Design of Two-Dimensional FIR Digital Filters Using Fourier Reconstruction Techniques--Error Evaluation and New Applications--


IEICE TRANSACTIONS (1976-1990)   Vol.E65   No.1   pp.44-50
Publication Date: 1982/01/25
Online ISSN: 
Print ISSN: 0000-0000
Type of Manuscript: PAPER
Category: Miscellaneous

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Fourier reconstruction has orginally been one of the methods for three-dimensional structure reconstruction in medical applications such as the computed tomography (CT). The technique is found to be applicable to designing circularly symmetric FIR digital filters. The algorithm is simple, straightforward and practical. The approach basically consists of designing a one-dimensional (1-D) FIR prototype, rotating its frequency response in the two-dimensional (2-D) frequency plane, inverse Fourier transforming and then windowing the result. An unlimited number of profections at different orientations of the obtained impulse response are essentially identical with the 1-D FIR prototype. The even size 2-D FIR filters can also be designed. The impulse response has eightfold (octagonal) symmetry. The frequency response is shown to have nearly circular symmetry that is evaluated with rms and maximum absolute errors.