¹ï©ó¥ô·Nªº°T¸¹ x[n]¡A§ÚÌ¥i¥H±N¨äªí¥Ü¦¨¬°³æ¦ì¯ß½Ä°T¸¹¡]Unit Impulse Signal¡^ªº²Õ¦X¡A¦p¤U¡G
x[n] = Sk=0¡Ûx[k]d[n-k]
¤Wz¦¡¤l¥i¥H¬Ý¦¨¬O¡uk ¥Nªí®É¶¡¡Ax[k] ©T©w¤£°Ê¡Ad[n-k] ÀH¤£¦Pªº n ¦Ó²¾°Ê¡v¡C
¦P²z¡A¤W¦¡¤]¥i¥H¼g¦¨¡G
x[n] = Sk=0¡Ûx[n-k]d[k]
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¦]¦¹¹ï©ó¤@Ó LTI ¨t²Î L{¡E}¡A·í¨ä¿é¤J¬° x[n] ®É¡A¨ä¿é¥X¬° y[n]¡A¥i¥Î¤U¦CÃö«Y¦¡¨Ó´yz¡G
y[n] | = | L{x[n]}
|
| = | L{Sk=0¡Ûx[k]d[n-k]}
|
| = | Sk=0¡Ûx[k]L{d[n-k]}
|
| = | Sk=0¡Ûx[k]h[n-k]
|
¨ä¤¤ h(n-k)=L{d(n-k)} ¬O¨t²Î¹ï©ó¦ì©ó n=k ªº³æ¦ì¯ß½Ä°T¸¹©Ò²£¥ÍªºÅTÀ³¡]Response¡^¡C´«¥y¸Ü»¡¡A¤@Ó LTI ¨t²Îªº¿é¥X¡A§¹¥þ¥i¥H¥Ñ¿é¤J°T¸¹ x[n] ©M¨t²Îªº¯ß½ÄÅTÀ³¡]Impulse Response¡^ h[n] ¨Ó¨M©w¡C´«¥y¸Ü»¡¡A¤@Ó LTI ¨t²Îªº¯ß½ÄÅTÀ³´N¨M©w¤F³oÓ¨t²Îªº¥þ³¡¯S©Ê¡I
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¦pªG±Ä¥Î¥»¸`ªº²Ä¤GÓ¤èµ{¦¡¡A«h y[n] ¥i¥Hªí¥Ü¦¨
y[n] | = | L{x[n]}
|
| = | L{Sk=0¡Ûx[n-k]d[k]}
|
| = | Sk=0¡Ûx[n-k]L{d[k]}
|
| = | Sk=0¡Ûx[n-k]h[k]}
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¥Ñ©ó¤Wzªº¹Bºâ±`³Q¥Î¨ì¡A¦]¦¹§Ú̱N¤§©w¸q¦¨¡u±Û¿n¡v¡]Convolution¡^¡G
y[n] = x[n]*h[n] = Sk=0¡Ûx[k]h[n-k]} = Sk=0¡Ûx[n-k]h[k]}
±Û¿n¹Bºâ¨ã¦³¤U¦C¯S©Ê¡G
- ¥æ´««ß¡G
- µ²¦X«ß¡G
(x[n]*y[n])*z[n] = x[n]*(y[n]*z[n])
- ¤À°t«ß¡G
x[n]*(y[n]+z[n]) = x[n]*y[n]+x[n]*z[n]
- ©µ¿ð©Ê½è¡G
y[n]=x[n]*h[n] ¡÷ y[n-n1-n2]=x[n-n1]*h[n-n2]
Audio Signal Processing and Recognition (µ°T³B²z»P¿ëÃÑ)