f(x,y)=δ(x-a)的二维傅里叶变换是什么 圆的函数的二维傅里叶变换
\u72c4\u62c9\u514b\u51fd\u6570\u03b4(x-a)\u7684\u5085\u91cc\u53f6\u53d8\u6362\u662f\u4ec0\u4e48\u8fd9\u4e2a\u6d89\u53ca\u5230\u7684\u662f\u5e7f\u4e49\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u4f60\u53bb\u770b\u4e00\u4e0b\u5173\u4e8e\u72c4\u62c9\u514b\u51fd\u6570\u7684\u5085\u7acb\u53f6\u53d8\u6362\u5c31\u77e5\u9053\u4e86
\u5728a>0\u65f6\uff0cf(x)=e^-ax^2\u7684\u5085\u7acb\u53f6\u53d8\u6362\u662fF(\u03be)=[1/\u221a(2a)]e^-[\u03be^2/(4a)]\u662f\u7531\u516c\u5f0fF(\u03be)=[1/\u221a(2\u03c0)]\u222b(-\u221e,+\u221e)f(x)e^-(i\u03bex)dx
As follow:
绛旓細As follow:
绛旓細鍑芥暟鐨勮繎浠ｅ畾涔夋槸缁欏畾涓涓暟闆咥,鍋囪鍏朵腑鐨勫厓绱犱负x,瀵笰涓殑鍏冪礌x鏂藉姞瀵瑰簲娉曞垯f,璁颁綔f(x),寰楀埌鍙︿竴鏁伴泦B,鍋囪B涓殑鍏冪礌涓簓,鍒檡涓巟涔嬮棿鐨勭瓑閲忓叧绯诲彲浠ョ敤y=f(x)琛ㄧず,鍑芥暟姒傚康鍚湁涓変釜瑕佺礌:瀹氫箟鍩烝銆佸煎煙B鍜屽搴旀硶鍒檉銆傚叾涓牳蹇冩槸瀵瑰簲娉曞垯f,瀹冩槸鍑芥暟鍏崇郴鐨勬湰璐ㄧ壒寰併 [1]鍑芥暟,鏈鏃╃敱涓浗娓呮湞鏁板瀹舵潕鍠勫叞缈...
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绛旓細浜屻佽绠楁椂琛ㄨ揪寮忎笉鍚屻1銆乨y=f'(x)dx銆傚綋鍑芥暟鍙井鏃讹紝螖y = A 螖x + a(x), 鍏朵腑A鏄父鏁锛宎(x)褰撐攛->0鏃舵槸姣斘攛楂橀樁鐨勬棤绌峰皬閲忥紝寰垎 dy = A 螖x = A dx銆2銆佄y=f(x+螖x)-f(x)銆傚嚱鏁扮殑澧為噺螖y = f(x + 螖x) - f(x)鍙〃绀轰负 螖y = A螖x + o(螖x)銆
绛旓細绛旀2y 瑙ｉ杩囩▼濡備笅锛歞z=y^2dx+2xydy =y^2dx+xdy^2 鈭磟=xy^2+C 未z/dx=y^2 (未^2)z/未x未y=2y
绛旓細鎶奨琛ㄨ揪鎴愯繛缁彉閲,鍒 f(x)=(1/2)未(x)+(1/2)未(x-1) --- 杩欓噷未鏄剦鍐插嚱鏁.f(y)=u(y)-u(y-1) --- 杩欓噷u鏄樁璺冨嚱鏁.X,Y 鐙珛,Z=X+Y,鎵浠(z)鏄痜(x)鍜宖(y)鐨勫嵎绉.f(z)=f(x)*f(y) --- * 鏄嵎绉. x澶勮甯﹀叆z. y澶勪篃瑕佸甫鍏.f(z)=(1/2)(未(z)+...
绛旓細x,y)dxdy=f(畏,尉)未锛屽叾涓璂涓虹Н鍒嗗尯鍩燂紝未涓虹Н鍒嗗尯鍩熺殑闈㈢Н锛(畏,尉)鈭圖銆傛湰棰樹腑锛-a/2<畏<a/2銆-a/2<尉<a/2锛屛=a^2銆傝岋紝褰揳鈫0鏃讹紝畏鈫0銆佄锯啋0锛屸埓鍘熷紡=lim(a鈫0)f(畏,尉)銆傚張锛f(x,y)鏄繛缁嚱鏁帮紝鈭村師寮=lim(a鈫0)f(畏,尉)=f(0,0)銆備緵鍙傝冦
绛旓細浜岀淮未鍑芥暟瀹氫箟搴旇灏辨槸未(x,y)=未(x)未(y)锛岃屼竴缁次村嚱鏁版湁涓涓噸瑕佹ц川灏辨槸未(ax)=1/|a| 未(x)锛岃繖涓紡瀛愬彲浠ョ敤绉垎璇佹槑銆傚浜庝换鎰忎竴涓楠屽嚱鏁f(x)锛屸埆(-鈭炲埌+鈭)f(x)未(ax)dx t=ax鏇挎崲鍙橀噺锛屽鏋渁>0锛岀Н鍒嗕笂涓嬮檺閮戒笉鍙橈紝杩樻槸璐熸棤绌峰埌姝ｆ棤绌凤紝鍙樻垚 (1/a)鈭(-鈭炲埌+鈭)f(t...
绛旓細鍑芥暟鏄綅浜庢暟瀛﹂鍩熶腑鐨勪竴绉嶅搴斿叧绯,鏄粠闈炵┖鏁伴泦A鍒板疄鏁伴泦B鐨勫搴斻傜畝鍗曞湴璇,鐢查殢鐫涔欏彉,鐢插氨鏄箼鐨勫嚱鏁般傜簿纭湴璇,璁X鏄竴涓潪绌洪泦鍚,Y鏄潪绌烘暟闆 ,f鏄釜瀵瑰簲娉曞垯 ,鑻ュX涓殑姣忎釜x,鎸夊搴旀硶鍒檉,浣縔涓瓨鍦ㄥ敮涓鐨勪竴涓厓绱爕涓庝箣瀵瑰簲 ,灏辩О瀵瑰簲娉曞垯f鏄疿涓婄殑涓涓嚱鏁,璁颁綔y=f(x),绉癤涓哄嚱鏁癴(x...
绛旓細鐢变簬X~N锛0锛未²锛锛孻~N锛0锛屛²锛夛紝X鍜孻鐨勬鐜囧瘑搴﹀嚱鏁版槸鍋跺嚱鏁帮紝寰桺(X<=2)+P(Y<=-2)=1銆傛墍浠 P{X>2锛孻>-2}=P(X<=2,Y<=-2)]=0.25 锛堜簩锛夌敱X鐨勫瘑搴﹀嚱鏁f(x)=Ae^(-x²)锛岀珛鍗冲彲鐭ワ紝X~N(0,1/2)锛岀户鑰屽彲寰 A=1/(蟺^0.5)锛孌(X)=1/2銆
