id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-1630	Aarthi D	Stability and Preservation of Fuzzy Membership Functions in Adaptive Gaussian Derivative Filters	2024	15	.pdf	application/pdf	6041	280	57	The theorem and corollaries stated above establish that the adaptive 1D and 2D Gaussian filters is BIBO stable, preserves the essential properties of fuzzy membership function and acts as a low pass filter in the frequency domain. Since, 𝐴(𝑖, 𝑗) is bounded and the properties of Gaussian filter then, 𝑔(𝑥, 𝑦) ≤ ∑∑|𝐴(𝑖, 𝑗)| 𝑗 | 1 2𝜋𝜎𝑥𝜎𝑦 [1 − 𝛼 𝑥 𝜎𝑥 2 − 𝛽 𝑦 𝜎𝑦 2 ] 𝑒𝑥𝑝 (− 𝑥2 2𝜎𝑥 2 − 𝑦2 2𝜎𝑦 2 )|	cache/cana-1630.pdf	txt/cana-1630.txt