Information
- Publication Type: Technical Report
- Workgroup(s)/Project(s): not specified
- Date: April 2000
- Number: TR-186-2-00-08
- Keywords: Taylor series expansion, frequency response, windowing, ideal reconstruction
Abstract
Ideal reconstruction filters, for function or arbitrary derivative reconstruction, have to be bounded in order to be practicable since they are infinite in their spatial extent. This can be accomplished by multiplying them with windowing functions. In this paper we discuss and assess the quality of commonly used windows and show that most of them are unsatisfactory in terms of numerical accuracy. The best performing windows are Blackman, Kaiser and Gaussian windows. The latter two are particularly useful since both have a parameter to control their shape, which, on the other hand, requires to find appropriate values for these parameters. We show how to derive optimal parameter values for Kaiser and Gaussian windows using a Taylor series expansion of the convolution sum. Optimal values for function and first derivative reconstruction for window widths of two, three, four and five are presented explicitly.Additional Files and Images
Weblinks
No further information available.BibTeX
@techreport{Theussl-2000-MWI, title = "Mastering Windows: Improving Reconstruction", author = "Thomas Theu{\ss}l and Helwig Hauser and Eduard Gr\"{o}ller", year = "2000", abstract = "Ideal reconstruction filters, for function or arbitrary derivative reconstruction, have to be bounded in order to be practicable since they are infinite in their spatial extent. This can be accomplished by multiplying them with windowing functions. In this paper we discuss and assess the quality of commonly used windows and show that most of them are unsatisfactory in terms of numerical accuracy. The best performing windows are Blackman, Kaiser and Gaussian windows. The latter two are particularly useful since both have a parameter to control their shape, which, on the other hand, requires to find appropriate values for these parameters. We show how to derive optimal parameter values for Kaiser and Gaussian windows using a Taylor series expansion of the convolution sum. Optimal values for function and first derivative reconstruction for window widths of two, three, four and five are presented explicitly.", month = apr, number = "TR-186-2-00-08", address = "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria", institution = "Institute of Computer Graphics and Algorithms, Vienna University of Technology ", note = "human contact: technical-report@cg.tuwien.ac.at", keywords = "Taylor series expansion, frequency response, windowing, ideal reconstruction", URL = "https://www.cg.tuwien.ac.at/research/publications/2000/Theussl-2000-MWI/", }