Fractal Log-Domain Signal Processing: A Fractal State-Space Approach
Circuits, Systems, and Signal Processing, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s00034-026-03766-1
- Dergi Adı: Circuits, Systems, and Signal Processing
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Compendex, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Materials Science & Engineering Collection (ProQuest), Pharma Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Fractal calculus, Fractal dimension, Fractal structure of time, Log-domain signal processing
- Van Yüzüncü Yıl Üniversitesi Adresli: Evet
Özet
Besides conventional signal processing, there exists log-domain signal processing, which offers significant advantages, e.g., wide dynamic range, power measurement simplification, analysis efficiency, and improved linearity of the response. In the circuit design aspect, the log-domain signal processing enables low-voltage/low-power design and design simplicity. The resulting circuit also employs an optimal signal-to-noise ratio and dynamic range. These virtues of log-domain signal processing and the emergence of the theory of fractal signal processing motivate us to propose a framework for fractal log-domain signal processing, where the fractal state space equation has been adopted as the basis. The demonstration of the framework has been performed by using the fractal lowpass log-domain filter, where we have found that the fractal dimension of time significantly affects the filter’s performance in both time and frequency domains. Interestingly, the non-smooth variation with frequency of the magnitude responses starts to occur at the cut-off frequency that is independent of the fractal dimension of time. The proposed theoretical framework has been verified based on a candidate integer-order log-domain signal processing circuit, where it has been found that the calculated magnitude and phase frequency responses strongly agree with their SPICE simulated counterparts. This validates our framework.