Generalized Fractional Ambiguity Function and Its Applications
The ambiguity function (AF) is an essential time-frequency analysis tool to analyze the radar waveform properties in radar applications. It can be used effectively and reliably to analyze properties like the peak-to-side-lobe ratio, time delay resolution, Doppler resolution and tolerance characteris...
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| Veröffentlicht in: | Circuits, systems, and signal processing systems, and signal processing, 2020-10, Vol.39 (10), p.4980-5019 |
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| container_title | Circuits, systems, and signal processing |
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| creator | Sahay, Peeyush Shaik Rasheed, Izaz Ahamed Kulkarni, Pranav Jain, Shubham Anand Anjarlekar, Ameya Radhakrishna, P. Gadre, Vikram M. |
| description | The ambiguity function (AF) is an essential time-frequency analysis tool to analyze the radar waveform properties in radar applications. It can be used effectively and reliably to analyze properties like the peak-to-side-lobe ratio, time delay resolution, Doppler resolution and tolerance characteristic. However, it fails to analyze higher-order chirp waveforms and is unable to estimate their parameters. To solve this problem, a generalized time-frequency transform-based generalized fractional AF (GFAF) and generalized fractional Wigner–Ville distribution (GFWVD) are proposed. GFAF is also a generalization of the Fourier transform-based ambiguity function and the fractional Fourier transform-based ambiguity function. The uncertainty principle for GFAF and GFWVD is derived. Examples are presented to demonstrate the effectiveness of GFAF in analyzing cubic chirp waveforms and estimating parameters of multicomponent cubic chirps. The superiority of GFAF is demonstrated by comparing the mean square error to Cramer–Rao lower bound and high-order ambiguity function under different input-signal-to-noise ratio conditions. The robustness is demonstrated by comparing the signal-to-noise ratio gain to that of the time domain-matched filtering and other ambiguity functions. Finally, fourth-order parameters of a real bat echolocation signal are estimated. |
| doi_str_mv | 10.1007/s00034-020-01398-7 |
| format | Article |
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It can be used effectively and reliably to analyze properties like the peak-to-side-lobe ratio, time delay resolution, Doppler resolution and tolerance characteristic. However, it fails to analyze higher-order chirp waveforms and is unable to estimate their parameters. To solve this problem, a generalized time-frequency transform-based generalized fractional AF (GFAF) and generalized fractional Wigner–Ville distribution (GFWVD) are proposed. GFAF is also a generalization of the Fourier transform-based ambiguity function and the fractional Fourier transform-based ambiguity function. The uncertainty principle for GFAF and GFWVD is derived. Examples are presented to demonstrate the effectiveness of GFAF in analyzing cubic chirp waveforms and estimating parameters of multicomponent cubic chirps. The superiority of GFAF is demonstrated by comparing the mean square error to Cramer–Rao lower bound and high-order ambiguity function under different input-signal-to-noise ratio conditions. The robustness is demonstrated by comparing the signal-to-noise ratio gain to that of the time domain-matched filtering and other ambiguity functions. Finally, fourth-order parameters of a real bat echolocation signal are estimated.</description><identifier>ISSN: 0278-081X</identifier><identifier>EISSN: 1531-5878</identifier><identifier>DOI: 10.1007/s00034-020-01398-7</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Ambiguity ; Audio frequencies ; Chirp ; Circuits and Systems ; Electrical Engineering ; Electronics and Microelectronics ; Engineering ; Fourier transforms ; Instrumentation ; Lower bounds ; Order parameters ; Parameter estimation ; Signal to noise ratio ; Signal,Image and Speech Processing ; Time lag ; Time-frequency analysis ; Waveforms</subject><ispartof>Circuits, systems, and signal processing, 2020-10, Vol.39 (10), p.4980-5019</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-caee1e32c6f6afb91116412e9069e5ff76c8bc5d2361a8403509d22dd02703433</citedby><cites>FETCH-LOGICAL-c319t-caee1e32c6f6afb91116412e9069e5ff76c8bc5d2361a8403509d22dd02703433</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00034-020-01398-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00034-020-01398-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Sahay, Peeyush</creatorcontrib><creatorcontrib>Shaik Rasheed, Izaz Ahamed</creatorcontrib><creatorcontrib>Kulkarni, Pranav</creatorcontrib><creatorcontrib>Jain, Shubham Anand</creatorcontrib><creatorcontrib>Anjarlekar, Ameya</creatorcontrib><creatorcontrib>Radhakrishna, P.</creatorcontrib><creatorcontrib>Gadre, Vikram M.</creatorcontrib><title>Generalized Fractional Ambiguity Function and Its Applications</title><title>Circuits, systems, and signal processing</title><addtitle>Circuits Syst Signal Process</addtitle><description>The ambiguity function (AF) is an essential time-frequency analysis tool to analyze the radar waveform properties in radar applications. It can be used effectively and reliably to analyze properties like the peak-to-side-lobe ratio, time delay resolution, Doppler resolution and tolerance characteristic. However, it fails to analyze higher-order chirp waveforms and is unable to estimate their parameters. To solve this problem, a generalized time-frequency transform-based generalized fractional AF (GFAF) and generalized fractional Wigner–Ville distribution (GFWVD) are proposed. GFAF is also a generalization of the Fourier transform-based ambiguity function and the fractional Fourier transform-based ambiguity function. The uncertainty principle for GFAF and GFWVD is derived. Examples are presented to demonstrate the effectiveness of GFAF in analyzing cubic chirp waveforms and estimating parameters of multicomponent cubic chirps. The superiority of GFAF is demonstrated by comparing the mean square error to Cramer–Rao lower bound and high-order ambiguity function under different input-signal-to-noise ratio conditions. The robustness is demonstrated by comparing the signal-to-noise ratio gain to that of the time domain-matched filtering and other ambiguity functions. Finally, fourth-order parameters of a real bat echolocation signal are estimated.</description><subject>Ambiguity</subject><subject>Audio frequencies</subject><subject>Chirp</subject><subject>Circuits and Systems</subject><subject>Electrical Engineering</subject><subject>Electronics and Microelectronics</subject><subject>Engineering</subject><subject>Fourier transforms</subject><subject>Instrumentation</subject><subject>Lower bounds</subject><subject>Order parameters</subject><subject>Parameter estimation</subject><subject>Signal to noise ratio</subject><subject>Signal,Image and Speech Processing</subject><subject>Time lag</subject><subject>Time-frequency analysis</subject><subject>Waveforms</subject><issn>0278-081X</issn><issn>1531-5878</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kE9LxDAUxIMoWFe_gKeC5-h7Sf8kF6Es7rqw4EXBW0jTdOnSbWvSHtZPb3YrePP0YPjNMG8IuUd4RID8yQMATygwoIBcCppfkAhTjjQVubgkEbBcUBD4eU1uvN8DoEwki8jz2nbW6bb5tlW8ctqMTd_pNi4OZbObmvEYr6buLMa6q-LN6ONiGNrG6JPmb8lVrVtv737vgnysXt6Xr3T7tt4siy01HOVIjbYWLWcmqzNdlxIRswSZlZBJm9Z1nhlRmrRiPEMtEuApyIqxqgq1w1-cL8jDnDu4_muyflT7fnKhqFcsCTRIkEmg2EwZ13vvbK0G1xy0OyoEddpJzTupsJM676TyYOKzyQe421n3F_2P6wfWFmnn</recordid><startdate>20201001</startdate><enddate>20201001</enddate><creator>Sahay, Peeyush</creator><creator>Shaik Rasheed, Izaz Ahamed</creator><creator>Kulkarni, Pranav</creator><creator>Jain, Shubham Anand</creator><creator>Anjarlekar, Ameya</creator><creator>Radhakrishna, P.</creator><creator>Gadre, Vikram M.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7SP</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0W</scope></search><sort><creationdate>20201001</creationdate><title>Generalized Fractional Ambiguity Function and Its Applications</title><author>Sahay, Peeyush ; Shaik Rasheed, Izaz Ahamed ; Kulkarni, Pranav ; Jain, Shubham Anand ; Anjarlekar, Ameya ; Radhakrishna, P. ; Gadre, Vikram M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-caee1e32c6f6afb91116412e9069e5ff76c8bc5d2361a8403509d22dd02703433</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Ambiguity</topic><topic>Audio frequencies</topic><topic>Chirp</topic><topic>Circuits and Systems</topic><topic>Electrical Engineering</topic><topic>Electronics and Microelectronics</topic><topic>Engineering</topic><topic>Fourier transforms</topic><topic>Instrumentation</topic><topic>Lower bounds</topic><topic>Order parameters</topic><topic>Parameter estimation</topic><topic>Signal to noise ratio</topic><topic>Signal,Image and Speech Processing</topic><topic>Time lag</topic><topic>Time-frequency analysis</topic><topic>Waveforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sahay, Peeyush</creatorcontrib><creatorcontrib>Shaik Rasheed, Izaz Ahamed</creatorcontrib><creatorcontrib>Kulkarni, Pranav</creatorcontrib><creatorcontrib>Jain, Shubham Anand</creatorcontrib><creatorcontrib>Anjarlekar, Ameya</creatorcontrib><creatorcontrib>Radhakrishna, P.</creatorcontrib><creatorcontrib>Gadre, Vikram M.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DELNET Engineering & Technology Collection</collection><jtitle>Circuits, systems, and signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sahay, Peeyush</au><au>Shaik Rasheed, Izaz Ahamed</au><au>Kulkarni, Pranav</au><au>Jain, Shubham Anand</au><au>Anjarlekar, Ameya</au><au>Radhakrishna, P.</au><au>Gadre, Vikram M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalized Fractional Ambiguity Function and Its Applications</atitle><jtitle>Circuits, systems, and signal processing</jtitle><stitle>Circuits Syst Signal Process</stitle><date>2020-10-01</date><risdate>2020</risdate><volume>39</volume><issue>10</issue><spage>4980</spage><epage>5019</epage><pages>4980-5019</pages><issn>0278-081X</issn><eissn>1531-5878</eissn><abstract>The ambiguity function (AF) is an essential time-frequency analysis tool to analyze the radar waveform properties in radar applications. It can be used effectively and reliably to analyze properties like the peak-to-side-lobe ratio, time delay resolution, Doppler resolution and tolerance characteristic. However, it fails to analyze higher-order chirp waveforms and is unable to estimate their parameters. To solve this problem, a generalized time-frequency transform-based generalized fractional AF (GFAF) and generalized fractional Wigner–Ville distribution (GFWVD) are proposed. GFAF is also a generalization of the Fourier transform-based ambiguity function and the fractional Fourier transform-based ambiguity function. The uncertainty principle for GFAF and GFWVD is derived. Examples are presented to demonstrate the effectiveness of GFAF in analyzing cubic chirp waveforms and estimating parameters of multicomponent cubic chirps. The superiority of GFAF is demonstrated by comparing the mean square error to Cramer–Rao lower bound and high-order ambiguity function under different input-signal-to-noise ratio conditions. 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| subjects | Ambiguity Audio frequencies Chirp Circuits and Systems Electrical Engineering Electronics and Microelectronics Engineering Fourier transforms Instrumentation Lower bounds Order parameters Parameter estimation Signal to noise ratio Signal,Image and Speech Processing Time lag Time-frequency analysis Waveforms |
| title | Generalized Fractional Ambiguity Function and Its Applications |
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