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«ü¥O residue ¥i¥Î©ó­pºâ¤@¤À¦¡ªº³¡¥÷¤À¦¡®i¶}¡C­Y $A(s)$ ©M $B(s)$ ¬°¦h¶µ¦¡¡A¥B $B(s)$ µL­«®Ú¡A«h¤À¦¡ $\frac{B(s)}{A(s)}$ ¥i¥Hªí¥Ü¬°

$$ \frac{B(s)}{A(s)} = \frac{r_1}{s-p_1}+\frac{r_2}{s-p_2}+\cdots+\frac{r_n}{s-p_n}+C(s) $$

¨ä¤¤ $p_1, p_2, ..., p_n$ ¬° $A(s)$ ªº®Ú¡]©Î¬O $\frac{B(s)}{A(s)}$ ªº·¥ÂI¡^¡A$r_1, r_2, ..., r_n$ ¬°±`¼Æ¡A$C(s)$ ¬°¤@¦h¶µ¦¡¡C¨Ò¦p¡G±ý¨D $\frac{3s+8}{s^2+5s+6}$ ªº³¡¥÷¤À¦¡®i¶}¡A¥i¿é¤J¦p¤U¡G

Example 1: 07-¦h¶µ¦¡ªº³B²z»P¤ÀªR/residue01.mb = [3 8]; a = [1 5 6]; [r, p, k] = residue(b, a)r = 1.0000 2.0000 p = -3.0000 -2.0000 k = []

¥Ñ¥H¤Wµ²ªG±oª¾¡G $$\frac{3s+8}{s^2+5s+6} = \frac{1}{s+3} + \frac{2}{s+2}$$

³¡¥÷¤À¦¡®i¶}¯S§O¾A¥Î©ó½u©Ê¨t²Î¤§Âà´«¨ç¼Æ¡]Transfer Function¡^ªº¤ÀªR¡C¥H¤W¨Ò¦Ó¨¥¡A­Y $\frac{3s+8}{s^2+5s+6}$ ¬°¤@¨t²Î¤§Âà´«¨ç¼Æ¡A¸g¥Ñ¤W­z³¡¥÷¤À¦¡®i¶}«á¡A¥iª¾¨ä¯ß½ÄÅTÀ³¡]Impulse Response¡^¬°$e^{-3t}+2e^{-2t}$¡C

residue «ü¥O¥ç¥i±N³¡¥÷¤À¦¡Âà¦^­ì¨Óªº§Î¦¡¡A¦p¤U¡G

Example 2: 07-¦h¶µ¦¡ªº³B²z»P¤ÀªR/residue02.mr = [1 2]; p = [-3 -2]; k = []; [b2, a2] = residue(r, p, k)b2 = 3 8 a2 = 1 5 6

¤W­z½d¨Ò¥Nªí§Ú­Ì¥i¥H¥Ñ±N³¡¥÷¤À¦¡µ²¦X¦¨³æ¤@¤À¦¡¡G

$$\frac{1}{s+3} + \frac{2}{s+2} = \frac{3s+8}{s^2+5s+6}$$
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