Different forms of Plancherel theorem for fractional quaternion Fourier transform

作者：Wei, Deyun^*; Li, Yuanmin

来源：Optik, 2013, 124(24): 6999-7002.

DOI：10.1016/j.ijleo.2013.05.163

• Fractional Fourier transform
• Quaternion Fourier transform
• Fractional quaternion Fourier transform
• Plancherel theorem

Fractional Fourier transform (FRFT) plays an important role in many field of optics and signal processing. The recently developed concept of two side fractional quaternion Fourier transform (FRQFT) based on quaternion algebra and FRFT has been found useful for signal and image processing. It is a generalization of the quaternion Fourier transform (QFT). Many properties of the FRQFT are already known, but an extension of the QFT's Plancherel theorem is still missing. The purpose of this paper is to introduce extensions of this theorem. Firstly, we establish scalar value Plancherel theorem for the FRQFT. Then, the concept of right side fractional quaternion Fourier transform (FRQFTr) is proposed. Furthermore, we establish quaternion value Plancherel theorem for the FRQFTr. The Plancherel theorems in QFT domain are shown to be special cases of the achieved results.

• 出版日期2013
• 单位西安电子科技大学