Generalized joint fractional fourier transform correlators: a compact approach

Area of Science:

• Optics and Photonics
• Signal Processing
• Image Processing

Background:

• Joint transform correlators (JTC) are widely used for pattern recognition.
• Fractional correlation offers unique signal processing capabilities.
• Existing methods for fractional correlation can be computationally intensive.

Purpose of the Study:

• To generalize the joint transform correlator (JTC) architecture to achieve joint fractional correlation (JFrTC).
• To explore four distinct JFrTC architectures.
• To demonstrate the advantages of JFrTC for noise reduction and adjustable correlation signal separation.

Main Methods:

• Replacing the Fourier transform in JTC with the fractional Fourier transform.
• Developing mathematical derivations for four JFrTC architectures.
• Verifying JFrTC performance through simulations.

Main Results:

• The JFrTC provides a delta function-like correlation signal with high noise immunity.
• The separation distance of correlation signals in JFrTC can be flexibly controlled.
• The proposed JFrTC requires only two fractional Fourier transformations, reducing complexity.

Conclusions:

• The JFrTC is a powerful generalization of JTC, enabling robust fractional correlation.
• The tunable separation distance of correlation signals makes JFrTC suitable for real-time target tracking.
• This work simplifies the implementation of fractional correlation compared to previous methods.