9-1 Discrete-Time Signals (?¢æ•£?‚é?訊è?)

´X¥G¦b©Ò¦³¦ÛµM¬Éªº°T¸¹³£¬O³sÄòªº¡A¦ý¬O¦b¹q¸£¥@¬Éªº°T¸¹¡A¥Ñ©ó³£¬O¥H¦ì¤¸¬°³æ¦ì¨ÓÀx¦s¡A©Ò¥H³o¨Ç°T¸¹³£¬OÂ÷´²ªº¡A²ºÙ¡uÂ÷´²®É¶¡°T¸¹¡v¡]Discrete Time Signal¡^¡A§Ú­Ì³q±`¥i¥H±N³o¤@¦Cªº°T¸¹ªí¥Ü¦¨ x(nT)¡AT ¬O¨ú¼Ë¶g´Á¡An ¬O¾ã¼Æ¡AnT «h¥Nªí®É¶¡¡C¬°¤F²¤Æ°_¨£¡A§Ú­Ì¤]¥i¥H¨Ï¥Î x[n] ¥NªíÂ÷´²®É¶¡°T¸¹¦b nT ªº­È¡C¥H¤U±N¤¶²Ð´X­Ó±`¨£ªºÂ÷´²®É¶¡°T¸¹¡C

³æ¦ì¯ß½Ä°T¸¹¡]Unit Impulse Signal¡^¥u¦³¦b n = 0 ªº®É­Ô¦³¤@­Ó­È¬° 1¡A¨ä¥L³£¬O¹s¡C¥i¥Î¼Æ¾Ç¦¡ªí¥Ü¦p¤U¡G

d[n] = 1, if n=0

d[n] = 0, otherwise

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Example 1: impulse01.m

% Plot an unit impulse signal n = -5:5; x = 0*n; index=find(n==0); x(index)=1; % plot stem(n, x); axis([-inf, inf, -0.2, 1.2]); xlabel('n'); ylabel('x'); title('Unit Impulse Signal \delta[n]');

¦pªG³æ¦ì¯ß½Ä°T¸¹¦b®É¶¡¤W©µ¿ð¤F k ­Ó¨ú¼ËÂI¡A´N¥i¥H±o¨ì¤U¦C¼Æ¾Ç¦¡¡G

d[n-k] = 1, if n=k

d[n-k] = 0, otherwise

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Example 2: impulse02.m

% Plot an unit impulse signal n = -5:5; x = 0*n; index=find(n==0); x(index)=1; % plot stem(n, x); axis([-inf, inf, -0.2, 1.2]); xlabel('n'); ylabel('x'); title('Delayed Unit Impulse Signal \delta[n-k]'); set(gca, 'xticklabel', {'k-5', 'k-4', 'k-3', 'k-2', 'k-1', 'k', 'k+1', 'k+2', 'k+3', 'k+4', 'k+5'});

³æ¦ì¯ß½Ä°T¸¹¨ã¦³¡u¿z¿ï¡vªº¯S©Ê¡A¥ô¦ó°T¸¹ x[n]¡]n = -¡Û¡ã¡Û¡^»P d[n-k] ¬Û­¼¡A´N¥u³Ñ¤U²Ä k ¶µ¡A¥i¥Î¼Æ¾Ç¦¡´y­z¦p¤U¡G

x[k] = Sn=-¡Û¡Ûd[n-k]¡Ex[n]

§Q¥Î³o­Ó¯S©Ê¡A§Ú­Ì¥i¥H±N¥ô¦ó¤@­ÓÂ÷´²®É¶¡°T¸¹ªí¥Ü¦¨³æ¦ì¯ß½Ä°T¸¹ªº²Õ¦X¡A¦b­pºâ±Û¿n¡]Convolution¡^®É¡A«D±`«K§Q¡C

³æ¦ì¨B¶i°T¸¹¡]Unit Step Signal¡^¥u¦³¦b n >= 0 ®É¨ä­È¬° 1¡A¨ä¥L³£¬O¹s¡C¥i¥Î¼Æ¾Ç¦¡ªí¥Ü¦p¤U¡G

u[n] = 1, if n>=0

u[n] = 0, otherwise

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Example 3: unitStep01.m

% Plot an unit impulse signal n = -5:5; x = 0*n; index=find(n>=0); x(index)=1; % plot stem(n, x); axis([-inf, inf, -0.2, 1.2]); xlabel('n'); ylabel('x'); title('Unit Step Signal u[n]');

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Example 4: sinusoid01.m

% Plot a sinusoidal signal n = 0:40; omega=0.3; x = sin(omega*n); % plot stem(n, x); axis([-inf, inf, -1.2, 1.2]); xlabel('n'); ylabel('x'); title('sin[\omega n]');

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