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      • Dept. of Electrical and Electronics Engineering - Master's degree
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      •   BUIR Home
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      • Bilkent Theses
      • Theses - Department of Electrical and Electronics Engineering
      • Dept. of Electrical and Electronics Engineering - Master's degree
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      Finite representation of finite energy signals

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      Author(s)
      Gülcü, Talha Cihad
      Advisor
      Özaktaş, Haldun M.
      Date
      2011
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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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 Signals
      Sampling
      Finite Sample Representation
      Degree of Freedom (DOF)
      Space Bandwidth Product
      Reconstruction Error
      Uniform Quantization
      Vector Quantization
      Quantization Error
      Rate Distortion Theory
      Permalink
      http://hdl.handle.net/11693/15240
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      • Dept. of Electrical and Electronics Engineering - Master's degree 654
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