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zaq123321

ר¼Ò¹ËÎÊ (ÖøÃûдÊÖ)

[ÇóÖú] Çë½ÌHilbert ±ä»»¼òµ¥ÎÊÌâÒ»¸ö ÒÑÓÐ2È˲ÎÓë

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f(x) = |x|^r.  (x is real, 0<r<1).
ÎÒÖªµÀ´ð°¸£¬¾ÍÊÇŪ²»³öÁË£¬Ò²¾ÍÊÇÍüÁËCauchy principal value integral.  
Hilbert ±ä»¯¼ûͼƬ
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feixiaolin

ÈÙÓþ°æÖ÷ (ÎÄ̳¾«Ó¢)

ÓÅÐã°æÖ÷

|x|^r=x^r*sgn(x)
H[|x|^r]=x^r*sgn(x)¾í»ý1/(pi*t)
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2Â¥2014-08-08 12:57:54
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zaq123321

ר¼Ò¹ËÎÊ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
2Â¥: Originally posted by feixiaolin at 2014-08-08 12:57:54
|x|^r=x^r*sgn(x)
H=x^r*sgn(x)¾í»ý1/(pi*t)
ÔÚÆµÓò´¦Àí£¬±ä»ØÀ´¡£

Can you expand
ÔÚÆµÓò´¦Àí£¬±ä»ØÀ´
a little bit more?

Thanks a lot. We are on the right track.
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3Â¥2014-08-09 00:59:38
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Edstrayer

°æÖ÷ (ÖøÃûдÊÖ)

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http://wenku.baidu.com/link?url= ... iBflJKO4E3li-JtFJzC
ÕâÆªÂÛÎÄ̸µ½ÁËHilbert±ä»»¼°Æä»ù±¾ÐÔÖÊ£¬¿ÉÒԲο¼Âð£¿

» ±¾ÌûÒÑ»ñµÃµÄºì»¨£¨×îÐÂ10¶ä£©

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4Â¥2014-08-09 08:19:57
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ztt405

гæ (СÓÐÃûÆø)

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ÖÜÃñÇ¿µÄ"µ÷ºÍ·ÖÎö½²Òå"µÚ112Ò³Óн²L^2ÉϵÄHilbert±ä»», Äã¿ÉÒԲο¼.
5Â¥2014-08-09 08:53:21
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feixiaolin

ÈÙÓþ°æÖ÷ (ÎÄ̳¾«Ó¢)

ÓÅÐã°æÖ÷

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¡ï ¡ï ¡ï
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zaq123321: ½ð±Ò+3, ¡ïÓаïÖú, Äܲ»ÄÜzaiÌÖÂÛһϠ2014-08-12 09:28:35
H[|x|^r]=H¡¾x^r*sgn(x)¾í»ý1/(pi*t)¡¿

=¡¾2*pi*j^r*delt^n(w)¾í»ý2/(j*w)¡¿*¡¾-j*sgn(w)¡¿

» ±¾ÌûÒÑ»ñµÃµÄºì»¨£¨×îÐÂ10¶ä£©

6Â¥2014-08-09 10:00:02
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

zaq123321

ר¼Ò¹ËÎÊ (ÖøÃûдÊÖ)

Ëͺ컨һ¶ä
ÒýÓûØÌû:
4Â¥: Originally posted by Edstrayer at 2014-08-09 08:19:57
http://wenku.baidu.com/link?url=W_YL2Z3YLtWiLXBuTGGzd1UDUDM9Z9sZnhA2iCHQSStyOLGGq4BwkbH33TxTIqMkUNuVLRaP7vRJ_8jswI5RTWnZiBflJKO4E3li-JtFJzC
ÕâÆªÂÛÎÄ̸µ½ÁËHilbert±ä»»¼°Æä»ù±¾ÐÔÖÊ£¬¿ÉÒԲο¼Âð£¿...

Hi Edstrayer;
   I looked at the paper. It's interesting. Thanks,
Сľ³æ¸øÎÒÎÂů£¬¸øÎÒÏ£Íû£¬°®¾ÍÒª°®Ð¡Ä¾³æ¡£
7Â¥2014-08-09 21:57:27
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

zaq123321

ר¼Ò¹ËÎÊ (ÖøÃûдÊÖ)

Ëͺ컨һ¶ä
ÒýÓûØÌû:
6Â¥: Originally posted by feixiaolin at 2014-08-09 10:00:02
H=H¡¾x^r*sgn(x)¾í»ý1/(pi*t)¡¿

=¡¾2*pi*j^r*delt^n(w)¾í»ý2/(j*w)¡¿*¡¾-j*sgn(w)¡¿

It seems still complicated and includes convolution and not easy to use.
The answer should be
tan(pi*r/2)sgn(x)|x|^r.
Сľ³æ¸øÎÒÎÂů£¬¸øÎÒÏ£Íû£¬°®¾ÍÒª°®Ð¡Ä¾³æ¡£
8Â¥2014-08-09 22:15:16
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zaq123321

ר¼Ò¹ËÎÊ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
5Â¥: Originally posted by ztt405 at 2014-08-09 08:53:21
ÖÜÃñÇ¿µÄ"µ÷ºÍ·ÖÎö½²Òå"µÚ112Ò³Óн²L^2ÉϵÄHilbert±ä»», Äã¿ÉÒԲο¼.

Thanks a lot.
Сľ³æ¸øÎÒÎÂů£¬¸øÎÒÏ£Íû£¬°®¾ÍÒª°®Ð¡Ä¾³æ¡£
9Â¥2014-08-09 23:00:01
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