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Algorithms for Optics: Generalized version of the inverse fast Fourier transform is computationally

À̸§ : (ÁÖ)ºí·çÇò

2019-12-24 16:28:36 Á¶È¸ :3089

Algorithms for Optics: Generalized version of the inverse fast Fourier transform is computationally efficient

The fast Fourier transform (FFT) and IFFT are key to many photonics-related algorithms; now, they are more useful than ever.


ÀÌ ½Ã°¢È­´Â ±âÁ¸ CZT ¾Ë°í¸®Áò»Ó¸¸ ¾Æ´Ï¶ó »õ·Î¿î ICZT ¾Ë°í¸®ÁòÀÌ Ã³¸® ÇÒ ¼öÀÖ´Â ¼¼ °¡Áö ´Ù¸¥ À¯ÇüÀÇ ÁÖÆļö ±¸¼º ¿ä¼Ò¸¦ º¸¿©ÁÝ´Ï´Ù (Re´Â ½ÇÁ¦ Ãà, IMÀº °¡»ó Ãà).  ¿ÞÂÊÀÇ À̹ÌÁö´Â ±âÇÏ ±Þ¼öÀûÀ¸·Î °¨¼èÇÏ´Â ÁÖÆļö ¼ººÐÀ» º¸¿©ÁÝ´Ï´Ù.  Áß¾Ó¿¡¼­ ½Ã°£ÀûÀ¸·Î º¯ÇÏÁö ¾Ê´Â ÁÖÆļö ¼ººÐÀÇ Æ¯º°ÇÑ °æ¿ì;  ¿À¸¥ÂÊ¿¡´Â ±âÇÏ ±Þ¼öÀûÀ¸·Î Áõ°¡ÇÏ´Â ÁÖÆļö ¿ä¼Ò°¡ ÀÖ½À´Ï´Ù.

ÀÌ ½Ã°¢È­´Â ±âÁ¸ CZT ¾Ë°í¸®Áò»Ó¸¸ ¾Æ´Ï¶ó »õ·Î¿î ICZT ¾Ë°í¸®ÁòÀÌ Ã³¸® ÇÒ ¼öÀÖ´Â ¼¼ °¡Áö ´Ù¸¥ À¯ÇüÀÇ ÁÖÆļö ±¸¼º ¿ä¼Ò¸¦ º¸¿©ÁÝ´Ï´Ù (Re´Â ½ÇÁ¦ Ãà, IMÀº °¡»ó Ãà). ¿ÞÂÊÀÇ À̹ÌÁö´Â ±âÇÏ ±Þ¼öÀûÀ¸·Î °¨¼èÇÏ´Â ÁÖÆļö ¼ººÐÀ» º¸¿©ÁÝ´Ï´Ù. Áß¾Ó¿¡¼­ ½Ã°£ÀûÀ¸·Î º¯ÇÏÁö ¾Ê´Â ÁÖÆļö ¼ººÐÀÇ Æ¯º°ÇÑ °æ¿ì; ¿À¸¥ÂÊ¿¡´Â ±âÇÏ ±Þ¼öÀûÀ¸·Î Áõ°¡ÇÏ´Â ÁÖÆļö ¿ä¼Ò°¡ ÀÖ½À´Ï´Ù.

Ǫ¸®¿¡ º¯È¯À» °áÁ¤Çϱâ À§ÇØ Çϳª¸¦ Çã¿ëÇÏ´Â ¼öÇÐÀû ¿¬»êÀº, ¿¹¸¦ µé¸é, È­»óÀÇ °ø°£ ÁÖÆļö ¼ººÐ - ¿ªÇà·ÄÀº Á÷¼³Àû ¿ª Ǫ¸®¿¡ º¯È¯ (°¡)¶ó°íÇÑ´Ù. ÀÌ µÎ °¡Áö ÀÛ¾÷Àº ±¤ÇÐ ¹× Æ÷Åä´Ð½ºÀÇ ±âº»ÀÔ´Ï´Ù. ½ÇÁ¦ ÇüÅ·ΠǪ¸®¿¡ º¯È¯À» ±¸ÇöÇÏ´Â ¾Ë°í¸®Áò ÀÎ FFT (°í¼Ó Ǫ¸®¿¡ º¯È¯) ¹× IFFT (¿ª ¾Ë°í¸®Áò)´Â À̹ÌÁö ¾ÐÃà¿¡¼­ ±¤¼¶À¯ ÀÎÄÚµù¿¡ À̸£±â±îÁö ¼ö¸¹Àº ÀÀ¿ë ÇÁ·Î±×·¥¿¡ »ç¿ëµË´Ï´Ù. ÆÄ¸é °¨Áö , ±¤ ½ºÆåÆ®·³ ºÐ¼® , ÀÎÅÍÆä·Î ±×·¥ ºÐ¼®, Áøµ¿ Á¦¾î , ºÐ±¤¹ý µî

 À§¿¡¼­ ¾ð±Þ ÇÑ µ¥ÀÌÅÍ ¼¼Æ®¿Í Ǫ¸®¿¡ º¯È¯ »çÀÌÀÇ ¹ÐÁ¢ÇÑ °ü°è¿¡ ´ëÇÑ ¿¹¿¡¼­, ÁÖ¾îÁø ·»Áî¿¡ ´ëÇØ ¹«ÇÑÈ÷ ¹à°í Á÷¼± ÀÎ ·»Áî À̹ÌÁöÀÇ ´Ü¸é °­µµ Æ®·¹À̽º ÀÎ ¶óÀÎ ½ºÇÁ·¹µå ±â´É ¾îµÎ¿î ¹è°æÀº Ǫ¸®¿¡ º¯È¯µÇ¾î 1D º¯Á¶ Àü¼Û ÇÔ¼ö (MTF)¸¦ »ý¼º ÇÒ ¼ö Àִµ¥, ÀÌ´Â ·»Áî°¡ 0¿¡¼­ ½ÃÀÛÇÏ¿© °ø°£ ÁÖÆļö¸¦ À̹Ì¡ÇÏ´Â ´É·ÂÀ» º¸¿©ÁÖ´Â Ç÷ÔÀÔ´Ï´Ù.

FFT ¾Ë°í¸®ÁòÀº 1965³â¿¡ ÃâÆǵǾú½À´Ï´Ù. 4³â ÈÄ, ¿¬±¸¿øµéÀº CZT(chirp z-transform)¶ó ºÒ¸®´Âº¸´Ù ´Ù¾çÇÑ ¹ü¿ë ¹öÀüÀ» °³¹ßÇßÁö¸¸ IFFT ¾Ë°í¸®ÁòÀÇ À¯»çÇÑ ÀϹÝÈ­´Â 50³â µ¿¾È ÇØ°áµÇÁö ¾Ê¾Ò½À´Ï´Ù. ÀÌÁ¦ ¾ÆÀÌ¿À¿Í ÁÖ¸³´ë Çб³(IA)ÀÇ µÎ ¿¬±¸¿ø ÀÎ Alexander Stoytchev¿Í Vladimir Sukhoy´Â ¿ª óÇÁ z- º¯È¯ (ICZT)À̶ó´Â ¿À·£ ¾Ë°í¸®ÁòÀ» °í¾ÈÇß´Ù. 1 


±¤ÇÐ °è»êÀÇ ÀåÁ¡

¸ðµç ¾Ë°í¸®Áò°ú ¸¶Âù°¡Áö·Î ICZT´Â ¹®Á¦¸¦ ÇØ°áÇÏ´Â ´Ü°èº° ÇÁ·Î¼¼½ºÀÔ´Ï´Ù. ÀÌ °æ¿ì CZT ¾Ë°í¸®ÁòÀÇ Ãâ·ÂÀ» ´Ù½Ã ÀԷ¿¡ ¸ÊÇÎÇÕ´Ï´Ù. ÀÌ ¾Ë°í¸®ÁòÀº »ó´ëÀÇ °è»ê º¹À⼺ ¶Ç´Â ¼Óµµ¿Í ÀÏÄ¡ÇÏ¸ç ¼öÄ¡ Á¤È®µµ¿¡ ´ëÇØ Å×½ºÆ®µÇ¾úÀ¸¸ç IFFT¿Í ´Þ¸® ±âÇÏ ±Þ¼öÀûÀ¸·Î ºÎÆÐÇϰųª ÁÖÆļö ¼ººÐÀ» Áõ°¡½ÃÅ°´Â µ¥ »ç¿ëÇÒ ¼ö ÀÖ½À´Ï´Ù (±×¸² ÂüÁ¶). ÀÌ ¸¶Áö¸· ÁöÁ¡Àº ¼Ò¸ê ÀüÀÚ±âÆÄ¿¡ ÀÇÁ¸ÇÏ´Â ±Ù°Å¸® ±¤ ÀüÆÄ¿¡ ´ëÇØ °è»êÀ» ¼öÇà ÇÒ ¼ö Àֱ⠶§¹®¿¡ Áß¿äÇÕ´Ï´Ù.

Sukhoy´Â ¿ª ¾Ë°í¸®ÁòÀÌ ¿ø·¡ÀÇ ¼ø¹æÇâ ¾Ë°í¸®Áòº¸´Ù ¾î·Á¿î ¹®Á¦À̹ǷΠ"Á¤È®ÇÏ°í °­·ÂÇÑ ÄÄÇ»Å͸¦ °ø°ÝÇؾßÇß½À´Ï´Ù"¶ó°í ¸»ÇÕ´Ï´Ù. ¶ÇÇÑ ±¸Á¶È­ µÈ Çà·ÄÀÇ ¼öÇÐÀû ÇÁ·¹ÀÓ ¿öÅ© ³»¿¡¼­ ¾Ë°í¸®ÁòÀ» º¸´Â °ÍÀÌ ÇÙ½ÉÀ̾ú½À´Ï´Ù. ICZT ¾Ë°í¸®ÁòÀÇ Á¤È®¼ºÀº ÀÚµ¿ Å×½ºÆ®¸¦ ÅëÇØ °áÁ¤µÇ¾ú½À´Ï´Ù.

»õ·Î °³¹ß ICZT ¾Ë°í¸®ÁòÀÌ ±âÁ¸ CZT ¹× IFFT ¾Ë°í¸®ÁòÀÇ °è»ê º¹À⼺°ú ÀÏÄ¡ º¹À⼺ (N ·Î±× N) O ¼ÒÀ§ÀÖ´Ù - ´Ù¸¥ ¸»·ÎÇÏ¿©,º¸´Ù °è»êÀû ICZT ¾Ë°í¸®ÁòÀ» ÀϹÝÈ­Çϱâ ÀÌÀüÀÇ ½Ãµµ¿Í´Â ´Þ¸®, º¹ÀâÇÏÁö ¾Ê´Ù.

Âü°í 1. V. Sukhoy¿Í A. Stoytchev, Sci. ´ã´çÀÚ (2019); https://doi.org/10.1038/s41598-019-50234-9 .



Ãâó : https://www.laserfocusworld.com/test-measurement/article/14069147/generalized-version-of-the-inverse-fast-fourier-transform-is-computationally-efficient

 

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