I am a native of Jammu and Kashmir, India. I have completed my BSc degree with Physics, Mathematics and Electronics as the major subjects, followed by an MSc degree in Mathematics, from the University of Kashmir, India. Subsequently, I completed my PhD degree in Mathematics, from the University of Kashmir, South Campus, India in the year 2022. Presently, I am working as a Postdoc Fellow at the Department of Computer Science and Engineering, Indian Institute of Technology Bombay. My broad field of research is Harmonic Analysis and my research interests include Fourier Analysis, Wavelet Theory, Sampling Theory, Filtering Theory and Mathematical Signal Processing, in general. Nevertheless, I have also worked as a Junior Research Fellow (JRF) in the major research project entitled Fractional Wavelet Analysis: Theory and Applications funded by the Science and Engineering Research Board of the Department of Science and Technology, Government of India during the period 2018-2021. During my six-year-long research career, I have worked on some of the prolific research problems on the subject of Fourier and wavelet transforms. As of now, I have co-authored about twenty research articles, which have been published (or communicated) in diverse international journals of repute. Most importantly, I have co-authored a monograph with my PhD supervisor, entitled Wavelet Transforms: Kith and Kin bearing ISBN 9781032007960. The book is published by the CRC Press and is the first of its kind dealing with the notion of continuous wavelet transforms, together with their erstwhile and subsequent chronological developments. Besides, I am also an occasional columnist for several English dailies with circulations in different parts of the country.
BROAD RESEARCH AREA
SPECIALIZATION
RESEARCH INTERESTS
PHD RESEARCH WORK
The title of my PhD thesis is An Analysis of the Stockwell Transforms in Different Time-frequency Domains. It is imperative to mention that the Stockwell transform (S-transform) was introduced by R.G. Stockwell in 1996 as a bridge between the short-time Fourier transform and the wavelet transform. Owing to its relationship with the wavelet transform, the Stockwell transform is also referred to as the phase-corrected wavelet transform. In the thesis work, we have accomplished two major objectives: First, we investigated upon the Stockwell transform beyond the conventional Fourier domain by introducing the notions of the fractional Stockwell transform and the linear canonical Stockwell transform; these novel Stockwell transforms are demonstrated to have optimized concentrations in the time-frequency plane, which makes them befitting for the class of signals which do not completely reveal their characteristics within the Fourier domain. Second, we extended the Stockwell transform to the higher-dimensional domains via two fundamental approaches; one relying upon the higher-dimensional analyzing functions and the other based on the concept of projections by invoking the well-known Radon transform. The thesis also embodies applications of the proposed work to different aspects of signal processing and it is demonstrated that the newly proposed Stockwell transforms outperform the classical tools of time-frequency analysis, including the short-time Fourier transform, wavelet transform, as well as the classical Stockwell transform.
KEY PUBLICATIONS (YEARLY)
Azhar Y. Tantary, Firdous A. Shah and Ahmed I. Zayed, Papoulis’ Sampling Theorem: Revisited, Applied and Computational Harmonic Analysis, 64, 118-142 (2023). Impact Factor 3.055
Firdous A. Shah and Azhar Y. Tantary, Sampling and Multiplicative Filtering Associated with the Quadratic-phase Fourier Transform, Signal Image and Video Processing, (2022), doi.org/10.1007/s11760-022-02385-y. Impact Factor 2.157
Firdous A. Shah and Azhar Y. Tantary, Lattice-based Multi-channel Sampling Theorem for Linear Canonical Transform, Digital Signal Processing, 117, 103168 (2021). Impact Factor 3.381
Azhar Y. Tantary and Firdous A. Shah, An Intertwining of Curvelet and Linear Canonical Transforms, Journal of Mathematics, Article ID 8814998 (2020), doi.org/10.1155/2020/8814998. Impact Factor 1.555
INVITED TALKS
Delivered a talk on the theme Time-frequency Analysis Beyond the Fourier Domain at the Department of Electrical Engineering, Indian Institute of Technology, Jammu, India on September 17, 2022.
AWARDS/NOMINATIONS
Junior Research Fellow (JRF) for a period of 3 Years in the SERB-DST funded major research project “Fractional Wavelet Analysis: Theory and Applications” (File No. EMR/2016/007951) with the principal investigator as Dr Firdous A. Shah, Department of Mathematics, South Campus, University of Kashmir, Anantnag-192101.
International Travel Support (File No. ITS/2019/004187) from Science and Engineering Research Board, Department of Science and Technology, India for attending International Workshop on Frames, Wavelets, Approximation Methods and Applications, September 15-22, 2019 organized by the Department of Mathematics and Computer Science, Palmero University, Italy (Couldn’t attend the event due to post August 2019 clampdown in Jammu and Kashmir, India).
Young Researcher Award, 2021 from INSc Banglore, India for the paper entitled An Intertwining of Curvelet and Linear Canonical Transforms, published in Journal of Mathematics (2020).
Nominated for Annual Research Awards 2021 by Dr K.V Rao Scientific Society (KVRSS) Hyderabad, for the paper entitled Multi-dimensional Linear Canonical Transform with Applications to Sampling and Multiplicative Filtering.
CONFERENCES/WORKSHOPS ATTENDED
Participated in a week-long workshop on Mathematics and Its Applications, September 16-22, 2022 organized by the Department of Mathematics, South Campus of University of Kashmir, Anantnag in collaboration with the Mathematics Consortium, Pune and Kashmir Mathematical society.
Participated in a 3-Day workshop on Research Methodology, March 28-30, 2022 organized by the South Campus of University of Kashmir, Anantnag.
Participated and presented a paper entitled “Multidimensional Linear Canonical Transform with Applications to Sampling and Multiplicative Filtering” in the International Webinar on Special Functions and Their Applications, March 21-25, 2022 organized by Department of Mathematics in association with IQAC, University of Kerala, India.
Participated and presented a paper entitled “Multi-channel Sampling Associated with the Multi-dimensional Linear Canonical Transform” in the First Online International Conference on Modern Fractional Calculus and its Applications, December 04-06, 2020 organized by Biruni University, Istanbul, Turkey.
Participated in the national level workshop on Introduction to Maple, June 29, 2020 organized by Binary Semantics, India.
Participated in the national level workshop on Algebra and Analysis, June 18-20, 2019 organized by the Department of Mathematics, Central University of Kashmir, Srinagar, India.
Participated and presented a paper entitled “Non-isotropic Angular Stockwell Transform and the Associated Uncertainty Principles” in the national level seminar on Mathematics and its Applications, June 21, 2019 organized by the Department of Mathematics, Central University of Kashmir, Srinagar, India.
Participated and presented a paper entitled “A Novel Fractional Stockwell Transform” in the International Conference on Mathematical Modelling and Computations (ICMMC-2018), December 01-03, 2018 organized by the Department of Mathematics, South Asian University, Delhi, India.
Participated and presented a paper entitled “A Novel Fractional Stockwell Transform” in the International Conference on Banach Algebras, Harmonic Analysis and Operator Theory, November 20-22, 2018 organized by the Department of Mathematics, Sardar Patel University, Gujrat, India.
Participated in the national level workshop on Geometrical interpretation of Mathematical concepts August 28-29, 2018 organized by the Department of Mathematics, University of Kashmir, Srinagar, India, in collaboration with Dass Scientific Research Laboratory (DSRL)-Ahmedabad.
Participated and presented a paper entitled “Polar Wavelet Transform and the Associated Uncertainty Principles” in the 13th Session of Jammu and Kashmir Science Congress (13th JKSC) organized by the University of Kashmir, Srinagar, India in collaboration with the Jammu and Kashmir State Science, technology, and Innovation Council, April 2-4, 2018.
Participated in the week long national level workshop on Research Methodology, November 23-29, 2017 organized by the Department of Mathematics, Central University of Kashmir, Srinagar, India.
OTHER RESEARCH ACTIVITIES
Reviewer for Mathematical Reviews, American Mathematical Society, Reviewer ID 155968.
Reviewer for Zentralblatt MATH (zbMATH), Reviewer ID 17035.
EDITED SPECIAL ISSUES
Guest Editor for the special issue on the research topic Contemporary Developments in Sampling and Filtering for Mathematics of Computation and Data Science in the journal Frontiers in Applied Mathematics and Statistics.
Guest Editor for the special issue on the research topic Recent Advances in Applied and Computational Harmonic Analysis for Universal Wiser Publisher.
SOCIAL ACTIVITIES
Participated and donated a unit of blood in the Blood Donation Camp organized by Humanity Welfare Organization Healthcare in collaboration with MMABM Hospital Anantnag and University of Kashmir, South Campus, Anantnag on May 23, 2017.
Participated in the Plantation-cum-Cleanliness Drive (Clean India-Green India) organized by the National Service Scheme (NSS), University of Kashmir, South Campus, Anantnag in collaboration with the Department of Social Forestry, Anantnag on March 25, 2021.
Participated in the Plantation Drive (Saga 2.0-A Chinar Corps Initiative) under the banner Swachh Anantnag-Green Anantnag, conducted at University of Kashmir, South Campus, Anantnag on October 06, 2021.