Finite representation of finite energy signals
Author(s)
Advisor
Özaktaş, Haldun M.Date
2011Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
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Abstract
In this thesis, we study how to encode finite energy signals by finitely many bits.
Since such an encoding is bound to be lossy, there is an inevitable reconstruction
error in the recovery of the original signal. We also analyze this reconstruction
error. In our work, we not only verify the intuition that finiteness of the energy
for a signal implies finite degree of freedom, but also optimize the reconstruction
parameters to get the minimum possible reconstruction error by using a given
number of bits and to achieve a given reconstruction error by using minimum
number of bits. This optimization leads to a number of bits vs reconstruction
error curve consisting of the best achievable points, which reminds us the rate
distortion curve in information theory. However, the rate distortion theorem are
not concerned with sampling, whereas we need to take sampling into consideration
in order to reduce the finite energy signal we deal with to finitely many
variables to be quantized. Therefore, we first propose a finite sample representation
scheme and question the optimality of it. Then, after representing the signal
of interest by finite number of samples at the expense of a certain error, we discuss
several quantization methods for these finitely many samples and compare
their performances.
Keywords
Finite Energy SignalsSampling
Finite Sample Representation
Degree of Freedom (DOF)
Space Bandwidth Product
Reconstruction Error
Uniform Quantization
Vector Quantization
Quantization Error
Rate Distortion Theory