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On the Zeros of Ramanujan Filters

Kulkarni, Pranav and Vaidyanathan, P. P. (2020) On the Zeros of Ramanujan Filters. IEEE Signal Processing Letters, 27 . pp. 735-739. ISSN 1070-9908. https://resolver.caltech.edu/CaltechAUTHORS:20200430-151240761

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Abstract

Ramanujan filter banks have been used for identifying periodicity structure in streaming data. This letter studies the locations of zeros of Ramanujan filters. All the zeros of Ramanujan filters are shown to lie on or inside the unit circle in the z-plane. A convenient factorization appears as a corollary of this result, which is useful to identify common factors between different Ramanujan filters in a filter bank. For certain families of Ramanujan filters, further structure is identified in the locations of zeros of those filters. It is shown that increasing the number of periods of Ramanujan sums in the filter definition only increases zeros on the unit circle in z -plane. A potential application of these results is that by identifying common factors between Ramanujan filters, one can obtain efficient implementations of Ramanujan filter banks (RFB) as demonstrated here.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/lsp.2020.2990610DOIArticle
ORCID:
AuthorORCID
Kulkarni, Pranav0000-0002-1461-0948
Vaidyanathan, P. P.0000-0003-3003-7042
Additional Information:© 2020 IEEE. Manuscript received February 26, 2020; revised April 8, 2020; accepted April 13, 2020. Date of publication April 27, 2020; date of current version May 21, 2020. This work was supported in part by the ONR under Grant N00014-18-1-2390, in part by the NSF under Grant CCF-1712633, and in part by the California Institute of Technology. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Jens Ahrens.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-18-1-2390
NSFCCF-1712633
CaltechUNSPECIFIED
Subject Keywords:Ramanujan sums, Ramanujan filter banks, period estimation, cyclotomic polynomials
Record Number:CaltechAUTHORS:20200430-151240761
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200430-151240761
Official Citation:P. Kulkarni and P. P. Vaidyanathan, "On the Zeros of Ramanujan Filters," in IEEE Signal Processing Letters, vol. 27, pp. 735-739, 2020, doi: 10.1109/LSP.2020.2990610
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102946
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:01 May 2020 14:05
Last Modified:12 Jun 2020 16:45

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