# University of Twente Student Theses

## Optimal signal reconstruction : quantification and graphical representation of optimal signal reconstructions

Snippe, A.
(2011)
*Optimal signal reconstruction : quantification and graphical representation of optimal signal reconstructions.*

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Abstract: | This report will use, in order to measure the performance of a (mathematical) system, the L2 norm for systems. For a BIBO-stable (Bounded Input Bounded Output) and Linear Continuous Time Invariant (LCTI) system usually a transfer function is defined. Using this transfer function it is possible to calculate the L2 norm of the system. In the process of sampling and reconstruction of a signal two systems are used: a sampler and a hold. Most of the time these systems are not LCTI but only linear and h-shift invariant or equivalently Linear Discrete Time Invariant (LDTI). For this class of systems a way of calculating the L2 system norm is presented. This calculation is based on the Frequency Power Response (FPR) of a system which is introduced in this report as well. This FPR is for an LDTI system what the frequency response, e.g. |G(iω)|2 is for an LCTI system. It has already been shown that the optimal combination of sampler and hold for a given sampling period h is always LCTI. This means that the L2 norm of the system can be calculated in a classical way. This report shows how to calculate the L2 norm of the optimal combination of sampler and hold. Also a graphical interpretation is given for this optimal combination. Because of the FPR, the L2 norm can now be calculated not only for LCTI systems but for LDTI systems as well. And it is shown how to determine the optimal hold for a given sampler and sampling period h. Additionally the L2 norm of the system can be calculated and graphically represented: how good (or how bad) is a certain hold in combination with the given sampler. |

Item Type: | Essay (Master) |

Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |

Subject: | 31 mathematics |

Programme: | Applied Mathematics MSc (60348) |

Link to this item: | https://purl.utwente.nl/essays/61510 |

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