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Updated: Jun 8, 2026
08:59
Morphology-Based Distinction Between Healthy and Pathological Cells Utilizing Fourier Transforms and Self-Organizing Maps
Published on: October 28, 2018
Summary
Self-Fourier functions, which are their own Fourier transforms, are explored as self-imaging functions. Their space-bandwidth product is analyzed, with examples including Wigner distribution functions and experimental data.
Area of Science:
- Physics
- Mathematics
- Signal Processing
Background:
- A self-Fourier function is defined as a function that equals its own Fourier transform.
- The complete set of such functions was recently defined by Caola (1991).
Purpose of the Study:
- To investigate the behavior of self-Fourier functions as self-imaging functions.
- To analyze the space-bandwidth product of these functions.
Main Methods:
- Theoretical analysis of self-Fourier functions.
- Examination of their properties as self-imaging functions.
- Calculation of the space-bandwidth product.
Main Results:
- Self-Fourier functions exhibit self-imaging properties.
- The space-bandwidth product for these functions is investigated.
- An example using a Wigner distribution function is provided.
Conclusions:
- The study elucidates the relationship between self-Fourier and self-imaging functions.
- Provides insights into their mathematical and physical properties.
- Includes experimental validation.
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