Derivation of Time-domain Constraints Implicit in the Transform-domain Description of Signals

Abstract

Derivation of time-domain constraint that is implicit in the transform-domain description of a signal is discussed in this paper. It is pointed out that though the transform-domain approach may be at times easier for solving problems, it may not help in understanding the concepts in Signals and Systems. The idea is illustrated through solution to one problem in a widely used textbook by deriving the not-so-obvious time-domain constraints from careful inspection of the transform-domain description of a signal.

Keywords:

• Differential equations
• Fourier transform
• Time-domain constraint
• Transform domain description
• homogeneous solution
• particular solution

Additional information

Notes on contributors

Subrata Bhattacharya

Dr. Subrata Bhattacharya passed B.Tech in Electronics & Electrical Communication Engineering from IIT Kharagpur in the year 1985, M.Tech and Ph.D. from the same institute in the years 1988 and 1996, respectively. He joined Regional Engineering College (at present, National Institute of Technology), Durgapur as Lecturer in Electronics and Communication Engineering Department in 1990. In the year 1999, he joined Indian School of Mines (ISM) as an Assistant Professor in the Department of Electronics & Instrumentation (E&I). At present, he is Professor in the same department at ISM. His research interests are in the field of Speech signal processing, Adaptive filtering, application of Signal processing in communication with real-time implementation. He is the adapted aumor of the book tided Schaum’s Outlines Digital Signal Processing, published by Tata McGraw-Hill Publishing Co. Ltd.