Proper Definition and Handling of Dirac Delta Functions [Lecture Notes]

Date

2021-05-01

Author

Candan, Çağatay

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Dirac delta functions are introduced to students of signal processing in their sophomore year. Quite understandably, Dirac delta functions, which should be more aptly called generalized functions or distributions, cannot be comprehensively given to a young audience at the beginning of their engineering education. A simplified and abridged definition is presented, and the implications of the definition in signal processing problems are illustrated through numerous examples. The inclusion of the Dirac delta function to the calculus of ordinary functions enables the differentiation of discontinuous functions, paving the way toward a consistent analysis of highly practical engineering problems, such as circuit theory problems involving switches, unified treatment for mixed random variables and others.

Subject Keywords

Calculations, Circuit theory, Differentiation (calculus), Signal processing

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85105055949&origin=inward
https://hdl.handle.net/11511/90703

Journal

IEEE Signal Processing Magazine

DOI

https://doi.org/10.1109/msp.2021.3055025

Collections

Department of Electrical and Electronics Engineering, Article

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Citation Formats

Ç. Candan, “Proper Definition and Handling of Dirac Delta Functions [Lecture Notes],” IEEE Signal Processing Magazine, pp. 186–203, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85105055949&origin=inward.