Impact of Differential Equations on Transfer Functions, Impulse and Frequency Responses in Filters
Gordien TAMBA OF'R *
Department of Mathematics and Computer Science, Faculty of Science and Technology, National Pedagogical University BP 8815, Kinshasa-DRC, Democratic Republic of Congo.
Camile LIKOTELO BINENE
Department of Mathematics and Computer Science, Faculty of Science and Technology, National Pedagogical University BP 8815, Kinshasa-DRC, Democratic Republic of Congo.
Grace NKWESE MAZONI
Department of Mathematics and Computer Science, Faculty of Science and Technology, National Pedagogical University BP 8815, Kinshasa-DRC, Democratic Republic of Congo.
Emilien LORANU LONDJIRINGA
Department of Mathematics Physics, ISP BUNIA, Ituri, DRC.
*Author to whom correspondence should be addressed.
Abstract
For some examples of filters, defined by the "input-output" correspondence, a correspondence that can be translated in many cases by linear differential equations (first or second order filters), we specify the notions of step response, impulse response, transfer function, frequency response. We also specify the qualities of the filters considered from the point of view of causality, stability and rationality. To avoid any risk of confusion, some usual definitions and criteria are repeated below.
Keywords: differential equations, step response, impulse response, transfer function, frequency response