Improved discrete fractional Fourier transform.

Area of Science:

• Mathematics
• Signal Processing
• Applied Physics

Background:

• The continuous Fourier transform is a fundamental tool in signal processing.
• Existing discrete fractional Fourier transforms (DFRFTs) do not accurately replicate the continuous transform's behavior.
• A need exists for a DFRFT that preserves the properties of the continuous fractional Fourier transform.

Purpose of the Study:

• To introduce a novel discrete fractional Fourier transform (DFRFT).
• To develop a DFRFT that accurately approximates the continuous fractional Fourier transform.
• To ensure the proposed DFRFT retains the important rotation properties.

Main Methods:

• Development of a new algorithm for the discrete fractional Fourier transform.
• Mathematical formulation and derivation of the proposed DFRFT.
• Comparative analysis with existing DFRFT methods and the continuous fractional Fourier transform.

Main Results:

• The proposed DFRFT yields results highly similar to the continuous fractional Fourier transform.
• The new DFRFT successfully preserves the inherent rotation properties.
• Demonstrated superiority over previous DFRFT implementations in accuracy and property retention.

Conclusions:

• The novel DFRFT offers a more faithful digital implementation of the fractional Fourier transform.
• This improved DFRFT is valuable for applications requiring accurate signal analysis and manipulation.
• The retained rotation properties enhance its utility in various scientific and engineering fields.