26 September 1997 Elliptically generalized discrete Fourier transform with applications
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The discrete Fourier transform is of fundamental importance in the digital processing of signals. By using the Jacobian elliptic functions sn (u,m) and cn(u,m) as basis functions, in place of the trigonometric sine and cosine, one can obtain a generalized transform which includes the Fourier transform as a special case (viz., m equals 0). Since m, the squared modulus, can have any positive value less than 1, the new transform is extremely flexible. It is found that the associated inverse transform consists of basis functions whose appearance can be described as a set of dithered trigonometric functions. The dithering level increases in monotonic fashion with the parameter m. Sample applications of this non-linear form of signal processing are discussed.
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James J. Soltis, James J. Soltis, } "Elliptically generalized discrete Fourier transform with applications", Proc. SPIE 3208, Intelligent Robots and Computer Vision XVI: Algorithms, Techniques, Active Vision, and Materials Handling, (26 September 1997); doi: 10.1117/12.290329; https://doi.org/10.1117/12.290329

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