📅 03 December 2025
DOI: 10.62383/bilangan.v3i6.849
Uncertainty Principle for the Hartley Transform: Direct and Fourier–Based Approaches
Bilangan : Jurnal Ilmiah Matematika, Kebumian dan Angkasa
Asosiasi Riset Ilmu Matematika dan Sains Indonesia (ARIMSI)
📄 Abstract
The Hartley transform provides a real-valued alternative to the classical Fourier transform, offering structural advantages for the analysis of real-valued signals. This paper presents a systematic study of the continuous Hartley transform, including its definition, inversion formula, Plancherel identity, and core operational properties such as shifting, modulation, and convolution. The analytical framework is developed in parallel with the classical Fourier theory to highlight structural similarities and distinctions between the two transforms. Furthermore, we establish a Hartley-type Heisenberg uncertainty principle using two complementary approaches: a direct method based on intrinsic properties of the Hartley kernel, and a Fourier-based method that exploits the algebraic relationship between the Hartley and Fourier transforms. These results provide a unified and rigorous foundation for understanding uncertainty relations within real-valued transform frameworks, and they demonstrate the continued relevance of the Hartley transform in harmonic analysis, integral transforms, and modern signal processing.
🔖 Keywords
#Fourier transform; Hartley transform; Heisenberg inequality; Signal Analysis; Uncertainty principle
ℹ️ Informasi Publikasi
Tanggal Publikasi
03 December 2025
Volume / Nomor / Tahun
Volume 3, Nomor 6, Tahun 2025
📝 HOW TO CITE
Nur, Andi Tenri Ajeng; Khotimah, Husnul; Cayo, Putri Nilam, "Uncertainty Principle for the Hartley Transform: Direct and Fourier–Based Approaches," Bilangan : Jurnal Ilmiah Matematika, Kebumian dan Angkasa, vol. 3, no. 6, Dec. 2025.
ACM
ACS
APA
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Download Citation
0
Sitasi
Cek Google Scholar