Year
2025
Season
Summer
Paper Type
Master's Thesis
College
College of Arts and Sciences
Degree Name
Master of Science in Mathematical Sciences (MS)
Department
Mathematics & Statistics
NACO controlled Corporate Body
University of North Florida. Department of Mathematics and Statistics
Committee Chairperson
Dr. Daniel Dreibelbis
Second Advisor
Dr. Mahbubur Rahman
Third Advisor
Dr. Kening Wang
Department Chair
Dr. Richard Patterson
College Dean
Kaveri Subrahmanyam
Abstract
Fourier analysis plays an important role in signal processing and imaging applications,
with computed tomography (CT) being a prominent example. CT imaging relies on recon-
structing cross-sectional images of objects from multiple projections, a process deeply rooted
in the mathematical framework of the Fourier series and its extensions. This thesis explores
the mathematical principle behind CT, demonstrating how periodic and non-periodic func-
tions can be decomposed into sinusoidal components to facilitate image reconstruction. We
begin by reviewing the Fourier series and its ability to represent periodic signals, and then
extend this concept to non-periodic functions through Fourier transforms. The connection
between Fourier analysis and the Radon transform, a key mathematical tool in CT, is ex-
amined to illustrate how projections of an object can be synthesized into a complete image.
Additionally, we discuss reconstruction techniques such as the Fourier Slice Theorem and
filtered back projection, which leverage Fourier-based methods to enhance image accuracy
and resolution. By connecting Fourier series with computed tomography, this work high-
lights the mathematical elegance and practical significance of frequency-domain analysis in
medical imaging and beyond.
Suggested Citation
Hossain, Sabrina, "Fourier transformation of non-periodic functions and its application in computed tomography" (2025). UNF Graduate Theses and Dissertations. 1352.
https://digitalcommons.unf.edu/etd/1352