniform
Sampling)
Consider a scalar signal f(t) consisting of
frequency components in the range . If
this signal is sampled at period , then thesignal can be perfectly reconstructed from the
samples using:
[ ]
( )
( )
sin2
( )
2
s
sk
t k
y t y k
t k
w
w
= -
- D = - D
,2 2
s sw w-
2
s
pwD