Sonlu enerjili sinyallerin sonlu gösterimi

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 reconstructionerror 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 energyfor a signal implies finite degree of freedom, but also optimize the reconstructionparameters to get the minimum possible reconstruction error by using a given numberof 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 curveconsisting of the best achievable points, which reminds usthe rate distortion curve in information theory. However, the rate distortiontheorem are not concerned with sampling, whereas we need to take samplinginto consideration in order to reduce the finite energy signal we deal with to finitelymany variables to be quantized. Therefore, we first propose a finite sample representationscheme and question the optimality of it. Then, after representing the signal of interest byfinite 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