libfftw ¿¡¼­ fft ¿¬»ê °á°úÀÇ ±æÀÌ ¹®ÀÇ

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쪽팔리면 질문하지 맙시다. 소중한 답변 댓글을 삭제하는건 부끄러운 일 입니다 


libfftw를 이용하여 주파수 분석을 하려는데


fftw_plan_dft_r2c_1d() 함수에

N개의 입력을 넣었다면

N/2 + 1 개의 출력이 나옵니다.


DFT에 의해서 N/2가 되는건 알겠는데 1은 어떤 정보가 나오는지 모르겠습니다.


혹시 +1의 신호가 어떤 것인지 참고할 만한 문서가 있을까요?



+

이미지 추가


딸 넷 아들 하나 아빠 (큰 딸, 작은 딸, 왕큰 딸, 암 뭉뭉이, 수 뭉뭉이) - minimonk.net
ªÀº±Û Àϼö·Ï ½ÅÁßÇÏ°Ô.
¹«¾Æ 2023-04
¾î.. DFT ¶ó¸é ÀÔ·Â ¸¸Å­ Ãâ·ÂÀÌ ³ª¿ÃÅÙµ¥¿ä?
     
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¶óÀ̺귯¸®¸¶´Ù ´Ù¸¥°ÇÁö fftw´Â N/2+1·Î ³ª¿Â´Ù°í Çϳ׿ä


Here, n is the ¡°logical¡± size of the DFT, not necessarily the physical size of the array. In particular, the real (double) array has n elements, while the complex (fftw_complex) array has n/2+1 elements (where the division is rounded down). For an in-place transform, in and out are aliased to the same array, which must be big enough to hold both; so, the real array would actually have 2*(n/2+1) elements, where the elements beyond the first n are unused padding. (Note that this is very different from the concept of ¡°zero-padding¡± a transform to a larger length, which changes the logical size of the DFT by actually adding new input data.) The kth element of the complex array is exactly the same as the kth element of the corresponding complex DFT. All positive n are supported; products of small factors are most efficient, but an O(n log n) algorithm is used even for prime sizes.

https://www.fftw.org/fftw3_doc/One_002dDimensional-DFTs-of-Real-Data.html#One_002dDimensional-DFTs-of-Real-Data

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piloteer 2023-04
½Ç¼ö¸¦ fftÇϸé N/2+1°³¸¸ À¯È¿ÇÑ Á¤º¸ÀÌ°í, º¹¼Ò¼ö¸¦ fftÇϸé N°³ ÀüºÎ ´Ù À¯È¿ÇÑ Á¤º¸ÀÔ´Ï´Ù. fftw´Â ½Ç¼ö¶ó¸é ¾Ë¾Æ¼­ N/2+1°³¸¸ °è»êÇϳª º¾´Ï´Ù. ±×·¸°Ô ÇÏ´Â ÆíÀÌ ¿¬»ê È¿À²ÀÌ ´õ ÁÁ±ä ÇÒ °Ì´Ï´Ù.
               
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fft ÀԷ°ªÀº 800,000 / 16777216(24bit) ·Î ³ª´©¾î¼­ 0~1 »çÀÌÀÇ ½Ç¼ö·Î º¯È¯ÇÏ¿´½À´Ï´Ù.
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piloteer 2023-04
ÀÏ´Ü ¹«¾Æ´Ô ¸»¾¸¿¡ µ¿ÀÇÇÏ°í¿ä, µ¡ºÙÀÌÀÚ¸é fft¸¦ ÇÏ½Ç °æ¿ì Parseval's theoremÀ̶õ °É ¾²¸é ´ëÃæ ¾î´ÀÁ¤µµ°¡ Á¤»óÀûÀÎ °ªÀÇ ¹üÀ§ÀÎÁö¸¦ ¾Ë ¼ö ÀÖ½À´Ï´Ù.
http://www.ktword.co.kr/test/view/view.php?no=3725
                         
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ÁÁÀº ³»¿ë °¨»çÇÕ´Ï´Ù.
õõÈ÷ Àоî´Â º¸°ÚÁö¸¸.. Àü±â/ÀüÀÚ Àü°øÀÌ ¾Æ´Ï¶ó ÀÌÇØÇϱ⠽±Áö°¡ ¾Ê³×¿ä ¤Ð¤Ð
     
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ÇÔ¼ö¸¦ À߸ø½è³ª r2c·Î ÇÏ°í Àִµ¥ c2c³ª r2r·Î ÇؾßÇϳª °í¹ÎÁßÀ̱ä ÇÕ´Ï´Ù.
i0 is 0 because you're using real data , so it isn't stored in out.

stackoverlfow º¸¸é À§¿Í °°ÀÌ ½áÀִµ¥ ±×³É 1~N/2+1 ±îÁö ¾²¸é µÉ °Í °°³×¿ä
°¨»çÇÕ´Ï´Ù.
¹«¾Æ 2023-04
For a real-to-complex transform you get N / 2 + 1 complex outputs for N real inputs (the redundant symmetric outputs are not generated).

The 0 Hz component is in bin 0.

This is all covered in the FFTW manual.

¶ó´Â ¸»ÀÌ ÀÖ´Â °Å º¸´Ï +1 Àº DC ¼ººÐ À̳׿ä. Á¤È®È÷´Â 0 ¹ø° À妽º°ÚÁÒ.

"complex outputs for N real inputs" Ãâ·ÂÀÌ º¹¼Ò¼ö¶ó¼­.
     
±¸Â÷´Ï 2023-04
¼ÖÂïÈ÷ º¹¼Ò¼ö Ãâ·Â°ú 0¹ø° °ªÀÌ ¹«½¼ ¿¬°üÀÌ ÀÖ´ÂÁö ¸ð¸£°Ú½À´Ï´Ù.

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´Ù¸¸.. stackoverflow³ª À̰ųª.. ¹ø¿ªÇØÁ൵ ÀÌÇظ¦ ¸øÇÏ°Ú´Ù´Â°Ô ÇÔÁ¤À̳׿ä.

FFTW ¶óÀ̺귯¸®¿¡¼­ Fast Fourier Transform (FFT)¸¦ Àû¿ëÇϸé, ±æÀÌ°¡ NÀÎ ½Ç¼ö ÀÔ·Â µ¥ÀÌÅÍ¿¡ ´ëÇØ º¹¼Ò¼ö Ãâ·Â µ¥ÀÌÅÍ N/2+1°³°¡ »ý¼ºµË´Ï´Ù. ÀÌ´Â FFT ¾Ë°í¸®ÁòÀÌ µ¿ÀÛÇÏ´Â ¹æ½Ä ¶§¹®ÀÔ´Ï´Ù.

FFTW¿¡¼­ »ç¿ëµÇ´Â FFT ¾Ë°í¸®ÁòÀº "real-to-complex" FFT¶ó°í ºÒ¸®¸ç, ½Ç¼ö°ª ÀÔ·Â µ¥ÀÌÅ͸¦ º¹¼Ò¼ö°ª Ãâ·Â µ¥ÀÌÅÍ·Î º¯È¯ÇÕ´Ï´Ù. ÀÌ ¾Ë°í¸®ÁòÀº ½Ç¼ö°ª ½ÅÈ£ÀÇ Çª¸®¿¡ º¯È¯ÀÇ ´ëĪ¼º(symmetric) Ư¼ºÀ» È°¿ëÇÕ´Ï´Ù. ±¸Ã¼ÀûÀ¸·Î, ½Ç¼ö°ª ½ÅÈ£ x(t)ÀÇ Çª¸®¿¡ º¯È¯ X(f)Àº X(-f) = conj(X(f)) ¶ó´Â º¹¼Ò¼ö °ø¾×´ëĪ¼º(complex-conjugate symmetric)À» ¸¸Á·ÇÕ´Ï´Ù. ¿©±â¼­ "conj"´Â º¹¼Ò¼ö °ø¾×(conjugate)¸¦ ÀǹÌÇÕ´Ï´Ù.

ÀÌ ´ëĪ¼º Ư¼º ¶§¹®¿¡ FFT ¾Ë°í¸®ÁòÀÇ Ãâ·Â°ª Áß Àý¹ÝÀº Áߺ¹µÇ´Â °ªÀ̸ç, ³ª¸ÓÁö Àý¹ÝÀº ÀÌ Áߺ¹µÈ °ªµé·ÎºÎÅÍ °è»êµÉ ¼ö ÀÖ½À´Ï´Ù. ±¸Ã¼ÀûÀ¸·Î, 0ºÎÅÍ N/2±îÁöÀÇ ÁÖÆļö ´ë¿ª¿¡¼­´Â °íÀ¯ÇÑ Ãâ·Â°ªÀÌ Á¸ÀçÇϸç, N/2+1ºÎÅÍ N-1±îÁöÀÇ ÁÖÆļö ´ë¿ª¿¡¼­´Â ´ëÀÀÇÏ´Â 1ºÎÅÍ N/2-1±îÁöÀÇ ÁÖÆļö ´ë¿ªÀÇ º¹¼Ò¼ö °ø¾×°ªÀ» °è»êÇÏ¿© ±¸ÇÒ ¼ö ÀÖ½À´Ï´Ù.

µû¶ó¼­ FFTW´Â ¿¬»ê ½Ã°£°ú ¸Þ¸ð¸®¸¦ Àý¾àÇϱâ À§ÇØ, 0ºÎÅÍ N/2±îÁöÀÇ ÁÖÆļö ´ë¿ª¿¡ ´ëÇÑ °íÀ¯ÇÑ Ãâ·Â°ª°ú, NÀÌ Â¦¼öÀÎ °æ¿ì ÁÖÆļö N/2¿¡ ´ëÇÑ Ãâ·Â°ªÀ» °è»êÇÕ´Ï´Ù. ÀÌ·¸°Ô °è»êµÈ Ãâ·Â°ªÀÇ ÃÑ °³¼ö´Â N/2+1°³°¡ µË´Ï´Ù.

0Hz ¶ó°í Çϸé AC°¡ ¾Æ´Ñ DC ¼ººÐÀ¸·Î Àüü ½ÅÈ£°¡ ¸¸¾à +2000 ¸¸Å­ ¶°ÀÖ´Ù¸é 2000ÀÌ ±â·ÏµÇ´Â°É±î¿ä?
          
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piloteer ´ñ±Û ´ë·Î ÀÌÇØÇÏ½Ã¸é µË´Ï´Ù.

>>0Hz ¶ó°í Çϸé AC°¡ ¾Æ´Ñ DC ¼ººÐÀ¸·Î Àüü ½ÅÈ£°¡ ¸¸¾à +2000 ¸¸Å­ ¶°ÀÖ´Ù¸é 2000ÀÌ ±â·ÏµÇ´Â°É±î¿ä?
³×.
               
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N°³°¡ µé¾î¿ÔÀ¸´Ï N/2 ÁÖÆļö ±îÁöÀÌ°í
0 + N/2 ÁÖÆļö ´Ï±î ÃÑ N/2+1 °³À̸ç
0Hz¿¡´Â ½ÅÈ£ÀÇ DC ¼ººÐ(0Hz) ³»¿ëÀÌ ÀÖ´Ù°í ÀÌÇØÇϵµ·Ï ÇÏ°Ú½À´Ï´Ù.

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¾Æ´¢. rms ´Â Root Mean Squar °ªÀ» ¸»ÇÏ´Â °ÍÀÌ°í ÀÌ´Â AC ¼ººÐÀÇ ½ÅÈ£ Å©±â¸¦ Ç¥½ÃÇÕ´Ï´Ù. ¿ì¸®°¡ AC 220V ¶ó°í Ç¥ÇöÇÏ´Â °ªÀº 60Hz ÀÇ Á¤ÇöÆÄ¿¡ ´ëÇÏ¿© rms °ªÀ¸·Î 220V °¡ ³ª¿Â´Ù (peak °ªÀÌ ¾Æ´Ï¶ó).. ¹¹ ±×·± ÀǹÌÀÔ´Ï´Ù. 0HzÀÎ DC ¶ûÀº ´Þ¶ó¿ä.
               
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