Abstract
In this chapter, theory of hybrid function domain convolution technique is presented. First, the rules for convolution for sample-and-hold functions and triangular functions are derived. Then, these two component results are combined to get the rules for convolution in HF domain. This idea is used to determine the result of convolution of two time functions in HF domain. One example and eleven figures are presented to illustrate the idea.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ogata, K.: Modern Control Engineering, 5th edn. Prentice-Hall of India Ltd., New Delhi (1997)
Brigham, E.O.: The Fast Fourier Transform and Its Applications. Prentice-Hall International Inc., New Jersey (1988)
Jiang, J.H., Schaufelberger, W.: Block Pulse Functions and their Application in Control System. LNCIS, vol. 179. Springer, Berlin (1992)
Deb, A., Sarkar, G., Sen, S.K.: Linearly pulse-width modulated block pulse functions and their application to linear SISO feedback control system identification. Proc. IEE, Part D Control Theory Appl. 142(1), 44–50 (1995)
Kwong, C.P., Chen, C.F.: Linear feedback system identification via block pulse functions. Int. J. Syst. Sci. 12(5), 635–642 (1981)
Deb, A., Sarkar, G., Bhattacharjee, M., Sen, S.K.: A new set of piecewise constant orthogonal functions for the analysis of linear SISO systems with sample-and-hold. J. Franklin Instt. 335B(2), 333–358 (1998)
Deb, Anish, Sarkar, Gautam, Sengupta, Anindita: Triangular Orthogonal Functions for the Analysis of Continuous Time Systems. Anthem Press, London (2011)
Biswas, A.: Analysis and synthesis of continuous control systems using a set of orthogonal hybrid functions, Ph. D. dissertation, University of Calcutta (2015)
Deb, Anish, Sarkar, Gautam, Dasgupta, Anindita: A complementary pair of orthogonal triangular function sets and its application to the analysis of SISO control systems. J. Instt. Engrs. (India) 84, 120–129 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Deb, A., Roychoudhury, S., Sarkar, G. (2016). Convolution of Time Functions. In: Analysis and Identification of Time-Invariant Systems, Time-Varying Systems, and Multi-Delay Systems using Orthogonal Hybrid Functions. Studies in Systems, Decision and Control, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-319-26684-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-26684-8_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26682-4
Online ISBN: 978-3-319-26684-8
eBook Packages: EngineeringEngineering (R0)