已知f(jw)=2cos(3w)利用傅里叶变换的性质,求傅里叶逆变换 求傅里叶反变换

\u5df2\u77e5f\uff08t\uff09\u7684\u9891\u8c31\u4e3aF\uff08w\uff09\uff0c\u8bd5\u7528\u5085\u91cc\u53f6\u53d8\u6362\u7684\u6027\u8d28\u6c42tf\uff082t\uff09\u548ctdf\uff08t\uff09/dt\u7684\u5085\u91cc\u53f6\u53d8\u6362

\u5177\u4f53\u56de\u7b54\u5982\u56fe\uff1a




\u5085\u7acb\u53f6\u53d8\u6362\uff0c\u8868\u793a\u80fd\u5c06\u6ee1\u8db3\u4e00\u5b9a\u6761\u4ef6\u7684\u67d0\u4e2a\u51fd\u6570\u8868\u793a\u6210\u4e09\u89d2\u51fd\u6570\uff08\u6b63\u5f26\u548c\uff0f\u6216\u4f59\u5f26\u51fd\u6570\uff09\u6216\u8005\u5b83\u4eec\u7684\u79ef\u5206\u7684\u7ebf\u6027\u7ec4\u5408\u3002\u5728\u4e0d\u540c\u7684\u7814\u7a76\u9886\u57df\uff0c\u5085\u7acb\u53f6\u53d8\u6362\u5177\u6709\u591a\u79cd\u4e0d\u540c\u7684\u53d8\u4f53\u5f62\u5f0f\uff0c\u5982\u8fde\u7eed\u5085\u7acb\u53f6\u53d8\u6362\u548c\u79bb\u6563\u5085\u7acb\u53f6\u53d8\u6362\u3002\u6700\u521d\u5085\u7acb\u53f6\u5206\u6790\u662f\u4f5c\u4e3a\u70ed\u8fc7\u7a0b\u7684\u89e3\u6790\u5206\u6790\u7684\u5de5\u5177\u88ab\u63d0\u51fa\u7684\u3002

\u6269\u5c55\u8d44\u6599\uff1a

\u5468\u671f\u51fd\u6570f\uff08t\uff09t\uff0c\u5982\u679ct\u6ee1\u8db3\u5fb7\u8d6blai\u6761\u4ef6\uff1a\u5728\u4e00\u4e2a\u5468\u671f2tf\uff08X\uff09\u6216\u53ea\u6709\u6709\u9650\u6570\u91cf\u7684\u7b2c\u4e00\u7c7b\u4e0d\u8fde\u7eed\u70b9\u8fde\u7eed\uff0cf\uff08X\uff09\u5355\u8c03\u6216\u9644\u52a0\u53ef\u5206\u4e3a\u6709\u9650\u6570\u91cf\u7684\u5355\u8c03\u533a\u95f4\uff0c\u90a3\u4e48f\uff08X\uff092t\u5468\u671f\u5085\u91cc\u53f6\u7ea7\u6570\u6536\u655b\uff0c\u548c\u51fd\u6570S\uff08X\uff09\u4e5f\u4e0e2t\u5468\u671f\u51fd\u6570\u7684\u5468\u671f\uff0c\u548c\u8fd9\u4e9b\u4e0d\u8fde\u7eed\u51fd\u6570\u662f\u6709\u9650\u7684\u4ef7\u503c\uff1b\u5b83\u5728\u4e00\u4e2a\u5468\u671f\u5185\u6709\u6709\u9650\u4e2a\u6781\u503c\u70b9\u3002\u7edd\u5bf9\u53ef\u79ef\u3002

\u8fde\u7eed\u5f62\u5f0f\u7684\u5085\u91cc\u53f6\u53d8\u6362\u5b9e\u9645\u4e0a\u662f\u5085\u91cc\u53f6\u7ea7\u6570\u7684\u63a8\u5e7f\uff0c\u56e0\u4e3a\u79ef\u5206\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u6781\u9650\u5f62\u5f0f\u7684\u6c42\u548c\u7b97\u5b50\u3002\u4e3a\u4e86\u5728\u79d1\u5b66\u8ba1\u7b97\u548c\u6570\u5b57\u4fe1\u53f7\u5904\u7406\u4e2d\u4f7f\u7528\u8ba1\u7b97\u673a\u8fdb\u884c\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u51fd\u6570\u5fc5\u987b\u5728\u79bb\u6563\u70b9\u4e0a\u5b9a\u4e49\uff0c\u800c\u4e0d\u662f\u5728\u8fde\u7eed\u57df\u4e2d\u5b9a\u4e49\uff0c\u5e76\u4e14\u5fc5\u987b\u6ee1\u8db3\u51fd\u6570\u7684\u6709\u9650\u6027\u6216\u5468\u671f\u6027\u6761\u4ef6\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u2014\u5085\u91cc\u53f6\u53d8\u6362

\u53ef\u4ee5\u5229\u7528\u5085\u91cc\u53f6\u53d8\u5316\u7684\u5bf9\u79f0\u6027\u8d28\u73b0\u5728\u77e5\u9053F\uff08w\uff09=cos\uff082w\uff09\uff1b\u90a3\u4e48\u53ef\u4ee5\u53d8\u6210F\uff08t\uff09=cos\uff082t\uff09\uff1b\u518d\u5bf9F\uff08t\uff09\u8fdb\u884c\u5085\u91cc\u53f6\u53d8\u5316F[F\uff08t\uff09]=pi*[\u03c3\uff08w+2\uff09+\u03c3(w-2)]=2pi*f(-w);\u6240\u4ee5f\uff08-w\uff09=0.5*[\u03c3(w+2)+\u03c3(w-2)];\u5728\u8fdb\u884c\u53d8\u5316f\uff08w\uff09=0.5[\u03c3(-w+2)+\u03c3\uff08-w-2\uff09]\uff1b\u6700\u540e\u8bb2W\u53d8\u6210t\u53d8\u91cf\u5c31\u53ef\u4ee5\u4e86\u5566~

ft=$(w+3)+$(w-3)

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