Some network-theoretic applications of convolutional analysis and linear operators of the Hilbert space of energy signals

• Main Author: Estalilla, Aliento V.
• Format: text
• Language: English
• Published: Animo Repository 1993
• Subjects: Convolutions (Mathematics); Linear operators; Hilbert space; Signal processing > Digital techniques; Network analysis (Planning); Electrical and Electronics; Electronic Devices and Semiconductor Manufacturing; Other Electrical and Computer Engineering
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/1506
• Institution: De La Salle University

Using Young's inequality and other properties of continuous-time convolution of absolutely integrable functions, it is shown in Part I that when an absolutely integrable signal is fed into a linear time-invariant BIBO-stable network, the output will be bounded, absolutely integrable and of finite energy even if the input is unbounded and of infinite energy. In Part II, the properties of inner products are utilized to reduce the number of integrators in certain networks. Operator identities specially in the Hilbert space of energy signals, are shown to effect transformations of some networks that are equivalent to and often simpler than the original networks.