M.Sc Student | Altberg Tzahi |
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Subject | Smoothness recovery of causal interpolation kernels |

Department | Department of Mechanical Engineering |

Supervisor | Professor Leonid Mirkin |

Full Thesis text |

Digital to analog conversion (DAC) is important in contemporary technology due to extensive use of computers. A key ingredient of DAC is the so-called interpolation kernel (hold function), which shapes a reconstructed analog signal between digital samples. An approach to the design of DAC's is to model involved analog signals as outputs of known systems (signal generators) and then to cast the reconstruction problem as an optimal sampled-data estimation problem. This formulation facilitates the incorporation of causality constraints to produce optimal DAC's with limited dependence on future samples. Causality constraints, however, give rise to non-differentiable interpolation kernels, which might be disadvantageous in some applications. This work proposes an approach to recover smoothness properties of optimal interpolation kernels, while retaining causality constraints and maintaining a desirable level of reconstruction performance. This is achieved by penalizing not only the reconstruction error, but also the reconstructed signal itself, filtered by a non-proper weighing function. In this formulation, differentiability (smoothness) properties of the interpolation kernel are determined by the relative degree of the non-proper weight. It is shown that such an optimization problem can be reduced to a more conventional estimation problem via the use of stabilization techniques. The resulting optimal solution is then the cascade of a discrete filter, a hold function having support in one sample interval, and an analog low-pass filter. It is shown that

the latter can always be obtained in the form of standard network synthesis filters, e.g., the Butterwoth filter, by a transparent tuning of the non-proper weighting function.