Quaternion approach to the theory of 2-D causal systems

• Autorzy: Snopek Kajetana M.

Identyfikatory

DOI

10.24425/ijet.2025.153602

• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to the signal- and frequency characteristics of 2-D causal systems. Two different approaches to this problem are presented. First, the 2-D complex Fourier transformation of the 2-D causal impulse response 𝒉(𝒙_𝟏, 𝒙_𝟐) of a 2-D system defines the 2-D complex frequency response 𝑯(𝒇_𝟏, 𝒇_𝟐). The modulus |𝑯(𝒇_𝟏, 𝒇₂)| is the 2-D magnitude response and 𝐚𝐫𝐠 𝑯(𝒇_𝟏, 𝒇₂) is the 2-D phase response of a system. On the other hand, applying the Pei’s formula relating the 2-D complex Fourier transform with the 2-D right-sided quaternion Fourier transform we introduce a concept of the quaternion-valued frequency response 𝑯_q(𝒇_𝟏, 𝒇_𝟏) of a 2-D causal system. We define the 2-D magnitude system response |𝑯_q(𝒇_𝟏, 𝒇₂)| and three 2-D phase responses. These concepts constitute an original contribution of this paper. The theoretical aspects are illustrated with examples of magnitude and phase responses of a causal 2-D analog low-pass filter.

Słowa kluczowe

EN

causal signal; anti-causal signal; causal systems; Gabor’s analytic signal; quaternion analytic signal; quaternion Fourier transform; dual symmetry; Pei’s formula; impulse response; frequency response

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2025
• Tom: Vol. 71, No. 2
• Strony: 537--543
• Opis fizyczny: Bibliogr. 23 poz., tab., rys.

Twórcy

autor

Snopek Kajetana M.

• Warsaw University of Technology

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).