<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2005000200010</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Time-domain flaw imaging system]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Medina]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Nacional Autónoma de México Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas Departamento de Ingeniería de Sistemas Computacionales y Automatización]]></institution>
<addr-line><![CDATA[México D.F.]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2005</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2005</year>
</pub-date>
<volume>51</volume>
<numero>2</numero>
<fpage>176</fpage>
<lpage>185</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2005000200010&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2005000200010&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2005000200010&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Ultrasonic Non Destructive Evaluation of materials is a useful tool for flaw detection and characterization. A typical ultrasonic imaging system may consist of a single transducer or an array of sensors working in a B-scan mode. This mode operates by transmitting a pulse of train of pulses from several locations and detecting the echoes coming from in-homogeneities. The reflected energy can be represented as a map of ultrasonic reflectivity. A time-delay beamformer has been successfully used to reconstruct the image, and localize the in-homogeneities within the scanned medium, by time shifting the signals, and summing them up. This process enables to locate regions at which signals are added constructively. It is however, a time consuming process and requires A/2 distance of motor steps or inter-element distance between array elements. An algorithm based on time-domain envelope beamformer is presented here. This algorithm is able to diminish the number of computational operations without losing relevant information about the location of in-homogeneities. A comparison between classical and envelope beam-formers is presented when applied to sets of simulated signals. Lateral and longitudinal resolutions are also computed when two targets are within the scanned medium.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Ensayos no destructivos con ultrasonido es una herramienta comúnmente usada para la detección y caracterización de fallas en materiales. Un sistema típico de imágenes ultrasónicas consiste en un solo transductor o arreglo de sensores que operan bajo el modo de rastreo B. Este modo consiste en transmitir un pulso o un tren de pulsos desde distintas posiciones, y para cada posición recibir ecos que pueden provenir de inhomogeneidades dentro del material inspeccionado. La energía reflejada puede desplegarse como un mapa de intensidades ultrasónicas. Uno de los métodos que han tenido gran éxito en la reconstrucción de imágenes y localización de inhomogeneidades es la llamada formación de haces, proceso digital en el dominio del tiempo. Esta técnica consiste en aplicar corrimientos en el tiempo específicos a cada serial registrada, para después sumar estas, encontrando así las zonas donde las señales se suman constructivamente. Sin embargo, esta técnica requiere largos periodos para su procesamiento así como la restricción de la distancia entre elementos no debe exceder de A/2. El trabajo que se presenta propone un algoritmo en el dominio del tiempo, que opera sobre la envolvente de las señales recibidas, disminuyendo el nú mero de operaciones computacionales sin perder información relevante de la localización de inhomogeneidades. Resultados comparativos entre la técnica clásica y la propuesta son presentados cuando ambas son aplicadas a un conjunto de señales simuladas. También resoluciones laterales y longitudinales han sido calculadas en el caso de que existan dos fallas puntuales en el medio inspeccionado.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Synthetic aperture focusing technique]]></kwd>
<kwd lng="en"><![CDATA[time-domain beam-forming technique]]></kwd>
<kwd lng="en"><![CDATA[flaws location]]></kwd>
<kwd lng="es"><![CDATA[Técnica de focalización de apertura sintética]]></kwd>
<kwd lng="es"><![CDATA[técnica de formación de haces en el dominio del tiempo]]></kwd>
<kwd lng="es"><![CDATA[localización de fallas]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  	    <p align="justify"><font face="verdana" size="4">Investigaci&oacute;n</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="center"><font face="verdana" size="4"><b>Time&#45;domain flaw imaging system</b></font></p>  	    <p align="center"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="center"><font face="verdana" size="2"><b>L. Medina</b></font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><i>Departamento de Ingenier&iacute;a de Sistemas Computacionales y Automatizaci&oacute;n, Instituto de Investigaciones en Matem&aacute;ticas Aplicadas y Sistemas, UNAM, Circuito Escolar, Ciudad Universitaria, 04510, M&eacute;xico D.F., M&eacute;xico,</i> e&#45;mail: <a href="mailto:lucia@uxdea4.iimas.unam.mx">lucia@uxdea4.iimas.unam.mx</a></font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2">Recibido el 7 de julio de 2004;    ]]></body>
<body><![CDATA[<br> 	aceptado el 23 de noviembre de 2004</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Abstract</b></font></p>  	    <p align="justify"><font face="verdana" size="2">Ultrasonic Non Destructive Evaluation of materials is a useful tool for flaw detection and characterization. A typical ultrasonic imaging system may consist of a single transducer or an array of sensors working in a B&#45;scan mode. This mode operates by transmitting a pulse of train of pulses from several locations and detecting the echoes coming from in&#45;homogeneities. The reflected energy can be represented as a map of ultrasonic reflectivity. A time&#45;delay beamformer has been successfully used to reconstruct the image, and localize the in&#45;homogeneities within the scanned medium, by time shifting the signals, and summing them up. This process enables to locate regions at which signals are added constructively. It is however, a time consuming process and requires A/2 distance of motor steps or inter&#45;element distance between array elements. An algorithm based on time&#45;domain envelope beamformer is presented here. This algorithm is able to diminish the number of computational operations without losing relevant information about the location of in&#45;homogeneities. A comparison between classical and envelope beam&#45;formers is presented when applied to sets of simulated signals. Lateral and longitudinal resolutions are also computed when two targets are within the scanned medium.</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Keywords:</b> Synthetic aperture focusing technique; time&#45;domain beam&#45;forming technique; flaws location.</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Resumen</b></font></p>  	    <p align="justify"><font face="verdana" size="2">Ensayos no destructivos con ultrasonido es una herramienta com&uacute;nmente usada para la detecci&oacute;n y caracterizaci&oacute;n de fallas en materiales. Un sistema t&iacute;pico de im&aacute;genes ultras&oacute;nicas consiste en un solo transductor o arreglo de sensores que operan bajo el modo de rastreo B. Este modo consiste en transmitir un pulso o un tren de pulsos desde distintas posiciones, y para cada posici&oacute;n recibir ecos que pueden provenir de inhomogeneidades dentro del material inspeccionado. La energ&iacute;a reflejada puede desplegarse como un mapa de intensidades ultras&oacute;nicas. Uno de los m&eacute;todos que han tenido gran &eacute;xito en la reconstrucci&oacute;n de im&aacute;genes y localizaci&oacute;n de inhomogeneidades es la llamada formaci&oacute;n de haces, proceso digital en el dominio del tiempo. Esta t&eacute;cnica consiste en aplicar corrimientos en el tiempo espec&iacute;ficos a cada serial registrada, para despu&eacute;s sumar estas, encontrando as&iacute; las zonas donde las se&ntilde;ales se suman constructivamente. Sin embargo, esta t&eacute;cnica requiere largos periodos para su procesamiento as&iacute; como la restricci&oacute;n de la distancia entre elementos no debe exceder de <i>A</i>/2. El trabajo que se presenta propone un algoritmo en el dominio del tiempo, que opera sobre la envolvente de las se&ntilde;ales recibidas, disminuyendo el n&uacute; mero de operaciones computacionales sin perder informaci&oacute;n relevante de la localizaci&oacute;n de inhomogeneidades. Resultados comparativos entre la t&eacute;cnica cl&aacute;sica y la propuesta son presentados cuando ambas son aplicadas a un conjunto de se&ntilde;ales simuladas. Tambi&eacute;n resoluciones laterales y longitudinales han sido calculadas en el caso de que existan dos fallas puntuales en el medio inspeccionado.</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Descriptores:</b> T&eacute;cnica de focalizaci&oacute;n de apertura sint&eacute;tica; t&eacute;cnica de formaci&oacute;n de haces en el dominio del tiempo; localizaci&oacute;n de fallas.</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">PACS: 43.60.+d; 43.60.Gk; 43.35.Sx</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><a href="/pdf/rmf/v51n2/v51n2a10.pdf" target="_blank">DESCARGAR ART&Iacute;CULO EN FORMATO PDF</a></font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>Acknowledgments</b></font></p>  	    <p align="justify"><font face="verdana" size="2">The author would like to thank to Universidad Nacional Aut&oacute;noma de M&eacute;xico (PAPITT&#45;IN105303) for its financial grant, and to Mr. Francisco Javier Cardenas Flores and Mr. Luis Alberto Aguilar Beltran for their technical assistance.</font></p>  	    <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>  	    <p align="justify"><font face="verdana" size="2"><b>References</b></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">1. D.W. Prine, <i>Proc Eng. Appl. Holog. SPIE</i> <b>287</b> (1972).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308764&pid=S0035-001X200500020001000001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    ]]></body>
<body><![CDATA[<!-- ref --><p align="justify"><font face="verdana" size="2">2. P.D. Corl, G.S. Kino, C.S. Desilet, and P.M. Grant, <i>Acoust. Holog.</i> <b>8</b> (1980) 39.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308766&pid=S0035-001X200500020001000002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">3. C.F. Scheuler, H. Lee, and G. Wade, <i>IEEE Trans. Sonics Ultrason.</i> <b>53</b> (1984) 195.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308768&pid=S0035-001X200500020001000003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">4. L.J. Busse, H.D. Collins, and S.R. Doctor, "Review and discussion of the development of synthetic aperture focusing technique for ultrasonic testing (SAFT&#45;UT)", Pacific Northwest Lab. Rep. NUREG/CR&#45;3625, PNL&#45;4957 (1984).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308770&pid=S0035-001X200500020001000004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">5. Rastello T., Vray D., Chatillon J., <i>IEEE Trans. Image Proc.</i> <b>8</b> (1999) 1309.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308772&pid=S0035-001X200500020001000005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">6. A.V. Osetrov, <i>Ultrasonics</i> <b>38</b> (2000) 739.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308774&pid=S0035-001X200500020001000006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    ]]></body>
<body><![CDATA[<!-- ref --><p align="justify"><font face="verdana" size="2">7. M. Lang and H. Ermert, <i>Biomedizinische Technik Band</i> <b>42</b> (1997) 108.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308776&pid=S0035-001X200500020001000007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">8. K.L. Gammelmark and J.A. <i>Jensen, Proc.</i> <b>4686</b> (2002) 25.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308778&pid=S0035-001X200500020001000008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">9. S.I. Nikolov, J.A. Jensen, R. Dufait, and A. Schoisswohl, <i>Proc. IEEE Inter. Ultrason. Symp.</i> (2002) 1585.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308780&pid=S0035-001X200500020001000009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">10. R.G. Pridham and R.A. Mucci, <i>J. Acoust. Soc. Am.</i> <b>63</b> (1978) 425.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308782&pid=S0035-001X200500020001000010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">11. R.A. Mucci, <i>IEEE Trans. Acoust., Speech, Sig. Proc.</i> <b>32</b> (1984) 548.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308784&pid=S0035-001X200500020001000011&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    ]]></body>
<body><![CDATA[<!-- ref --><p align="justify"><font face="verdana" size="2">12. V.D. Van Veen, K.M. Buckley, <i>IEEE Trans. ASSP Magazine</i> (1988) 4.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308786&pid=S0035-001X200500020001000012&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">13. J.R. Williams, <i>J. of the Acoust. Soc. of Am.</i> <b>44</b> (1968) 1454.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308788&pid=S0035-001X200500020001000013&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">14. C.A. Balanis, <i>Antenna Theory: Analysis and Design,</i> (Harper Row Publishers, Inc., New York, 1982).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308790&pid=S0035-001X200500020001000014&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">15 . W.S.H. Munro, <i>Ultrasonic Phased Arrays for use in Imaging and Automatic Vehicle Guidance,</i> (Ph. D. Thesis, Nottingham University, 1990).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308792&pid=S0035-001X200500020001000015&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">16. Y. Ozaki, H. Sumitani, T. Tomoda, and M. Tanaka, <i>IEEE Trans. Ultrason. Ferroelect. Freq. Contr.</i> <b>35</b> (1988) 828.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308794&pid=S0035-001X200500020001000016&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    ]]></body>
<body><![CDATA[<!-- ref --><p align="justify"><font face="verdana" size="2">17. D.H. Johnso and D.E. Dudgeon, <i>Array Signal Processing: Concepts and Techniques,</i> (Prentice Hall Inc., New Jersey, 1993).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308796&pid=S0035-001X200500020001000017&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">18. M. Born and E. Wolf, <i>Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light,</i> (4th ed., Pergamon Press Ltd., London, 1970).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308798&pid=S0035-001X200500020001000018&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">19. P. Webb and C. Wykes, <i>IEEE Trans. Robotics and Autom.</i> <b>12</b> (1996) 138.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308800&pid=S0035-001X200500020001000019&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">20. L. Medina and C. Wykes, <i>Ultrasonics</i> <b>39</b> (2001) 19.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308802&pid=S0035-001X200500020001000020&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">21. E.G. Steward, <i>Fourier Transform: An Introduction,</i> (John Wiley &amp; Sons, Inc., New York, 1983).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308804&pid=S0035-001X200500020001000021&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    ]]></body>
<body><![CDATA[<!-- ref --><p align="justify"><font face="verdana" size="2">22. R.A. Serway, <i>Physics for Scientists and Engineers: with Modern Physics,</i> (3th ed., Saunder College Publishing, Philadelphia, 1992).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308806&pid=S0035-001X200500020001000022&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">23. R.A. Gabel and R.A. Roberts, <i>Signals and Linear Systems,</i> (2nd ed. John Wiley and Sons, Inc., New York, 1980).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308808&pid=S0035-001X200500020001000023&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">24. B.P. Lathi, <i>Modern Digital and Analog Communication Systems,</i> (2nd ed., Holt, Rinehart and Winston, Inc., Philadelphia, 1989).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308810&pid=S0035-001X200500020001000024&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>  	    <!-- ref --><p align="justify"><font face="verdana" size="2">25. A.B. Carlson, <i>Communication Systems: An Introduction to Signals and Noise in Electrical Communication,</i> (McGraw&#45;Hill, Inc., New York, 1968).    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8308812&pid=S0035-001X200500020001000025&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --></font></p>      ]]></body><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Prine]]></surname>
<given-names><![CDATA[D.W.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proc Eng. Appl. Holog. SPIE]]></source>
<year>1972</year>
<volume>287</volume>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Corl]]></surname>
<given-names><![CDATA[P.D.]]></given-names>
</name>
<name>
<surname><![CDATA[Kino]]></surname>
<given-names><![CDATA[G.S.]]></given-names>
</name>
<name>
<surname><![CDATA[Desilet]]></surname>
<given-names><![CDATA[C.S.]]></given-names>
</name>
<name>
<surname><![CDATA[Grant]]></surname>
<given-names><![CDATA[P.M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Acoust. Holog.]]></source>
<year>1980</year>
<volume>8</volume>
<page-range>39</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Scheuler]]></surname>
<given-names><![CDATA[C.F.]]></given-names>
</name>
<name>
<surname><![CDATA[Lee]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Wade]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[IEEE Trans. Sonics Ultrason.]]></source>
<year>1984</year>
<volume>53</volume>
<page-range>195</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Busse]]></surname>
<given-names><![CDATA[L.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Collins]]></surname>
<given-names><![CDATA[H.D.]]></given-names>
</name>
<name>
<surname><![CDATA[Doctor]]></surname>
<given-names><![CDATA[S.R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Review and discussion of the development of synthetic aperture focusing technique for ultrasonic testing (SAFT-UT)]]></source>
<year>1984</year>
<publisher-name><![CDATA[Pacific Northwest Lab.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rastello]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Vray]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Chatillon]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[IEEE Trans. Image Proc.]]></source>
<year>1999</year>
<volume>8</volume>
<page-range>1309</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Osetrov]]></surname>
<given-names><![CDATA[A.V.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ultrasonics]]></source>
<year>2000</year>
<volume>38</volume>
<page-range>739</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lang]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Ermert]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Biomedizinische Technik Band]]></source>
<year>1997</year>
<volume>42</volume>
<page-range>108</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gammelmark]]></surname>
<given-names><![CDATA[K.L.]]></given-names>
</name>
<name>
<surname><![CDATA[Jensen]]></surname>
<given-names><![CDATA[J.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proc.]]></source>
<year>2002</year>
<volume>4686</volume>
<page-range>25</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nikolov]]></surname>
<given-names><![CDATA[S.I.]]></given-names>
</name>
<name>
<surname><![CDATA[Jensen]]></surname>
<given-names><![CDATA[J.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Dufait]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Schoisswohl]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proc. IEEE Inter. Ultrason. Symp.]]></source>
<year>2002</year>
<page-range>1585</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pridham]]></surname>
<given-names><![CDATA[R.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Mucci]]></surname>
<given-names><![CDATA[R.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Acoust. Soc. Am.]]></source>
<year>1978</year>
<volume>63</volume>
<page-range>425</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mucci]]></surname>
<given-names><![CDATA[R.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[IEEE Trans. Acoust., Speech, Sig. Proc.]]></source>
<year>1984</year>
<volume>32</volume>
<page-range>548</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Van Veen]]></surname>
<given-names><![CDATA[V.D.]]></given-names>
</name>
<name>
<surname><![CDATA[Buckley]]></surname>
<given-names><![CDATA[K.M.]]></given-names>
</name>
</person-group>
<source><![CDATA[IEEE Trans. ASSP Magazine]]></source>
<year>1988</year>
<page-range>4</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Williams]]></surname>
<given-names><![CDATA[J.R.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. of the Acoust. Soc. of Am.]]></source>
<year>1968</year>
<volume>44</volume>
<page-range>1454</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Balanis]]></surname>
<given-names><![CDATA[C.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Antenna Theory: Analysis and Design]]></source>
<year>1982</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Harper Row Publishers, Inc.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Munro]]></surname>
<given-names><![CDATA[W.S.H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ultrasonic Phased Arrays for use in Imaging and Automatic Vehicle Guidance]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ozaki]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Sumitani]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Tomoda]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Tanaka]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[IEEE Trans. Ultrason. Ferroelect. Freq. Contr.]]></source>
<year>1988</year>
<volume>35</volume>
<page-range>828</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Johnso]]></surname>
<given-names><![CDATA[D.H.]]></given-names>
</name>
<name>
<surname><![CDATA[Dudgeon]]></surname>
<given-names><![CDATA[D.E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Array Signal Processing: Concepts and Techniques]]></source>
<year>1993</year>
<publisher-loc><![CDATA[New Jersey ]]></publisher-loc>
<publisher-name><![CDATA[Prentice Hall Inc.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<label>18</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Born]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Wolf]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Principles of Optics: Electromagnetic Theory of Propagation]]></source>
<year>1970</year>
<edition>4</edition>
<publisher-loc><![CDATA[London ]]></publisher-loc>
<publisher-name><![CDATA[Pergamon Press Ltd.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<label>19</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Webb]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Wykes]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<source><![CDATA[IEEE Trans. Robotics and Autom.]]></source>
<year>1996</year>
<volume>12</volume>
<page-range>138</page-range></nlm-citation>
</ref>
<ref id="B20">
<label>20</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Medina]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Wykes]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ultrasonics]]></source>
<year>2001</year>
<volume>39</volume>
<page-range>19</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>21</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Steward]]></surname>
<given-names><![CDATA[E.G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Fourier Transform: An Introduction]]></source>
<year>1983</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley & Sons, Inc.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<label>22</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Serway]]></surname>
<given-names><![CDATA[R.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Physics for Scientists and Engineers: with Modern Physics]]></source>
<year>1992</year>
<edition>3</edition>
<publisher-loc><![CDATA[Philadelphia ]]></publisher-loc>
<publisher-name><![CDATA[Saunder College Publishing]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B23">
<label>23</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gabel]]></surname>
<given-names><![CDATA[R.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Roberts]]></surname>
<given-names><![CDATA[R.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Signals and Linear Systems]]></source>
<year>1980</year>
<edition>2</edition>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley and Sons, Inc.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B24">
<label>24</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lathi]]></surname>
<given-names><![CDATA[B.P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Modern Digital and Analog Communication Systems]]></source>
<year>1989</year>
<edition>2</edition>
<publisher-loc><![CDATA[Philadelphia ]]></publisher-loc>
<publisher-name><![CDATA[Holt, Rinehart and Winston, Inc.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B25">
<label>25</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Carlson]]></surname>
<given-names><![CDATA[A.B.]]></given-names>
</name>
</person-group>
<source><![CDATA[Communication Systems: An Introduction to Signals and Noise in Electrical Communication]]></source>
<year>1968</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[McGraw-Hill, Inc.]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
