Fast Reverse Jacket Transform As an Alternative Representation of the N-Point Fast Fourier Transform

Authors:
Seung-Rae Lee;June-Ho Yi
Affiliations:
Institute of New Media and Communications, Seoul National University, Seoul 151-742, Korea. srlee@acoustics.snu.ac.kr;School of Electrical and Computer Engineering, Sungkyunkwan University, Suwon 440-746, Korea. jhyi@yurim.skku.ac.kr
Venue:
Journal of Mathematical Imaging and Vision
Year:
2002

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Abstract

The Reverse Jacket matrix (RJM) is a generalized form of the Hadamard matrix. Thus RJM is closely related to the matrix for fast Fourier transform (FFT). It also has a very interesting structure, i.e. its inverse can be easily obtained and has the reversal form of the original matrix. In this paper, we have shown that a transform based on the RJM offers a simple structure of N-point FFT in terms of the decomposition of the corresponding matrix and that it computes very fast the center weighted Hadamard transform.