An introduction to the angular Fourier transform
- 1 January 1993
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 3 (15206149) , 257-260 vol.3
- https://doi.org/10.1109/icassp.1993.319481
Abstract
The author introduces the angular Fourier transform (AFT), a generalization of the classical Fourier transform. The AFT can be interpreted as a rotation on the time-frequency plane. An AFT with an angle of alpha = pi /2 corresponds to the classical Fourier transform, and an AFT with alpha =0 corresponds to the identity operator. The angles of successively performed AFTs simply add up, as do the angles of successive rotations. A number of properties of the AFT are given. Most important among these are the AFT's relationships with time-frequency representations such as the Wigner distribution, the ambiguity function, the short-time Fourier transform, and the spectrogram. These relationships have a very simple and natural form, which further enhances the AFT's interpretation as a rotation operator. An example of the application of the AFT to the study of swept-frequency filters is given.Keywords
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