Advances in Shannon Sampling Theory (Review Paper)

K. K. Sharma; S. D. Joshi; Shobha Sharma

doi:10.14429/dsj.63.3762

K. K. Sharma Malaviya National Institute of Technology, Jaipur
S. D. Joshi Indian Institute of Technology, New Delhi
Shobha Sharma Apex Institute of Engineering and Technology, Jaipur

DOI: https://doi.org/10.14429/dsj.63.3762

Keywords: Fourier transform, fractional Fourier transform, linear canonical transform, sampling theorem, signal reconstruction, Nyquist rate

Abstract

In this paper, the authors have provided a brief review of the recent advances in the Shannon sampling theory. In particular, they discuss the work related to 1-D signal reconstruction involving the samples taken below the Nyquist rate using nonlinear/time-variant systems. The extensions of the sampling theorems to the fractional Fourier and Linear canonical transform domains are also discussed.

Defence Science Journal, 2013, 63(1), pp.41-45, DOI:http://dx.doi.org/10.14429/dsj.63.3762

Author Biographies

K. K. Sharma, Malaviya National Institute of Technology, Jaipur

Dr Kamalesh K. Sharma received his BE (Hons.), and ME (Hons.) in Electronics and Communication Engineering from Malaviya National Institute of Technology, Jaipur, India in 1990 and 2001 respectively and PhD from Indian Institute of Technology, Delhi, India in 2008. Presently, he is working as Associate Professor at Malaviya National Institute of Technology, Jaipur, India. His research interests include sampling theory of signals, image processing, and fractional transforms.

S. D. Joshi, Indian Institute of Technology, New Delhi

Dr S.D. Joshi received his BTech from BITS Pilani, MTech, and PhD from IIT Delhi. He is presently serving as Professorat IIT Delhi. His research interests include: Sampling theory of signals, image processing, statistical signal processing, signal matched wavelets and fractional transforms and group theoritical approach to signal/image processing.

Shobha Sharma, Apex Institute of Engineering and Technology, Jaipur

Ms Shobha Sharma received her BE (Electronics and Communication Engineering) from Jaipur National University, Jaipur, India in 2012. She is presently teaching at Apex Group of Institutions, Jaipur. Her research interests include: Sampling theory of signals and fractional transforms.