求用matlab实现FFT函数的功能 求教matlab实现门函数的fft
\u7528matlab\u7f16\u5199\u5b9e\u73b0fft\u7684\u7a0b\u5e8f\u3002function y=myditfft(x)
%\u672c\u7a0b\u5e8f\u5bf9\u8f93\u5165\u5e8f\u5217\u5b9e\u73b0DIT-FFT\u57fa2\u7b97\u6cd5\uff0c\u70b9\u6570\u53d6\u5927\u4e8e\u7b49\u4e8e\u957f\u5ea6\u76842\u7684\u5e42\u6b21
%------------------------------------
%
myditfft.c
%------------------------------------
m=nextpow2(x);
%\u6c42\u7684x\u957f\u5ea6\u5bf9\u5e94\u76842\u7684\u6700\u4f4e\u5e42\u6b21m
N=2^m;
if length(x)<N
x=[x,zeros(1,N-length(x))];
%\u82e5\u7684\u957f\u5ea6\u4e0d\u662f2\u7684\u5e42\uff0c\u88650\u52302\u7684\u6574\u6570\u5e42
end
nxd=bin2dec(fliplr(dec2bin([1:N]-1,m)))+1;
%\u6c421\uff1a2^m\u6570\u5217\u7684\u5012\u5e8f
y=x(nxd);
%\u5c06\u5012\u5e8f\u6392\u5217\u4f5c\u4e3a\u7684\u521d\u59cb\u503c
for mm=1:m
%\u5c06DFT\u505am\u6b21\u57fa2\u5206\u89e3\uff0c\u4ece\u5de6\u5230\u53f3\uff0c\u5bf9\u6bcf\u6b21\u5206\u89e3\u4f5cDFT\u8fd0\u7b97
Nmr=2^mm;
u=1;
%\u65cb\u8f6c\u56e0\u5b50u\u521d\u59cb\u5316
WN=exp(-i*2*pi/Nmr);
%\u672c\u6b21\u5206\u89e3\u7684\u57fa\u672cDFT\u56e0\u5b50WN\uff1dexp(-i*2*pi/Nmr)
for j=1:Nmr/2
%\u672c\u6b21\u8de8\u8d8a\u95f4\u9694\u5185\u7684\u5404\u6b21\u789f\u5f62\u8fd0\u7b97
for k=j:Nmr:N
%\u672c\u6b21\u789f\u5f62\u8fd0\u7b97\u7684\u8de8\u8d8a\u95f4\u9694\u4e3aNmr=2^mm
kp=k+Nmr/2;
%\u786e\u5b9a\u789f\u5f62\u8fd0\u7b97\u7684\u5bf9\u5e94\u5355\u5143\u4e0b\u6807
t=y(kp)*u;
%\u789f\u5f62\u8fd0\u7b97\u7684\u4e58\u79ef\u9879
y(kp)=y(k)-t;
%\u789f\u5f62\u8fd0\u7b97\u7684\u52a0\u6cd5\u9879
y(k)=y(k)+t;
end
u=u*WN;
%\u4fee\u6539\u65cb\u8f6c\u56e0\u5b50\uff0c\u591a\u4e58\u4e00\u4e2a\u57fa\u672cDFT\u56e0\u5b50WN
end
end
\u5982\u679c\u4f60\u53ea\u5bf9[-0.5,0.5]\u4e4b\u95f4\u7684\u4fe1\u53f7\u8fdb\u884c\u91c7\u6837\uff0c\u90a3\u4e48\u4f60\u91c7\u7684\u5c06\u4f1a\u662f\u5e38\u65701\uff0c\u8fd9\u6837\u505a\u51fa\u7684FFT\u5e94\u8be5\u662f\u4e00\u4e2adelta\u51fd\u6570\uff0c\u4e5f\u5c31\u662f\u4e00\u4e2a\u51b2\u51fb\uff0c\u6240\u4ee5\u4f60\u5e94\u8be5\u91c7\u5305\u62ec\u5916\u8fb9\u7684\u503c\u624d\u80fd\u591f\u53cd\u6620\u51fa\u4fe1\u53f7\u7684\u7279\u6027\u3002
\u8fd9\u6837\u7ed3\u679c\u6ca1\u6709\u4efb\u4f55\u95ee\u9898\uff0c\u95ee\u9898\u662f\u4f60\u91c7\u6837\u7684\u503c\u592a\u5c11\u4e86\uff0c\u6362\u53e5\u8bdd\u8bf4\u5c31\u662f\u4f60\u91c7\u6837\u7684\u4fe1\u53f7\u53cd\u6620\u4e0d\u51fa\u8fd9\u662f\u4e2a\u95e8\u51fd\u6570\u7684\u7279\u6027\u6765\u3002
matlab\u91cc\u8fb9\u662f\u53ef\u4ee5\u5229\u7528\u5355\u8fb9\u51fd\u6570\u8868\u793a\u95e8\u51fd\u6570\u7684\u3002\u4f60\u53ef\u4ee5\u8dd1\u4e00\u4e0b\u4e0b\u8fb9\u7684\u7a0b\u5e8f\uff0c\u770b\u4e00\u4e0b\u95e8\u51fd\u6570\uff1a
fx=heaviside(x+0.5)-heaviside(x-0.5);
ezplot(fx,[-1,1]);
\u800c\u4e14matlab\u91cc\u8fb9\u8fd8\u6709\u5bf9\u7b26\u53f7\u8868\u8fbe\u5f0f\u505a\u5085\u91cc\u53f6\u53d8\u6362\u7684\u51fd\u6570fourier()\uff0c\u7528\u6cd5\u5982\u4e0b\uff1a
FX=fourier(fx);
ezplot(FX,[-30,30]);
title('fourier transformation of fx')
\u800c\u5982\u679c\u4f60\u975e\u60f3\u7528fft\u505a\uff0c\u5c31\u5fc5\u987b\u52a0\u5927\u91c7\u6837\u70b9\u6570\uff0c\u5c24\u5176\u662f\u95e8\u4e4b\u5916\u7684\u90e8\u5206\uff0c\u624d\u80fd\u591f\u5b8c\u6574\u7684\u63cf\u8ff0\u4fe1\u53f7\u3002
N=length(x);
M=log2(N);
xtmp=zeros(1,N);
value=zeros(1,M);
for i=0:N-1
repr=i;
for t=1:1:M
repr=bitshift(i,1-t);
value(t)=bitand(repr,1);
end
pos=0;
for k=1:1:M
pos=pos+value(k)*2^(M-k);
end
xtmp(pos+1)=x(i+1);
end
for i=1:M
deepth=2^(i-1);
width=2^(M-i);
for t=1:2^i:N
for k=1:deepth
tmp=xtmp(t+k-1);
wn=width*(k-1);
xtmp(t+k-1)=tmp+exp(-j*2*pi*wn/N)*xtmp(t+k+deepth-1);
xtmp(t+k+deepth-1)=tmp-exp(-j*2*pi*wn/N)*xtmp(t+k+deepth-1);
end
end
end
xn=xtmp;
function xn=myfft(x)
N=length(x);
M=log2(N);
xtmp=zeros(1,N);
value=zeros(1,M);
for i=0:N-1
repr=i;
for t=1:1:M
repr=bitshift(i,1-t);
value(t)=bitand(repr,1);
end
pos=0;
for k=1:1:M
pos=pos+value(k)*2^(M-k);
end
xtmp(pos+1)=x(i+1);
end
for i=1:M
deepth=2^(i-1);
width=2^(M-i);
for t=1:2^i:N
for k=1:deepth
tmp=xtmp(t+k-1);
wn=width*(k-1);
xtmp(t+k-1)=tmp+exp(-j*2*pi*wn/N)*xtmp(t+k+deepth-1);
xtmp(t+k+deepth-1)=tmp-exp(-j*2*pi*wn/N)*xtmp(t+k+deepth-1);
end
end
end
xn=xtmp;
绛旓細matlab鑷甫鐨刦ft鍑芥暟鏄揩閫熷倕閲屽彾鍙樻崲鍑芥暟銆備富瑕佺敤浜庨檷鍣鐞嗭紝閫氳繃浣跨敤鍌呴噷鍙跺彉鎹㈡眰鍣０涓殣钘忕殑淇″彿鐨勯鐜囧垎閲忋傝鍑芥暟浣跨敤鏂规硶锛氭柟娉曚竴锛歒 = fft(X) 鐢ㄥ揩閫熷倕閲屽彾鍙樻崲 (FFT) 绠楁硶璁＄畻 X 鐨勭鏁ｅ倕閲屽彾鍙樻崲 (DFT)銆傚鏋 X 鏄悜閲忥紝鍒 fft(X) 杩斿洖璇ュ悜閲忕殑鍌呴噷鍙跺彉鎹傚鏋 X 鏄煩闃碉紝鍒 fft...
绛旓細n=0:N-1;t=n/fs; %鏃堕棿搴忓垪 x1=sin(2*pi*100*t);x2=sin(2*pi*200*t);x3=sin(2*pi*3800*t);y1=fft(x1,N); %瀵逛俊鍙杩涜蹇烣ourier鍙樻崲 mag1=abs(y1); %姹傚緱Fourier鍙樻崲鍚庣殑鎸箙 y2=fft(x2,N); %瀵逛俊鍙疯繘琛屽揩閫烣ourier鍙樻崲 mag2=abs(y2); %姹傚緱Fourier...
绛旓細F(蠅) = 鈭 f(t) e^(-i蠅t) dt 鍏朵腑蠅鏄鐜囷紝i鏄櫄鏁板崟浣嶃傜劧鑰岋紝浣犵粰鍑虹殑鍑芥暟f(t) = e^(-2|t|)鍦╩atlab涓眰鍌呴噷鍙剁骇鏁版槸鏈変簺澶嶆潅鐨勶紝鍥犱负瀹冪殑绉垎鍙兘娑夊強鍒颁竴浜涚壒娈婂嚱鏁般傛澶栵紝鐢变簬璇ュ嚱鏁版槸鍋跺嚱鏁帮紝鍏跺倕閲屽彾鍙樻崲鐨勫疄閮ㄥ拰铏氶儴鏄绉扮殑锛屽洜姝ゅ彧闇瑕佽绠椾竴鍗婄殑棰戠巼鑼冨洿鍗冲彲銆備笉杩囷紝...
绛旓細function y=myditfft(x)鏈▼搴忓杈撳叆搴忓垪瀹炵幇DIT-FFT鍩2绠楁硶锛岀偣鏁板彇澶т簬绛変簬闀垮害鐨2鐨勫箓娆 --- myditfft.c --- m=nextpow2(x);姹傜殑x闀垮害瀵瑰簲鐨2鐨勬渶浣庡箓娆 N=2^m;if length(x)<N x=[x,zeros(1,N-length(x))];鑻ョ殑闀垮害涓嶆槸2鐨勫箓锛岃ˉ0鍒2鐨勬暣鏁板箓 end nxd=bin2dec(fliplr(...
绛旓細瑕佺粯鍒禘=1锛宼=1锛孴=2鐨勫懆鏈熺煩褰㈣剦鍐蹭俊鍙风殑涓夎鍑芥暟褰㈠紡鐨勫箙搴﹂璋卞浘锛屼綘鍙互浣跨敤MATLAB鐨凢FT锛團ast Fourier Transform锛夊嚱鏁般備互涓嬫槸涓涓彲鑳界殑绋嬪簭锛歮atlab澶嶅埗浠ｇ爜 鍙傛暟瀹氫箟 E = 1; % 骞呭害 t = 1; % 鏃堕棿鍋忕Щ T = 2; % 鍛ㄦ湡 Fs = 1000; % 閲囨牱棰戠巼 t_sample = 0:1/Fs:T; % 鏃堕棿...
绛旓細鍦∕ATLAB涓鍋欶FT锛岄鍏堢紪鍐鍑芥暟锛屽涓嶅悓鐨勯噰鏍烽鐜囧拰閲囨牱鐐规暟锛岃绠桭FT鍚庣殑棰戠巼搴忓垪鍙婂叾瀵瑰簲鐨勫箙鍊硷細function [f amplitude] = yopheeFFT(sampleRate,FFT_points)n = 0:FFT_points-1;t = n/sampleRate; %閲囨牱鏃堕棿搴忓垪 f_All = n*sampleRate/FFT_points; %棰戠巼搴忓垪 %鏋勯犳贩鏈夊櫔澹扮殑鍛ㄦ湡淇″彿骞...
绛旓細matlab涓fft鏈1d鍜2d鐨勶紝fft寰楀埌鐨勬槸淇″彿鐨勯璋卞嵆t锛嶃媐 濡 clear 缂栧啓楠嗛仴 fs=1000 t=0:1/fs:0.6;f1=100;f2=300;x=sin(2*pi*f1*t)+sin(2*pi*f2*t);subplot(711)plot(x);title('f1锛100hz锛塡f2(300hz)鐨勬寮︿俊鍙凤紝鍒濈浉0')xlabel('搴忓垪锛坣锛')grid on number=512 y=fft(x...
绛旓細fft鏄揩閫熷倕绔嬪彾鍙樻崲锛屽彲鐩存帴璋冪敤锛屽fft(A)绂绘暎鍌呯珛鍙跺彉鎹㈡槸dft 杩欐槸鎴戣嚜宸鍋鐨刣ft function X=dft(x)N=length(x);W=exp(-2i*pi/N);X=zeros(1,N);for k=1:N X(k)=sum(x.*W.^((0:N-1)*(k-1)));end
绛旓細Y = fft(y,N)/N*2; %闄や互N涔樹互2鎵嶆槸鐪熷疄骞呭硷紝N瓒婂ぇ锛屽箙鍊肩簿搴﹁秺楂 f = Fs/N*(0:1:N-1); %棰戠巼 A = abs(Y); %骞呭 P = angle(Y); %鐩稿 figure;subplot(211);plot(f(1:N/2),A(1:N/2)); %鍑芥暟fft杩斿洖鍊肩殑鏁版嵁缁撴瀯鍏锋湁瀵圭О鎬,鍥犳鎴戜滑鍙彇鍓嶄竴鍗 title...
绛旓細1銆佺洿鎺ュ鍏浣跨敤ceil鍑芥暟锛屽彲浠ュ悜涓婂彇鏁达細鍗冲ぇ浜庣瓑浜庣粰瀹氭暟鎹殑鏈灏忔暣鏁般2銆佷娇鐢╢loor鍑芥暟鍙互杩涜鍚戜笅鍙栨暣銆傚鍥撅紝灏嗙煩闃礎涓殑姣忎釜鍏冪礌鍙栧皬浜庣瓑浜庤鍏冪礌鐨勬渶澶ф暣鏁般3銆佷娇鐢╢ix鍑芥暟鍒欏彲浠ュ幓闄ゅ皬鏁伴儴鍒嗐傚浜庡ぇ浜0鐨勫厓绱犵浉褰撲簬floor锛屽浜庡皬浜0鐨勫厓绱犵浉褰撲簬ceil銆4銆佷娇鐢╮ound鍑芥暟鍙互鎶婃暟鎹洓鑸嶄簲鍏ュ埌鏈杩...
