鎮ㄥソ锛屾杩庝締鍒扮董搴浕瀛愬競鍫寸恫(w菐ng)
鐧婚寗 | 鍏嶈不(f猫i)娉ㄥ唺
銆�銆�鎵�璎傚偝閬炲嚱鏁�(sh霉)鍗崇窔鎬у畾甯哥郴绲�(t菕ng)鍦ㄩ浂鍒濆姊濅欢涓�锛岃几鍑洪噺鐨勬媺姘忚畩鎻涘紡鑸囪几鍏ラ噺鐨勬媺姘忚畩鎻涘紡涔嬫瘮銆傚偝閬炲嚱鏁�(sh霉)閫氬父鐢ㄤ簬鍠几鍏�銆佸柈杓稿嚭鐨�妯℃摤闆昏矾锛屼富瑕佺敤鍦ㄤ俊铏熻檿鐞�銆侀�氫俊鐞嗚珫銆佹帶鍒剁悊璜�銆傞�欏�嬭(sh霉)瑾炵稉(j墨ng)甯稿皥闁�鐢ㄤ簬濡傛湰鏂囨墍杩扮殑绶氭�ф檪涓嶈畩绯荤当(t菕ng)(LTI)銆傚(sh铆)闅涚郴绲�(t菕ng)鍩烘湰閮芥湁闈炵窔鎬х殑杓稿叆杓稿嚭鐗规��锛屼絾鏄ū澶氱郴绲�(t菕ng)鍦ㄦ(bi膩o)绋卞弮鏁�(sh霉)鑼冨湇鍏�(n猫i)鐨勯亱(y霉n)琛岀媭鎱�(t脿i)闈炲父鎺ヨ繎浜庣窔鎬�锛屾墍浠ュ(sh铆)闅涙噳(y墨ng)鐢ㄤ腑瀹屽叏鍙互鎳�(y墨ng)鐢ㄧ窔鎬ф檪涓嶈畩绯荤当(t菕ng)鐞嗚珫琛ㄧず鍏惰几鍏ヨ几鍑鸿鐐�锛屾湁鐨勬浉涓篃鎶婂叾璀偤锛氣�滆綁(zhu菐n)绉诲嚱鏁�(sh霉)鈥濄��
銆�銆�鍌抽仦鍑芥暩(sh霉)姒傚康鐨勯仼鐢ㄨ寖鍦嶉檺浜庣窔鎬у父寰垎鏂圭▼绯荤当(t菕ng).鐣�(d膩ng)鐒�,鍦ㄩ�欓绯荤当(t菕ng)鐨勫垎鏋愬拰瑷�(sh猫)瑷堜腑,鍌抽仦鍑芥暩(sh霉)鏂规硶鐨勬噳(y墨ng)鐢ㄦ槸寰堝唬娉涚殑.涓嬮潰鏄湁闂�(gu膩n)鍌抽仦鍑芥暩(sh霉)鐨勪竴浜涢噸瑕佽鏄�(涓嬪垪鍚勯爡(xi脿ng)瑾槑涓秹鍙婄殑鍧囩偤绶氭�у父寰垎鏂圭▼鎻忚堪鐨勭郴绲�(t菕ng)).
1. 绯荤当(t菕ng)鐨勫偝閬炲嚱鏁�(sh霉)鏄竴绋暩(sh霉)瀛�(xu茅)妯″瀷,瀹冭〃绀鸿伅(li谩n)绯昏几鍑鸿畩閲忚垏杓稿叆璁婇噺鐨勫井鍒嗘柟绋嬬殑涓�绋亱(y霉n)绠楁柟娉�.
2. 鍌抽仦鍑芥暩(sh霉)鏄郴绲�(t菕ng)鏈韩鐨勪竴绋爆鎬�,瀹冭垏杓稿叆閲忔垨椹�(q奴)鍕曞嚱鏁�(sh霉)鐨勫ぇ灏忓拰鎬ц唱(zh矛)鐒￠棞(gu膩n).
3. 鍌抽仦鍑芥暩(sh霉)鍖呭惈鑱�(li谩n)绯昏几鍏ラ噺鑸囪几鍑洪噺鎵�蹇呴渶鐨勫柈浣�,浣嗘槸瀹冧笉鎻愪緵鏈夐棞(gu膩n)绯荤当(t菕ng)鐗╃悊绲�(ji茅)妲�(g貌u)鐨勪换浣曚俊鎭�(瑷卞鐗╃悊涓婂畬鍏ㄤ笉鍚岀殑绯荤当(t菕ng),鍙互鍏锋湁鐩稿悓鐨勫偝閬炲嚱鏁�(sh霉),绋变箣鐐虹浉浼肩郴绲�(t菕ng)).
4. 濡傛灉绯荤当(t菕ng)鐨勫偝閬炲嚱鏁�(sh霉)宸茬煡,鍓囧彲浠ラ嚌灏嶅悇绋笉鍚屽舰寮忕殑杓稿叆閲忕爺绌剁郴绲�(t菕ng)鐨勮几鍑烘垨闊挎噳(y墨ng),浠ヤ究鎺屾彙绯荤当(t菕ng)鐨勬�ц唱(zh矛).
5. 濡傛灉涓嶇煡閬撶郴绲�(t菕ng)鐨勫偝閬炲嚱鏁�(sh霉),鍓囧彲閫氶亷寮曞叆宸茬煡杓稿叆閲忓苟鐮旂┒绯荤当(t菕ng)杓稿嚭閲忕殑瀵�(sh铆)椹�(y脿n)鏂规硶,纰哄畾绯荤当(t菕ng)鐨勫偝閬炲嚱鏁�(sh霉).绯荤当(t菕ng)鐨勫偝閬炲嚱鏁�(sh霉)涓�鏃﹁纰哄畾,灏辫兘灏嶇郴绲�(t菕ng)鐨勫嫊鎱�(t脿i)鐗规�ч��(j矛n)琛屽厖鍒嗘弿杩�,瀹冧笉鍚屼簬灏嶇郴绲�(t菕ng)鐨勭墿鐞嗘弿杩�.
6. 鐢ㄥ偝閬炲嚱鏁�(sh霉)琛ㄧず鐨勫父鐢ㄩ�ｇ簩(x霉)绯荤当(t菕ng)鏈夊叐绋瘮杓冨父鐢ㄧ殑鏁�(sh霉)瀛�(xu茅)妯″瀷,瑾槑濡備笅
绋〃绀烘柟寮忕偤:
绗簩绋〃绀烘柟寮忎篃鍙浂妤甸粸(di菐n)澧炵泭妯″瀷,鍏烽珨褰㈠紡鐐�:
銆�銆�1銆佸偝閬炲嚱鏁�(sh霉)鏄竴绋暩(sh霉)瀛�(xu茅)妯″瀷,鑸囩郴绲�(t菕ng)鐨勫井鍒嗘柟绋嬬浉灏嶆噳(y墨ng)銆�
銆�銆�2銆佹槸绯荤当(t菕ng)鏈韩鐨勪竴绋爆鎬�,鑸囪几鍏ラ噺鐨勫ぇ灏忓拰鎬ц唱(zh矛)鐒￠棞(gu膩n)銆�
銆�銆�3銆佸彧閬╃敤浜庣窔鎬у畾甯哥郴绲�(t菕ng)銆�
銆�銆�4銆佸偝閬炲嚱鏁�(sh霉)鏄柈璁婇噺绯荤当(t菕ng)鎻忚堪,澶栭儴鎻忚堪銆�
銆�銆�5銆佸偝閬炲嚱鏁�(sh霉)鏄湪闆跺垵濮嬫浠朵笅瀹氱京鐨�,涓嶈兘鍙嶆槧鍦ㄩ潪闆跺垵濮嬫浠朵笅绯荤当(t菕ng)鐨勯亱(y霉n)鍕曟儏娉併��
銆�銆�6銆佷竴鑸偤寰�(f霉)璁婇噺 S 鐨勬湁鐞嗗垎寮�,鍗� n 鈮� m銆備笖鎵�鏈夌殑绯绘暩(sh霉)鍧囩偤瀵�(sh铆)鏁�(sh霉)銆�
銆�銆�7銆佸鏋滃偝閬炲嚱鏁�(sh霉)宸茬煡,鍓囧彲閲濆皪鍚勭ó涓嶅悓褰㈠紡鐨勮几鍏ラ噺鐮旂┒绯荤当(t菕ng)鐨勮几鍑烘垨闊挎噳(y墨ng)銆�
銆�銆�8銆佸鏋滃偝閬炲嚱鏁�(sh霉)鏈煡,鍓囧彲閫氶亷寮曞叆宸茬煡杓稿叆閲忓苟鐮旂┒绯荤当(t菕ng)杓稿嚭閲忕殑瀵�(sh铆)椹�(y脿n)鏂规硶,纰哄畾绯荤当(t菕ng)鐨勫偝閬炲嚱鏁�(sh霉)銆�
銆�銆�9銆佸偝閬炲嚱鏁�(sh霉)鑸囪剤娌栭熆鎳�(y墨ng)鍑芥暩(sh霉)涓�涓�灏嶆噳(y墨ng),鑴堟矕闊挎噳(y墨ng)鍑芥暩(sh霉)鏄寚绯荤当(t菕ng)鍦ㄥ柈浣嶈剤娌栬几鍏ラ噺浣滅敤涓嬬殑杓稿嚭銆�
銆�銆�1锛庨牷鐜囨涓�鍖�
銆�銆�鍦ㄨō(sh猫)瑷堟烤娉㈠櫒鐨勫偝閬炲嚱鏁�(sh霉)鍜岀爺绌舵烤娉㈠櫒鐨勫箙闋荤壒鎬ц繎浼煎晱椤屾檪锛岀偤浜嗙啊鍖栬▓绠�锛屼娇瑷堢畻瑕�(gu墨)鏍煎寲鍜岄�氱敤鍖栵紝閫氬父閲囩敤闋荤巼姝镐竴鍖栫殑铏曠悊鏂规硶銆傛墍璎傞牷鐜囨涓�鍖�锛屾槸灏囧偝閬炲嚱鏁�(sh霉)寰�(f霉)闋荤巼s锛澪卞崄j蠅闄や互鍩烘簴(zh菙n)瑙掗牷鐜囅壩�锛屽緱鍒版涓�鍖栧京(f霉)闋荤巼
銆�銆�灏嶄簬浣庨��銆侀珮閫氭烤娉㈠櫒锛屼竴鑸噰鐢ㄦ埅姝㈣闋荤巼锛�1锛�锛屼綔鐐哄熀婧�(zh菙n)瑙掗牷鐜�锛涘皪浜庡付閫�銆佸付闃绘烤娉㈠櫒锛屼竴鑸噰鐢ㄤ腑蹇冭闋荤巼00浣滅偤鍩烘簴(zh菙n)瑙掗牷鐜�銆傚湪鐢ㄦ尝鐗瑰湒鎻忚堪婵炬尝鍣ㄧ殑骞呴牷鐗规�ф檪锛岄�氬父姗潗妯�(bi膩o)鐢ㄦ涓�鍖栭牷鐜囄╀唬鏇肯�銆�
銆�銆�2锛庡偝閬炲嚱鏁�(sh霉)鐨勫箙搴﹁繎浼�
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銆�銆�鎵�鏈塂AC閮芥渻琛ㄧ従(xi脿n)鍑轰竴瀹氱▼搴︾殑璜ф尝澶辩湡锛岃娉㈠け鐪熸槸鐢ㄤ締琛￠噺鐣�(d膩ng)DAC杓稿叆绔噰鐢ㄤ竴鍊嬬悊鎯崇殑鍧囧嫽閲囨ǎ姝ｅ鸡娉㈢殑鏁�(sh霉)鍊煎簭鍒楅﹨(q奴)鍕曟檪锛屽叾杓稿嚭绔兘鍦ㄥ澶х▼搴︿笂鍐嶇従(xi脿n)閫欏�嬬悊鎯崇殑姝ｅ鸡娉��傜敱浜嶥AC鐨勭灛鎱�(t脿i)鍜岄潨鎱�(t脿i)鐗规�у苟涓嶇悊鎯�锛屽洜姝よ几鍑洪牷璀滃皣鏈冨寘鍚娉㈡垚鍒�銆侱AC鐨勭灛鎱�(t脿i)杓稿嚭鐗规�у寘鎷鎿虹巼闄愬埗銆侀潪灏嶇ū涓婂崌鍜屼笅闄嶆檪闁�銆佹湁闄愬缓绔嬫檪闁�銆傞潨鎱�(t脿i)鐗规�ц垏鍌抽仦鍑芥暩(sh霉)鍋忛洟鐩寸窔鐨勭▼搴︽湁闂�(gu膩n)銆傛湰鏂囧皣閲嶉粸(di菐n)瑷庤珫闈滄厠(t脿i)鐗规��锛屽苟闂¤堪涓�绋敱杓稿嚭闋昏瓬涓瀵熷埌鐨勮娉㈡垚鍒嗗皫(d菐o)鍑篋AC鍌抽仦鍑芥暩(sh霉)鐨勬柟娉曘�傚垎鏋愪腑鍋囪ō(sh猫)锛屽偝閬炲嚱鏁�(sh霉)鑰岄潪鐬厠(t脿i)杓稿嚭鐗规�ф槸鎵�瑙�瀵熷埌鐨勮娉㈠け鐪熺殑涓昏渚嗘簮銆傛鍋囪ō(sh猫)鍦ㄤ綆闋绘檪鎴愮珛銆�
銆�銆�DAC鍌抽仦鍑芥暩(sh霉)
銆�銆�鍦�1椤ず涓�鍊嬬悊鎯崇殑DAC鍌抽仦鍑芥暩(sh霉)锛屽畠鏄竴姊濇枩绶�锛寉=mx+b銆傛暩(sh霉)瀛楄几鍏ヤ綅浜巟杌�锛屾ā鎿几鍑轰綅浜巠杌搞��
鍦�1. 鐞嗘兂鐨凞AC鍌抽仦鍑芥暩(sh霉)銆�
銆�銆�x杌镐笂鐨勭洰妯�(bi膩o)鑼冨湇鏄緸宸﹂倞鐨勬渶灏忕⒓(A)鍒板彸閭婄殑纰�(B)銆倅杌镐笂鐨勭洰妯�(bi膩o)鑼冨湇鏄緸搴曢儴鐨勬渶灏忚几鍑哄��(C)鍒版帴杩戦爞閮ㄧ殑杓稿嚭鍊�(D)銆傚畾缇╃悊鎯冲偝閬炲嚱鏁�(sh霉)鐨勬枩鐜�(m)鍜寉杌告埅璺�(b)鐨勬柟绋嬪紡鐢ㄩ倞鐣屽�糀(ch菙)銆丅銆丆銆丏琛ㄧず銆備俊铏焔(t)浠ｈ〃涓�鍊嬬劇澶辩湡鐨勬寮︽尝锛岀敱A鑷矪鑼冨湇鍏�(n猫i)鐨勬暩(sh霉)瀛楄几鍏ョ祫鎴�锛屾檪闁撹桓鍚戜笅銆備俊铏焨(t)浠ｈ〃妯℃摤杓稿嚭锛屽叾鍊煎湪C鑷矰鑼冨湇鍏�(n猫i)锛屾檪闁撹桓鍚戝彸銆�
銆�銆�杓稿嚭淇¤櫉鏄�氶亷鍌抽仦鍑芥暩(sh霉)鍙嶅皠鐨勮几鍏ヤ俊铏�銆傝珛娉ㄦ剰锛岃几鍑轰俊铏熸槸灏噂(t)涓婂悇榛�(di菐n)閺堟帴鍒皍(t)涓婄浉鎳�(y墨ng)榛�(di菐n)鐨勭祼(ji茅)鏋�銆傚湒1椤ず鍦ㄧ壒瀹氭檪闁撻粸(di菐n)t=tk鐨勫偝閬炴搷浣滀緥瀛愶紝瑭叉檪闁撻粸(di菐n)纰哄畾杓稿叆淇¤櫉涓婄殑榛�(di菐n)g(tk)銆傚偝閬炲嚱鏁�(sh霉)閫�(j矛n)鑰屽皣g(tk)閺堟帴鍒拌几鍑轰俊铏熶笂鐨勭浉鎳�(y墨ng)榛�(di菐n)u(tk)銆傚皪浜庣悊鎯崇殑绶氭�у偝閬炲嚱鏁�(sh霉)锛寀(t)鑸噂(t)鎴愭瘮渚嬮棞(gu膩n)绯�銆傝珛娉ㄦ剰锛実(tk)灏嶆噳(y墨ng)浜巟杌镐笂鐨勯粸(di菐n)xk锛屽畠閫氶亷鍌抽仦鍑芥暩(sh霉)鍙嶅皠鑷硑杌镐笂鐨勯粸(di菐n)yk銆傚�熷姪闂�(gu膩n)浜庤�﹀悎榛�(di菐n)闆�(g(tn),u(tn))鐨勫凡鏈夌煡璀�锛屽彲浠ョ⒑瀹氬偝閬炲嚱鏁�(sh霉)涓婄殑鐩搁棞(gu膩n)榛�(di菐n)(xn,yn)銆傚洜姝�锛岄�氶亷杓稿叆淇¤櫉g(t)涓婄殑榛�(di菐n)鑸囪几鍑轰俊铏焨(t)涓婄殑榛�(di菐n)涔嬮枔鐨勯棞(gu膩n)绯�锛屽畬鍏ㄥ彲瀹氱京鍌抽仦鍑芥暩(sh霉)銆�
銆�銆�灏嶄簬N浣岲AC锛岄倞鐣屽�糀(ch菙)鍜孊鍙栫壒瀹氬��锛屽嵆A = 0涓擝 = 2N鈥�1銆傝�岀偤浜嗘柟渚胯捣瑕�锛屾寚瀹氶倞鐣屽�糃鍜孌鐐篊 = A涓擠 = B銆傞�欐ǎ鎰忓懗瀵�(sh铆)闅汥AC杓稿嚭淇¤櫉鐨勬瘮渚嬪拰鍋忕Щ锛屽洜鑰屽叾宄板嘲鍊艰寖鍦嶇偤0鑷�2N鈥�1銆傚埄鐢ˋ銆丅銆丆銆丏鐨勯�欎簺鍊�锛屽洜?y脿n)妯剧敪钑� = 1涓旀埅璺漛 = 0锛屾墍浠ョ悊鎯冲偝閬炲嚱鏁�(sh霉)鍙啊鍖栫偤y = x銆�
銆�銆�鍒扮洰鍓嶇偤姝�锛岃◣璜栫殑閲嶉粸(di菐n)閭勬槸鐞嗘兂鐨凞AC鍌抽仦鍑芥暩(sh霉)锛屼絾鐝�(xi脿n)鍦ㄦ垜鍊戞湁浜嗗彲浠ヨ檿鐞嗗け鐪烡AC鍌抽仦鍑芥暩(sh霉)f(x)鐨勫伐鍏�锛屽鍦�2鎵�绀�銆傞渶瑕佹敞鎰忕殑涓昏鐗归粸(di菐n)鏄細鍌抽仦鍑芥暩(sh霉)涓嶅啀鏄洿绶歽 = x锛岃�屾槸涓�鍊嬪舰鐙�鍑芥暩(sh霉)f(x)锛涘湒涓毃鎰忎互骞虫粦寮у舰渚嗚〃绀恒�俧(x)灏嶈几鍑哄嚱鏁�(sh霉)u(t)鐨勫奖闊夸篃鍚屾ǎ閲嶈銆傜悊鎯宠几鍏(t)閫氶亷鍌抽仦鍑芥暩(sh霉)f(x)鍙嶅皠锛岀敘(ch菐n)鐢熷け鐪熻几鍑簎(t)銆傝垏鐝�(xi脿n)鎴怐AC鐨勫偝閬炲嚱鏁�(sh霉)鐩告瘮锛屽湒涓墍绀虹殑寮у舰鍌抽仦鍑芥暩(sh霉)杓冪偤澶稿嫉锛屽儏鐐哄姞寮�(qi谩ng)瑾槑鏁堟灉鑰屽凡?锛孎(xi脿n)浠AC鐨勫偝閬炲嚱鏁�(sh霉)鑸囩悊鎯崇殑鐩寸窔骞句箮娌掓湁鍋忓樊锛屼絾鍗充娇鏈�寰皬鐨勫亸宸篃鏈冨皫(d菐o)鑷磋几鍑洪牷璀滀腑鍑虹従(xi脿n)璜ф尝闆滄暎銆�
鍦�2. 澶辩湡鐨凞AC鍌抽仦鍑芥暩(sh霉)銆�
銆�銆�鑳藉惁鎴愬姛閲嶆(g貌u)DAC鍌抽仦鍑芥暩(sh霉)锛屽彇姹轰簬鏄惁鑳介�氶亷宸茬煡鐨刧(t)鍜寀(t)纰哄畾鍚勯粸(di菐n)(xk,f(xk))銆傞�欎竴閬庣▼鍒嗙偤鍏╂锛氶鍏堥噰鐢ㄤ竴鍊嬩唬琛ㄧ悊鎯抽噰妯ｆ寮︽尝鐨勬暩(sh霉)鍊煎簭鍒楅﹨(q奴)鍕旸AC杓稿叆锛屽埄鐢ㄩ牷璀滃垎鏋愬剙娓噺DAC杓稿嚭锛屽苟瑷橀寗鍩烘尝淇¤櫉鍜岀洝鍙兘澶氳娉㈡垚鍒嗙殑骞呭��锛涚劧鍚庡皣娓緱鐨勮娉㈠箙鍊艰綁(zhu菐n)鎻涚偤鐗瑰畾褰㈢媭鐨勫偝閬炲嚱鏁�(sh霉)銆傚鏋滄搷浣滃緱鐣�(d膩ng)锛屽皣g(t)浠ｅ叆f(x)浠跨湡u(t)灏囩敘(ch菐n)鐢熻垏娓噺绲�(ji茅)鏋滅浉鍚岀殑璜ф尝澶辩湡鍊�銆�
銆�銆�姝ワ細娓噺DAC璜ф尝
銆�銆�姝ラ渶瑕佷竴鍊嬭几鍏ュ簭鍒�锛岀敤渚嗕唬琛ㄤ竴鍊嬩互绛夎窛鏅傞枔闁撻殧閲囨ǎ鐨勭悊鎯虫寮︽尝鍛ㄦ湡銆傜洰妯�(bi膩o)鏄噸妲�(g貌u)DAC鍌抽仦鍑芥暩(sh霉)锛屽洜姝ゅ緸0鍒�N鈥�1鐨勬瘡鍊婦AC纰煎繀闋堝湪杓稿叆淇¤櫉涓嚦灏戝嚭鐝�(xi脿n)涓�娆�銆傝几鍏ュ簭鍒楅渶瑕�N浠ヤ笂鐨勯噰妯ｉ粸(di菐n)鎵嶈兘浠ョ瓑璺濋枔闅斾娇鐢ㄦ瘡鍊婦AC纰�锛屽(sh铆)闅涗笂鑷冲皯闇�瑕�N+3鍊嬮噰妯ｆ墠鑳戒繚璀夋瘡鍊嬬⒓閮藉嚭鐝�(xi脿n)銆備笅寮忓彲鐢�(ch菐n)鐢�2K DAC纰肩殑鐞嗘兂姝ｅ鸡搴忓垪(K 鈮� N+3)銆傚嚱鏁�(sh霉)round{x}灏噚鑸嶅叆鐐烘渶杩戠殑鏁存暩(sh霉)銆�
銆�銆�鍏朵腑n=0,1,2,3, ... 2K鈥�
銆�銆�姝ゆ柟绋嬪紡鍋囪ō(sh猫)DAC灏囨(bi膩o)婧�(zh菙n)浜岄��(j矛n)鍒舵牸寮忕殑鏁�(sh霉)瀛楄几鍏ュ瓧瑙ｇ⒓鐐�0鑷�N鈥�1鑼冨湇鍏�(n猫i)鐨勭劇绗﹁櫉鏁存暩(sh霉)銆傚皪浜庡亸绉讳簩閫�(j矛n)鍒舵垨浜岄��(j矛n)鍒惰(b菙)纰糄AC锛屽繀闋堣(di脿o)鏁磄n浠ヨ〃绀鸿矤(f霉)鍊�銆�
銆�銆�鏁�(sh霉)鍊煎簭鍒�(gn)浠ラ噰妯ｉ�熺巼fs閲嶅京(f霉)鎻愪緵绲AC锛屽洜姝AC杓稿嚭闋昏瓬鍚湁闋荤巼f0=fs/2k鐨勫熀娉俊铏熴�傝娉㈠嚭鐝�(xi脿n)鍦�2f0銆�3f0銆�4f0鍜宖0鐨勫叾瀹冩暣鏁�(sh霉)鍊�銆傜敱浜嶥AC杓稿嚭闋昏瓬鍏锋湁閲囨ǎ鎬ц唱(zh矛)锛屽洜姝ら�欎簺璜ф尝鐨勫箙搴﹀彈sin(x)/x闊挎噳(y墨ng)鐨勯檺鍒�銆備笉閬�锛宖0鑸噁s鐩告瘮寰笉瓒抽亾锛屽洜姝in(x)/x闊挎噳(y墨ng)瀵�(sh铆)闅涗笂鏄钩鍧︾殑锛屽彲蹇界暐涓嶈▓銆備緥濡�锛屽皪浜庝竴鍊�8浣岲AC锛孠 鈮� 11涓攆0 鈮� fs/2048锛�100娆¤娉㈢殑sin(x)/x灏囦笉瓒呴亷0.39% (0.034 dB)銆�
銆�銆�鐐轰簡婧�(zh菙n)纰洪噸妲�(g貌u)鍌抽仦鍑芥暩(sh霉)f(x)锛岄渶瑕佹牴鎿�(j霉)璜ф尝鏁�(sh霉)(h)闆嗙洝鍙兘瑷橀寗鏇村璜ф尝鐨勫箙鍊�銆傞�欎簺鏁存暩(sh霉)寰瀐 = 1锛堝熀娉㈤牷鐜囷級鑷砲=H锛屽叾涓璈琛ㄧず鍙栨脯閲忓箙鍊肩殑璜ф尝鏁�(sh霉)銆備緥濡�锛屽皪浜�10娆¤娉㈢殑娓噺锛孒 = 10锛岃┎璜ф尝鏁�(sh霉)闆嗙偤h={1, 2, 3, .. 10}銆�
銆�銆�鐒跺悗锛屽皣鍚勬脯閲忚娉㈢殑骞呭��(M)鑸囧叾璜ф尝鏁�(sh霉)闂�(gu膩n)鑱�(li谩n)銆備緥濡傦紝M1鏄�1娆¤娉紙鍩烘尝锛夌殑骞呭��锛孧2鏄�2娆¤娉㈢殑骞呭�硷紝渚濇椤炴帹鑷矼H銆傝娉㈠箙鍊奸�氬父鐢ㄧ浉灏嶄簬鍩烘尝骞呭�肩殑鍒嗚矟鏁�(sh霉)(dBc)渚嗚 閲�銆俤Bc杞�(zhu菐n)鎻涚偤绶氭�у柈浣嶇殑鍏紡濡備笅锛�
銆�銆�鍏朵腑D琛ㄧず娓緱鐨勮娉㈠箙鍊硷紝鍠綅鐐篸Bc銆備緥濡�锛屽鏋�3娆¤娉㈢殑骞呭�肩偤鈥�40 dBc锛屽墖绶氭�у箙鍊糓3 = 10鈥�40/20鎴�0.01銆侻1濮嬬祩绛変簬1锛屽洜?y脿n)妤﹂稌?j霉)瀹氱京锛屽熀娉㈢殑骞呭�肩偤0 dBc銆�
銆�銆�绗簩姝ワ細閲嶆(g貌u)DAC鍌抽仦鍑芥暩(sh霉)
銆�銆�瑭查亷绋嬬殑绗簩姝ユ秹鍙婂埌灏囪娉㈡脯閲忕祼(ji茅)鏋滆垏鍌抽仦鍑芥暩(sh霉)鐩搁棞(gu膩n)銆俧(x)涓婄殑榛�(di菐n)鍙栨焙浜巊(t)鍜寀(t)涓婂皪鎳�(y墨ng)榛�(di菐n)涔嬮枔鐨勯棞(gu膩n)绯�锛屽洜姝ら鍏堝繀闋堝皣闋诲煙涓殑璜ф尝骞呭�艰綁(zhu菐n)鎻涘埌鏅傚煙銆傝珛娉ㄦ剰锛岀祫鎴恎(t)鐨凞AC纰艰垏g(t)姝ｅ鸡褰㈠紡鐨勭浉闂�(gu膩n)鏅傞枔榛�(di菐n)涓�涓�灏嶆噳(y墨ng)銆傚洜姝�锛屾(g貌u)鎴恎(t)鐨凞AC纰艰垏鏅傚煙鐩搁棞(gu膩n)銆傛澶�锛寀(t)閫氶亷f(x)鑸噂(t)鐩搁棞(gu膩n)锛岃�実(t)鏄竴鍊嬫檪鍩熷嚱鏁�(sh霉)锛屽洜姝(t)涔熷繀闋堣〃绀虹偤鏅傚煙鍑芥暩(sh霉)銆傞�欐ǎ灏辫兘灏噂(t)涓殑鍚勬檪闁撻粸(di菐n)tk閺堟帴鍒皍(t)涓殑鐩搁棞(gu膩n)鏅傞枔榛�(di菐n)锛屽緸鑰岀敱g(t)鍜寀(t)纰哄畾f(x)銆�
銆�銆�灏囪娉㈠箙鍊艰綁(zhu菐n)鎻涘埌鏅傚煙闈炲父鍥伴洠锛屽洜?y脿n)闁�(x)蹇呴爤鏄庣⒑鑸噂(t)涓殑鍚勫彲鑳紻AC纰硷紙0鑷�N鈥�1锛夌浉闂�(gu膩n)銆俫(t)鏄竴鍊嬬悊鎯虫寮︽尝锛屽洜姝ょ⒑淇濇�х殑鏂规硶鏄皣鑼冨湇闄愬埗鍦ㄨ┎姝ｅ鸡娉㈠柈瑾�(di脿o)澧炲姞鐨勪綅缃紝濡傚湒3鍔犵矖閮ㄥ垎鎵�绀�銆傚鏋滄矑鏈夐�欎竴闄愬埗姊濅欢锛宖(x)涓婄殑涓�鍊嬮粸(di菐n)鍙兘鏈冩槧灏勫埌g(t)涓婄殑鍏╁�嬮粸(di菐n)锛屽緸鑰屽皫(d菐o)鑷翠笉鏄庣⒑銆�
銆�銆�鐐烘紨绀洪�欑ó涓嶅畾鎬�锛岃珛鎯宠薄灏囧崁(q奴)闁揟鍚戜笅绉诲嫊?锛孎(xi脿n)鍦�锛宖(x)涓婄殑榛�(di菐n)(xk, fkxk))鍙互鑸噂(t)涓婄殑鍏╁�嬮粸(di菐n)鐩搁棞(gu膩n)锛岄�欐槸涓嶅彲鎺ュ彈鐨勩�傚皣鑼冨湇T闄愬埗鍦ㄥ湒涓墍绀轰綅缃�锛屽皣涓嶅瓨鍦ㄤ笉瀹氭�с�俫(t)鐐烘寮︽尝锛屽洜姝ゆ墍闇�鑼冨湇T灏嶆噳(y墨ng)浜�½鍛ㄦ湡锛屽叾鍒濆鐩镐綅鍋忕Щ鐐�3蟺/2寮у害銆�
鍦�3. f(x)鑸噂(t)涔嬮枔鐨勯棞(gu膩n)绯�銆�
銆�銆�g(t)鐨勮寖鍦嶅彈T闄愬埗鎰忓懗钁梪(t)涔熷叿鏈夐浼肩殑鑼冨湇闄愬埗銆傚洜姝�锛屽皣鎵�瑷橀寗鐨勮娉㈠箙鍊艰綁(zhu菐n)鎻涘埌鏅傚煙鏅傦紝蹇呴爤纰轰繚灏噓(t)闄愬埗鍦ㄨ垏g(t)鐩稿悓鐨勮寖鍦峊锛屽鍦�4鎵�绀恒��
鍦�4. g(t)鍜寀(t)鐨勬檪鍩熻寖鍦�銆�
銆�銆�璜嬫敞鎰�锛屽(sh铆)闅涚殑鏅傞枔鑼冨湇T鐒￠棞(gu膩n)绶婅锛屽洜?y脿n)闁�(x)鍍呭湪g(t)鍜寀(t)浜岃�呯殑骞呭�间箣闁撹捣杞�(zhu菐n)鎻涗綔鐢�銆傜偤绨″寲鍒嗘瀽锛屽皣鍩烘尝闋荤巼(f0)姝镐竴鍖栫偤1銆傚洜姝�锛�2娆¤娉㈢殑闋荤巼鐐�2锛�3娆¤娉㈢殑闋荤巼鐐�3锛屽姝ら鎺�銆傛墍浠ワ紝璜ф尝闋荤巼鑸囪娉㈡暩(sh霉)(h)鐩哥瓑锛歠h=h銆傞�欎竴渚挎嵎闂�(gu膩n)绯诲彲绨″寲寰炶娉㈡脯閲忕祼(ji茅)鏋淢h鍓�(chu脿ng)寤簎(t)鐨勬暩(sh霉)瀛�(xu茅)瑷堢畻銆�
銆�銆�姝ｅ鸡娉㈢殑涓�鑸檪鍩熻〃閬�(d谩)寮忕偤锛�
銆�銆�鍏朵腑尾鐐哄嘲鍊兼尟骞�锛屛哥偤鍒濆鐩镐綅鍋忕Щ銆�
銆�銆�鐢╤浠ｆ浛f锛屽苟鐢∕h浠ｆ浛尾锛屽彲浠ョ嵅寰楀悇璜ф尝uh(t)鐨勬檪鍩熻〃閬�(d谩)寮忋�備笉閬庢噳(y墨ng)瑷樹綇锛実(t)鍋忕Щ3蟺/2寮у害銆傛澶栵紝g(t)鑸噓(t)涔嬮枔閫氶亷f(x)闂�(gu膩n)鑱�(li谩n)鎰忓懗钁梘(t)鍜寀(t)鍦ㄧ浉浣嶄笂鏄皪婧�(zh菙n)鐨�銆傜敤3蟺/2浠ｆ浛胃鍙彁渚涙墍闇�鐨勫皪婧�(zh菙n)銆備笅寮忎腑锛岃珛娉ㄦ剰0 鈮� t < 1涓斚�鍙栦唬浜�2蟺锛岀洰鐨勬槸灏囧熀娉㈤檺鍒跺湪鑼冨湇T鎵�琛ㄧず鐨勫崐鍊嬪懆鏈燂細
銆�銆�鍒╃敤鍚勮娉h(t)鐨勬檪鍩熻〃閬�(d谩)寮�锛屼究鍙互閲嶆(g貌u)寰�(f霉)鍚堣几鍑簎(t)锛岃〃绀虹偤鍩烘尝鍜岃娉俊铏熺殑鍜岋細
銆�銆�濡傚墠鎵�杩�锛屾垜鍊戠殑鐩(bi膩o)鏄皣g(t)鑸噓(t)鐩搁棞(gu膩n)浠ラ噸妲�(g貌u)DAC鍌抽仦鍑芥暩(sh霉)f(x)銆傛澶�锛実(t)蹇呴爤鎭板ソ鐢�2N鍊嬫ǎ鏈祫鎴愶紝浠ヤ究鑸噁(x)涓婄殑榛�(di菐n)涓�涓�灏嶆噳(y墨ng)銆傚洜姝�锛実(t)鐨勬ǎ鏈▓绠楀叕寮忕偤锛�
銆�銆�(n=0,1,2,3 .. 2N鈥�1)
銆�銆�g(t)鐢�2N鍊嬫ǎ鏈祫鎴�锛屽洜姝ょ敱鍖呮嫭2N鍊嬮噰妯ｇ殑u(t)閲囨ǎ鍊奸泦閲嶆(g貌u)f(x)浼间箮鏄悎鐞嗙殑銆傜劧鑰�锛屼簨瀵�(sh铆)鍗绘槸鑷冲皯闇�瑕�2N+3鍊嬮噰妯ｆ墠鑳界偤杓冨皬鐨凪h鍊兼彁渚涢仼鐣�(d膩ng)?sh霉)鏈伋鍙栵伎@绋儏娉佷笅锛寀(t)鍚勯噰妯ｉ粸(di菐n)鐨勮▓绠楀叕寮忔噳(y墨ng)濡備笅锛�
銆�銆�(n=0,1,2,3 .. 2N+3鈥�1)
銆�銆�璜嬫敞鎰�锛岄�欏皣灏�(d菐o)鑷磚(t)鎵�鍚殑閲囨ǎ鏁�(sh霉)澶氫簬g(t)锛寀(t)鐨勫鍊嬫ǎ鏈彲鑳借垏f(x)鍜実(t)涓婄殑涓�鍊嬮粸(di菐n)灏嶆噳(y墨ng)锛屽緸鑰屼娇u(t)鍜実(t)鍒癴(x)鐨勬槧灏勯棞(gu膩n)绯诲京(f霉)闆滃寲銆傚洜姝�锛屽繀闋堝皪鐗瑰畾鐨勬ǎ鏈祫姹傚钩鍧囧��锛屼互渚挎彁渚涘埌f(x)鐨勫悎鐞嗘槧灏勩�備笅闈㈢殑鍋戒唬纰煎弽鏄犱簡鎵�闇�鐨勬槧灏勯棞(gu膩n)绯�锛屽叾涓亣瑷�(sh猫)浣跨敤涓�鍊婲浣岲AC锛実(t)鏈�N鍊嬮粸(di菐n)锛寀(t)鏈�N+3鍊嬮粸(di菐n)銆傞櫍鍒桪acXfr鍚湁2N鍊嬪厓绱�锛屽垵濮嬪�煎潎鐐�0銆傚煼(zh铆)琛岃┎浠ｇ⒓鍚�锛岄櫍鍒桪acXfr鐨勫厓绱犲寘鍚涓�鍖栫殑DAC鍌抽仦鍑芥暩(sh霉)銆�
銆�銆�n = 0
銆�銆�FOR i = 0 TO 2N鈥�
銆�銆�AvgCnt = 0
銆�銆�WHILE i = g[n]
銆�銆�AvgCnt = AvgCnt + 1
銆�銆�DacXfr[i] = DacXfr[i] + u[n]
銆�銆�n = n + 1
銆�銆�IF n >= 2N+3
銆�銆�EXIT WHILE
銆�銆�END IF
銆�銆�END WHILE
銆�銆�IF AvgCnt = 0
銆�銆�EXIT (fail because array, g[ ], is missing a DAC code)
銆�銆�END IF
銆�銆�DacXfr[i] = (DacXfr[i]/AvgCnt)/2N
銆�銆�END FOR
銆�銆�椹�(y脿n)璀�
銆�銆�鐐洪(y脿n)璀夋湰鏂囨墍杩扮殑鏂规硶锛屼娇鐢ㄤ竴鑷洪牷璀滃垎鏋愬剙渚嗘脯閲忎竴鍊�14浣岲AC鐨勮几鍑�锛涜┎DAC鐢变竴鍊嬩唬琛ㄧ悊鎯虫寮︽尝鐨勮几鍏ュ簭鍒楅﹨(q奴)鍕�銆傝閷勪簡鍓�14娆¤娉㈢殑骞呭�硷紙2娆″埌15娆★紝鍠綅dBc锛�锛屽苟鍒╃敤閫欎簺鍊奸噸妲�(g貌u)DAC鍌抽仦鍑芥暩(sh霉)f(x)銆傜劧鍚�锛屽皣鐞嗘兂姝ｅ鸡杓稿叆搴忓垪g(sh霉)(t)浠ｅ叆閲嶆(g貌u)鐨凞AC鍌抽仦鍑芥暩(sh霉)f(x)閫�(j矛n)琛屾ā鎿�锛岀敘(ch菐n)鐢熶竴鍊嬭几鍑哄簭鍒�銆備竴鍊婩FT灏噓(t)杞�(zhu菐n)鎻涚偤闋诲煙绛夋晥鍊糢(蠅)銆傚緸U(蠅)鎻愬彇璜ф尝骞呭��锛屽苟灏囧叾鑸囬牷璀滃垎鏋愬剙鐨勬脯閲忕祼(ji茅)鏋滅浉姣旇純锛屽琛�1鎵�绀�銆傝珛娉ㄦ剰锛岃垏7娆¤娉㈢浉闂�(gu膩n)鐨勮宸儏鐐�0.065 dB銆�
銆�銆�鐢变簬姣斾緥闂�(gu膩n)绯�锛岄噸妲�(g貌u)鍌抽仦鍑芥暩(sh霉)鐨勫湒褰㈠憟鐝�(xi脿n)鐐轰竴姊濈洿绶�(y = x)銆備簨瀵�(sh铆)涓�锛岃┎鍌抽仦鍑芥暩(sh霉)鑸噛 = x鐨勫亸宸冻浠ョ敘(ch菐n)鐢熻〃1鎵�绀虹殑璜ф尝鎴愬垎銆傜偤骞姪鐞嗚В锛屽湒5鍍呴’绀轰簡瑭插偝閬炲嚱鏁�(sh霉)鑸囩悊鎯崇洿绶氱殑鍋忓樊銆傚瀭鐩磋桓鐨勫柈浣嶇偤LSB銆�
鍦�5. DAC鍌抽仦鍑芥暩(sh霉)鐨勬畼宸�銆�
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