数学Sa（x）的傅里叶变换频谱是矩形,矩形乘以其他函数，只会保留下某段频率//不太理解是如何保留下某段？ 正弦函数的傅里叶频谱有哪些特点?
\u54ea\u4f4dmatlab\u9ad8\u624b\u53ef\u4ee5\u5e2e\u5fd9\u5199\u4e2a\u7a0b\u5e8f\u554a\uff0c\u751f\u6210\u4e00\u4e2a\u77e9\u5f62\u7a97\u51fd\u6570\uff0c\u7136\u540e\u5085\u7acb\u53f6\u53d8\u6362\u6c42\u5b83\u7684\u9891\u8c31\u56fe\u3002N=21;
wp=0.3*pi;
ws=0.5*pi;
wc=ws-wp;
fc=wc/pi;
n=[0:N-1];
r=(N-1)/2;
m=n-r;
hd=fc*sinc(fc*m);%\u4ea7\u751f\u7406\u60f3\u4f4e\u901a\u6ee4\u6ce2\u5668\u7684\u8109\u51b2\u54cd\u5e94
wn=hamming(N);%\u4ea7\u751f\u6d77\u660e\u7a97\u51fd\u6570\u5e8f\u5217
hn=hd.*wn';%\u5bf9\u7406\u60f3\u4f4e\u901a\u6ee4\u6ce2\u5668\u52a0\u6d77\u660e\u7a97
[H,w]=freqz(hn,1,512,'whole',2);
db=20*log10(abs(H)/max(abs(H)));
subplot(221);
plot(w,db);
grid;
xlabel('\u5f52\u4e00\u5316\u9891\u7387w');
ylabel('\u76f8\u5bf9\u5e45\u5ea6/db');
title('(a) N=21\u65f6\u5e45\u5ea6\u54cd\u5e94\u7279\u6027');
\u8fd9\u662f\u6211\u505a\u768421\u9636\u6d77\u660e\u7a97\u51fd\u6570\uff0c\u77e9\u5f62\u7a97\u53ea\u9700\u8981\u628ahamming(N)\u51fd\u6570\u6362\u6210triang(N)\u5c31\u884c\u4e86\uff0c\u5176\u4ed6\u7a97\u51fd\u6570\u4e5f\u662f\u4e00\u6837\u3002
[H,w]=freqz(hn,1,512,'whole',2);\u8fd9\u53e5\u8bdd\u662f\u6c42\u9891\u8c31\u3002
\u6211\u672c\u79d1\u6bd5\u4e1a\u8bbe\u8ba1\u5c31\u662f\u505a\u7684\u57fa\u4e8ematlab\u7684FIR\u6ee4\u6ce2\u5668\u3002\u5f88\u6709\u591a\u8bba\u6587\u9700\u8981\u5728\u77e5\u7f51\u4ed8\u8d39\u4e0b\u8f7d\u3002
\u6709\u9700\u8981\u7684\u8bdd\u53e6\u5916\u63d0\u95ee\uff0c\u591a\u7ed9\u4e9b\u60ac\u8d4f\u5206\uff0c\u7559\u4e0b\u90ae\u7bb1\uff0c\u6211\u53d1\u7ed9\u4f60\u3002\u4e0d\u8fc7\u6211\u7684\u6bd5\u4e1a\u8bba\u6587\u4e0d\u7ed9\u54c8\uff0c\u4f46\u662f\u6709\u5f88\u591a\u5f88\u591a\u7684\u53c2\u8003\u6750\u6599
\u4ece\u7406\u8bba\u4e0a\u8bb2\uff0c\u6b63\u5f26\u51fd\u6570\u7684\u5085\u91cc\u53f6\u53d8\u6362\u662f\u51b2\u51fb\u51fd\u6570\uff1a
\u5b83\u7684\u5e45\u503c\u4e3a\u539f\u6b63\u5f26\u4fe1\u53f7\u5e45\u503c\u76841/2\u500d\uff1b\u5373\uff1a\u82e5x(t)=Acos(\u03a9t)\uff0c\u5219\u5176\u9891\u8c31\u5e45\u503c\u6700\u5927\u503c\u4e3aA/2\uff1b
\u4f46\u662f\uff0c\u6211\u4eec\u7528matlab\u6c42\u51fa\u6765\u7684\u9891\u8c31\u56fe\u5374\u4e0d\u662f\u8fd9\u6837\u7684\uff1b
\u539f\u56e0\u662f\uff1a
1.\u7406\u8bba\u4e2d\u7684\u6b63\u5f26\u4fe1\u53f7\u662f\u65e0\u9650\u957f\u8fde\u7eed\u4fe1\u53f7\uff0c\u800cmatlab\uff0c\u53c2\u4e0e\u8fd0\u7b97\u7684\u4fe1\u53f7\u53ea\u662f\u622a\u53d6\u4e86\u5176\u4e2d1\u4e2a\u5468\u671f\u6216\u591a\u4e2a\u5468\u671f\u7684\u4fe1\u53f7\uff0c\u5c31\u53d8\u6210 \u4e86\u6709\u9650\u957f\u4fe1\u53f7\u4e86\uff1b\u65e0\u9650\u957f\u4fe1\u53f7\u548c\u6709\u9650\u957f\u4fe1\u53f7\u7684\u5085\u91cc\u53f6\u53d8\u6362\u662f\u4e0d\u4e00\u6837\u7684\uff01
2.\u7406\u8bba\u4e2d\u7684\u6b63\u5f26\u4fe1\u53f7\u662f\u8fde\u7eed\u7684\u6a21\u62df\u4fe1\u53f7\uff0c\u800c\u5e94\u7528\u4e2d\u7684\u6b63\u5f26\u4fe1\u53f7\u90fd\u662f\u91c7\u6837\uff0c\u91cf\u5316\u5904\u7406\u7684\uff0c\u662f\u6570\u5b57\u4fe1\u53f7\uff1b\u6a21\u62df\u4fe1\u53f7\u548c\u6570\u5b57\u4fe1 \u53f7\u7684\u5085\u91cc\u53f6\u53d8\u6362\u662f\u4e0d\u4e00\u6837\u7684\uff01
\u5bf9\u4e8e\u5df2\u77e5\u5468\u671f\u7684\u4fe1\u53f7\uff0c\u901a\u5e38\u53ea\u9700\u8981\u53d6\u5176\u4e2d\u4e00\u4e2a\u5468\u671f\u505a\u4ee3\u8868\u5206\u6790\uff1b\u4f46\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u4fe1\u53f7\u7684\u9891\u7387\u901a\u5e38\u5df2\u77e5\uff0c\u4f46\u566a\u58f0\u7684\u9891\u7387\u5374\u4e0d\u56fa\u5b9a\uff0c\u6240\u4ee5\uff0c\u5e94\u5c3d\u53ef\u80fd\u957f\u7684\u622a\u53d6\u4fe1\u53f7\uff1b
\u4e0b\u9762\u4ecb\u7ecd\u5728Matlab\u4e2d\uff0c\u5982\u4f55\u5206\u6790\u6b63\u5f26\u51fd\u6570\u7684FFT\uff1a
\u5df2\u77e5\u6b63\u5f26\u4fe1\u53f7 x(t)=4.6sin(2*pi*f0*t)\uff0c\u6bcf\u5468\u6ce2\u91c7\u6837\u70b9\u6570Ns=512\uff0c\u91c7\u6837\u9891\u7387fs=f0*512\uff1b\uff08f0\u4e3a\u6b63\u5f26\u4fe1\u53f7\u7684\u56fa\u6709\u9891\u7387\uff09
\u5728Matlab\u4e2d\u9700\u8981\u505a\u4e00\u4e0b\u5904\u7406\uff1a
1.\u5c06\u65f6\u95f4\u8f74\u79bb\u6563\u5316\uff1a ts = tp * n=(T0/Ns) * n =n/f0*512=n/fs; n = 0:511\uff1b tp\u4e3a\u6bcf\u5468\u6ce2\u91c7\u6837512\u70b9\u7684\u65f6\u95f4\u95f4\u9694;
2.\u5c06\u8fde\u7eed\u4fe1\u53f7x(t)\u79bb\u6563\u5316\uff1ax(ts)= 4.6sin(2*pi*f0*ts) = 4.6sin(2*pi*n/N)\uff1b
\u53ef\u4ee5\u770b\u51fax(t)\u79bb\u6563\u5316\u540e\uff0c\u5df2\u7ecf\u4e0e\u4fe1\u53f7\u7684\u56fa\u6709\u9891\u7387\u6ca1\u5173\u7cfb\u4e86\uff0c\u8fd9\u4e2a\u4fe1\u53f7\u5df2\u7ecf\u53d8\u6210\u4e86\u4e0en\u76f8\u5173\u7684\u51fd\u6570\uff1a
x(n)= 4.6sin(2*pi*n/N)\uff1b n = 0:511\uff1b
3.\u79bb\u6563\u4fe1\u53f7\u5728Matlab\u4e2d\u6c42FFT\u5c31\u5f88\u5bb9\u6613\u4e86\uff1a
X(n)= FFT( x(n) ) *2 / Ns \uff1b
4.\u6839\u636e\u5468\u671f\u4fe1\u53f7\u7684\u5085\u91cc\u53f6\u53d8\u6362\u7684\u6027\u8d28\uff1a\u65f6\u57df\u7684\u5468\u671f\uff0c\u9020\u6210\u9891\u57df\u7684\u79bb\u6563\uff1b\u65f6\u95f4\u7684\u79bb\u6563\uff0c\u9020\u6210\u9891\u57df\u7684\u5468\u671f\uff1b
\u53ef\u77e5\uff1aX(n) \u4e3a\u79bb\u6563\u7684\uff0c\u4e14\u6709\u5468\u671f\uff1b\u79bb\u6563\u70b9\u7684\u95f4\u8ddd\u6b63\u597d\u662f\u6b63\u5f26\u4fe1\u53f7\u7684\u56fa\u6709\u9891\u7387f0 \uff1b\u5468\u671f\u4e3a\u91c7\u6837\u5468\u671f1/fs\uff1b
X(0),X(1)....\u5206\u522b\u5bf9\u5e94x(t)\u7684\u7b2c0\u6b21,1\u6b21...\u8c10\u6ce2\uff1b
5.\u5982\u679c\u8981\u5728\u4e8c\u7ef4\u56fe\u4e0a\u663e\u793a\u9891\u7387\u4e0e\u9891\u8c31\u5e45\u503c\u7684\u5173\u7cfb\uff0c\u8fd8\u9700\u8981\uff1a
\u5c06\u6a2a\u8f74\u6620\u5c04\u4e3a\u9891\u7387\u503c\uff0c\u6620\u5c04\u5173\u7cfb\u4e3a f = n*f0\uff1b
6.\u6839\u636e\u5948\u594e\u65af\u7279\u91c7\u6837\u5b9a\u7406\uff0c\u5f53\u91c7\u6837\u9891\u7387\u4e3afs\u65f6\uff0c\u53ef\u4ee5\u5f97\u5230FFT\u540e\u7684\u6700\u9ad8\u6709\u6548\u9891\u7387\u4e3afs/2\uff1b\u6700\u9ad8\u8c10\u6ce2\u6b21\u6570\u4e3aNs/2-1\uff1b
\u5177\u4f53\u5b9e\u73b0\u5982\u4e0b\uff08Matlab\u4e2d\uff0c\u5df2\u8c03\u8bd5\u901a\u8fc7\uff09\uff1a
%\u6c42\u6b63\u5f26\u4fe1\u53f7\u7684\u5085\u91cc\u53f6\u53d8\u6362
Ns = 512;%\u91c7\u6837\u70b9
n = 0 : Ns-1;
xn = 4.6*sin(2*pi*n/Ns); %\u79bb\u6563\u7684\u6b63\u5f26\u4fe1\u53f7
Xn = fft( xn ) ; %fft\u7684\u7ed3\u679c\u662f\u590d\u6570
Xn = abs(Xn) *2 /Ns; %\u6c42\u7edd\u5bf9\u503c\u5f97\u5230\u5e45\u503c\uff0c\u4e58\u4ee52\uff0c\u4e58\u4ee5Ns\u662f\u7531\u5085\u91cc\u53f6\u53d8\u6362\u516c\u5f0f\u5bfc\u81f4\u7684
%\u7528\u4e8c\u7ef4\u56fe\u663e\u793a\u539f\u59cb\u6b63\u5f26\u4fe1\u53f7
subplot(3,1,1),plot(n, xn); %\u753b\u51fa\u539f\u59cb\u6b63\u5f26\u4fe1\u53f7
xlabel('n = 0:511'); ylabel('\u632f\u5e45');
title('\u539f\u59cb\u7684\u6b63\u5f26\u4fe1\u53f7');
%\u7528\u4e8c\u7ef4\u56fe\u663e\u793a\u4fe1\u53f70~255\u6b21\u7684\u8c10\u6ce2
Nyquist = Ns/2-1;%\u6839\u636e\u5948\u594e\u65af\u7279\u5b9a\u7406\uff0c\u53ea\u9700\u663e\u793a\u524d255\u6b21\u7684\u8c10\u6ce2
subplot(3,1,2),plot(n(1:Nyquist), Xn(1:Nyquist));
xlabel('n = 0:255'); ylabel('\u8c10\u6ce2\u5e45\u503c');
title('0~255\u6b21\u7684\u8c10\u6ce2');
%\u7528\u4e8c\u7ef4\u56fe\u663e\u793a\u4fe1\u53f7\u9891\u7387\u4e0e\u5e45\u503c\u7684\u5173\u7cfb
f0 = 50; %\u5047\u8bbe\u4fe1\u53f7\u7684\u56fa\u6709\u9891\u7387\u4e3a50Hz
f = n*f0; %\u9891\u7387\u4e0e\u6a2a\u8f74\u5e8f\u5217n\u7684\u6620\u5c04\u5173\u7cfb
subplot(3,1,3),plot(f(1:Nyquist), Xn(1:Nyquist)); %\u6839\u636e\u5948\u594e\u65af\u7279\u5b9a\u7406\uff0c\u53ea\u9700\u663e\u793a\u524dfs/2\u90e8\u5206\u7684\u9891\u8c31
xlabel('f = 0, 50Hz... 255*f0 Hz '); ylabel('\u5e45\u503c');
title('\u9891\u7387\u4e0e\u5e45\u503c\u7684\u5173\u7cfb');
\u8fd0\u884c\u7ed3\u679c\u5982\u4e0b\uff1a
\u56fe\u4e2d\uff0c\u5728f = f0 = 50Hz\u65f6\uff0c\u5e45\u503c\u4e3a4.6\uff1b\u5373\u4e00\u6b21\u8c10\u6ce2\u5e45\u503c\u4e3a4.6.
绛旓細濡傛灉f(x)鐨勫浘褰㈡槸涓涓煩褰紝鍙湁涓涓尯娈(a,b)鐨勫嚱鏁板煎涓1锛岄櫎姝や互澶栫殑鍖哄煙鍑芥暟鍊煎潎涓0锛屽綋瀹冧笌鍏朵粬鍑芥暟g(x)鐩镐箻锛岃偗瀹氭槸g(x)鍙湪(a,b)鍖洪棿淇濈暀鍘熷硷紝鍏朵粬鍖洪棿閮借0涔樹簡锛屽綋鐒跺氨娌℃湁淇濈暀鍛銆傚湪棰戝煙鐩镐箻锛屽氨鏄尯闂村鐨勯鐜囨垚鍒嗛兘缃0锛屽彧淇濈暀鍖洪棿鍐呯殑棰戠巼鎴愬垎銆
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绛旓細xlabel('t');ylabel('Sa锛t锛');title('鍦ㄥ尯闂达紙-15锛15锛夊唴鏋勫缓Sa(t)鍑芥暟');grid on;涓嬮潰鏄兂瑕佸疄鐜板sinc鍑芥暟鐨勫倕閲屽彾鍙樻崲骞朵笖鏋勫浘銆傘備絾鏄笉鐭ラ亾fft鍑芥暟瑕佹庝箞鐢ㄣ俿ubplot(212);Fa=log(1+abs(fftshift(fft(Sa)));瀵筍a鍑芥暟杩涜鍌呴噷鍙跺彉鎹 plot(Fa);鍦紙-3,3锛夊唴鏋勯棰戣氨鍥 xlabel(...
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绛旓細rgb(255, 255, 238); font-variant-ligatures: normal; font-variant-caps: normal; -webkit-text-stroke-width: 0px;'>f(x)鍦▁=蟺澶勭殑宸︽瀬闄愪负0,鍙虫瀬闄愪负-蟺,鍏鍌呴噷鍙绾ф暟鍦▁=蟺澶勬敹鏁涗簬宸﹀彸鏋侀檺鐨勫钩鍧囧,鍗-蟺/2. style='font-family: arial, helvetica,sans-serif;...
