信号系统x(t)=cos[w0(t-t0)]的频谱函数 求余弦信号 x(t)=A cos ωt 的均值和均方值。
\u300a\u4fe1\u53f7\u4e0e\u7cfb\u7edf\u300b\u7684...\u4e60\u9898\u6c42\u89e3\u6b27\u62c9\u516c\u5f0f\u5c55\u5f00\uff0ccos[\u03c90t]=1/2[e^(j\u03c90t)+e^(-j\u03c90t)]\uff0c\u5085\u7acb\u53f6\u7ea7\u6570\u4e3aa1=1/2\uff0ca2=-1/2\uff0c\u5468\u671f\u51fd\u6570X(j\u03c9)=\u22112\u03c0ak*\u03b4(\u03c9-k\u03c90)\uff0c\u518d\u7b97\u4e0a\u65f6\u79fb\u7684t0\uff0c\u5373\u03c0[\u03b4(\u03c9+\u03c90)e^(j\u03c90t0)+\u03b4(\u03c9-\u03c90)e^-(j\u03c90t0)]
\u4e0d\u9700\u8981\u8fc7\u7a0b\uff0c\u5c5e\u4e8e\u57fa\u672c\u7684\u5085\u7acb\u53f6\u53d8\u6362\u5bf9\uff0c\u8003\u8bd5\u4f60\u8981\u8fd9\u90fd\u6ca1\u8bb0\u4f4f\uff0c\u54ea\u6709\u65f6\u95f4\u505a\u9898
\u4f59\u5f26\u4fe1\u53f7 x(t)=A cos \u03c9t \u7684\u5747\u503c\u548c\u5747\u65b9\u503c\u5206\u522b\u4e3a0\u548c0.5*A^2\u3002
\u4f59\u5f26\u4fe1\u53f7 x(t)=A cos\u03c9t \u5747\u503c\u662f0\uff0c\u56e0\u4e3a\u4f59\u5f26\u51fd\u6570\u7684\u51fd\u6570\u56fe\u50cf\u662f\u4ee5x=0\u5bf9\u79f0\u4e0a\u4e0b\u9707\u8361\u7684\u3002
\u7528\u9ad8\u4e2d\u4e09\u89d2\u51fd\u6570\u77e5\u8bc6\u4e2d\u7684\u4e8c\u500d\u89d2\u516c\u5f0f\u53d8\u5f62\u4e4b\uff0cx(t)^2=[A cos \u03c9t ]^2=\uff080.5*A^2\uff09+(0.5*A^2)*cos(2wt)\u5f97\u5230\u5747\u65b9\u503c\u662f0.5*A^2.
\u7ea2\u7ebf\u662fA*cos (w*t)\uff0c\u7eff\u7ebf\u662f\uff080.5*A^2\uff09+(0.5*A^2)*cos(2wt)\uff0c\u84dd\u7ebf0.5*A^2
\u6269\u5c55\u8d44\u6599
\u5747\u65b9\u503c(mean-square value)\u53c8\u79f0X(t)\u7684\u4e8c\u9636\u539f\u70b9\u77e9\uff0c\u662f\u968f\u673a\u53d8\u91cfX(t)\u7684\u5e73\u65b9\u7684\u5747\u503c\uff0c\u8bb0\u4e3aE[X2(t)] \uff0c\u5728\u5de5\u7a0b\u4e0a\u8868\u793a\u4fe1\u53f7\u7684\u5e73\u5747\u529f\u7387\uff0c\u5176\u5e73\u65b9\u6839\u79f0\u6709\u6548\u503c\u3002
\u968f\u673a\u4fe1\u53f7\u7684\u5f3a\u5ea6\uff0c\u53ef\u4ee5\u7528\u5176\u5747\u65b9\u503c\u6765\u63cf\u8ff0\u3002\u5bf9\u4e8e\u5e73\u7a33\u7684\u904d\u5386\u6027\u968f\u673a\u8fc7\u7a0b\uff0c\u968f\u673a\u4fe1\u53f7\u7684\u5747\u65b9\u503c\u7528\u6837\u672c\u51fd\u6570\u5e73\u65b9\u503c\u7684\u65f6\u95f4\u5e73\u5747\u6765\u8868\u793a\uff0c\u5373
\u79f0\u4e3a\u5747\u65b9\u503c\uff0c\u5747\u65b9\u503c\u7684\u6b63\u5e73\u65b9\u6839\u79f0\u4e3a\u5747\u65b9\u6839\u503c\uff0c\u8868\u793a\u4e3a \u3002
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1\u5747\u65b9\u503c
\u3002
傅立叶级数为a1=1/2,a2=-1/2
周期函数X(jω)=∑2πak*δ(ω-kω0)
再算上时移的t0,即π[δ(ω+ω0)e^(jω0t0)+δ(ω-ω0)e^-(jω0t0)]
绛旓細娆ф媺鍏紡灞曞紑,cos[蠅0t]=1/2[e^(j蠅0t)+e^(-j蠅0t)]鍌呯珛鍙剁骇鏁颁负a1=1/2,a2=-1/2 鍛ㄦ湡鍑芥暟X(j蠅)=鈭2蟺ak*未(蠅-k蠅0)鍐嶇畻涓婃椂绉荤殑t0,鍗诚[未(蠅+蠅0)e^(j蠅0t0)+未(蠅-蠅0)e^-(j蠅0t0)]
绛旓細鑷繁鍐嶅寲绠涓涓嬨
绛旓細鎵嬫満鐗 鎴戠殑鐭ラ亾 淇″彿涓绯荤粺 x(t)=cos(2蟺/3t)*鈭(u(t-3n)-u(t-1.5-3n))鐨勫倕绔嬪彾绾ф暟绯绘暟a1 寮忎腑姹傚拰鑼冨洿鏄痭浠庤礋鏃犵┓鍒版鏃犵┓,a1鐨1鏄笅鏍,鍦ㄧ嚎绛... 寮忎腑姹傚拰鑼冨洿鏄痭浠庤礋鏃犵┓鍒版鏃犵┓,a1鐨1鏄笅鏍,鍦ㄧ嚎绛 灞曞紑 鎴戞潵绛 鍒嗕韩 寰俊鎵竴鎵 鏂版氮寰崥 QQ绌洪棿涓炬姤 娴忚101 娆 1涓洖绛 #鐑#...
绛旓細cos(A)cos(B) = 1/2{cos(A-B) + cos(A+B)} cos(A)cos(B) 鐨勫倕閲屽彾鍙樻崲鍙互鐢ㄥ嵎绉殑鏂瑰紡璁＄畻锛欶{cos(A)cos(B)} = 1/2[ F{cos(A-B)} + F{cos(A+B)} ]閭ｄ箞鏈夛細x(t)=2cosw0t+cos(2w0t-2/蟺)=2cos(w0t)cos(0)-2sin(w0t)sin(0) + cos(2w0t)cos(2/蟺...
绛旓細cosw0t鐨勫倕閲屽彾鍙樻崲鏄 鎵浠ヤ綘鐢诲嚭xjw鐨勯璋卞浘鍚庯紝宸﹀彸鍚勮繘琛屼竴娆″钩绉诲啀鍚堣捣鏉ュ氨鏄瓟妗堜簡锛屽綋鐒讹紝骞呭艰闄や互2
绛旓細=cos(w0t)+jsin(w0t)鏄鏁扮殑鍙︿竴绉嶈〃杈炬柟娉 J灏辨槸鏁板涓殑i锛屽鏁扮殑琛ㄧず涓 x+jy锛寈涓哄疄閮紝y涓鸿櫄閮紝娌℃湁j鎴杋锛屽氨鎴愪簡瀹炴暟浜嗭紱鐪嬫潵浣犺琛ヨˉ 澶嶆暟鍙婂叾杩愮畻锛岃涓嶇劧瀛︿笉浜 淇″彿涓绯荤粺鍝
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绛旓細1. 1.鏀舵暃鍩熷寘鎷崟浣嶅渾 2.鎵鏈夌殑鏋佺偣鍏ㄥ湪鍗曚綅鍦嗗唴 2. 1.40pi^2 2.80pi^2 3
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