Lecture by Prof. Anubha Gupta

Department of Electrical Engineering, Indian Institute of Science 

and 

IEEE Signal Processing Society, Bangalore Chapter 

cordially invite you to a lecture on 

Proper Definition of Dirichlet Conditions and Convergence of Fourier Representations 

 By 

 Prof. Anubha Gupta 

Indraprastha Institute of Information Technology -Delhi 

 Date and time: January 11, 2023, 5 PM 

 Venue: Multimedia Classroom, Department of Electrical Engineering (EE), IISc. 

 Coffee will be served during the talk. 

 Abstract:  Fourier theory is the backbone of Signal Processing (SP) and Communication Engineering. It has been widely used in almost all branches of science and engineering in numerous applications since its inception. However, Fourier representations such as Fourier series (FS) and Fourier transform (FT) may not exist for some signals that fail to fulfil a predefined set of Dirichlet conditions (DCs). We note a subtle gap in explaining these conditions as available in the popular SP literature. For example, the original DCs require a signal to have bounded variations over one time period for the convergence of FS, where there can be at most countably infinite number of maxima and minima, and at most countably infinite number of discontinuities of finite magnitude. However, a large body of the literature replaces this statement with the requirements of a finite number of maxima and minima over one time period, and a finite number of finite discontinuities over one time period. Due to the latter, some signals fulfilling the original DCs are incorrectly perceived as not having convergent FS representation. A similar problem holds in the description of DCs for the FT. This talk is based on our recent lecture notes published in IEEE Signal Processing Magazine (Sep 2022 issue), wherein we provide the required clarifications and a lucid but precise description and explanation on the DCs along with a lot of suitable examples. 

 Brief Bio: 

Anubha Gupta (anubha@iiitd.ac.in) received her B.Tech and M.Tech from Delhi University, India in 1991 and 1997 in Electronics and Communication Engineering. She received her PhD. from Indian Institute of Technology (IIT), Delhi, India in 2006 in Electrical Engineering. She did her second master’s as a full-time student from the University of Maryland, College Park, USA from 2008-2010 in Education. She worked as Assistant Director with the Ministry of Information and Broadcasting, Govt. of India (through Indian Engineering Services) from 1993 to 1999 and, as faculty at NSUT-Delhi (2000-2008) and IIIT-Hyderabad (2011-2013), India. Currently, she is working as a Professor at IIIT-Delhi, where she served as the Dean, Academic Affairs from June 2019 to June 2020. She has authored/co-authored more than 100 technical papers in scientific journals and conferences. She received SERB POWER Fellowship, 2021 from DST. Govt. of India. She has published research papers in both engineering and education. A lot of exciting work is being taken up in her lab: SBILab (Lab: http://sbilab.iiitd.edu.in/index.html

). Her research interests include applications of machine learning in cancer genomics, cancer imaging, biomedical signal and image processing including fMRI, MRI, EEG, ECG signal processing, and Wavelets in deep learning. Dr. Gupta is a senior member of IEEE Signal Processing Society (SPS) and a member of IEEE Women in Engineering Society. She is a technical committee member of BISP committee of IEEE SPS Society for Jan 2022– Dec 2024.  

Host: Prof. Chandra Sekhar Seelamantula, EE, IISc. 

All are invited.