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Simplified fractional Fourier transforms.

S C Pei¹, J J Ding

¹Department of Electrical Engineering, National Taiwan University, Taipei. pei@cc.ee.ntu.edu.tw

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|January 5, 2001

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Researchers developed simplified fractional Fourier transforms (SFRFTs) that offer the same capabilities as the original FRFT for filtering and pattern recognition. These SFRFTs are computationally simpler and easier to implement in various systems.

Area of Science:

Signal Processing
Applied Mathematics
Optical Engineering

Background:

The fractional Fourier transform (FRFT) is a versatile tool with applications in fractional filtering and correlation.
Existing FRFT applications include chirp noise removal, fractional Hilbert transform, and scaled space-variant pattern recognition.

Purpose of the Study:

To introduce and analyze simplified fractional Fourier transforms (SFRFTs).
To identify the simplest transform with FRFT capabilities for practical applications.
To explore the formulas, properties, and implementation of SFRFTs.

Main Methods:

Defining SFRFTs as special cases of linear canonical transforms (ABCD transforms).
Analyzing the mathematical properties and formulas of SFRFTs.

Related Experiment Videos

Investigating the implementation aspects of SFRFTs in digital, optical, and radar systems.

Main Results:

SFRFTs demonstrate equivalent capabilities to FRFTs in fractional filtering and correlation.
SFRFTs offer significant simplifications in digital computation and optical implementation.
The study details the properties and implementation strategies for various SFRFT types.

Conclusions:

SFRFTs provide a simpler alternative to the standard FRFT for practical applications.
Despite lacking additivity properties, SFRFTs are suitable for real-world use.
SFRFTs have substantial potential to replace FRFTs in numerous existing applications.