大批杀害频16点FFT / DFT MATLAB源代码
本节的MATLAB源代码覆盖在DFT频率FFT或大量毁灭matlab代码。它比较FFT输出与matlab装入的FFT函数来验证代码。这一页封面16点大量毁灭FFT / DFT频率与一些反向输出。
最常见和熟悉radix-2 fft算法。然而其他根viz.少量然后10有时使用。例如,radix-4尤其有吸引力,因为抚弄因素都是1,1,j - j,可应用没有任何乘法。
什么是FFT基数
基数的大小是一个FFT分解。
捻系数
抚弄因素系数用于将前一阶段的结果输入到下一个阶段。
W = exp (j * 2 *π* n / n), n = 16点,n = 0到7。
大量毁灭在FFT
FFT算法可以de-composed使用偶数和奇数阶的离散点,叫做大批杀害FFT。
大量毁灭的频率FFT
FFT算法可以使用上半年/ de-composed下半年的方法,叫做频率FFT大批杀害。
才在时间和大量毁灭的频率可以使用相同的方法实现只蝴蝶结构是不同的,如上图所示。

% 16点FFT
%反转输出....
%大量毁灭的频率
清除所有;
关闭所有;
clc;
%输入系数
x0 = 1 + i * 1;
x1 = 2 + i * 1;
x2 = 1 - i * 2;
x3 = 2——我* 1;
x4 = 2 + i * 3;
x5 = 3 + i * 2;
x6 = 1 + i * 3;
x7 = 3 + i * 1;
×8 = 3 + i * 3;
x9 = 3 -我* 3;
x10 = 1 - i * 1;
x11 = 3 -我* 3;
x12 = 3 -我* 3;
* 13 = 1 - i * 1;
= 3,我* 3;
连接= 1 + i * 1;
x = (x0, x1, x2, x3, x4, x5;
x6;x7;的混合体;x9;x10;x11;
x12; * 13;x14; x15];
%抚弄因素
%第三阶段
tc0 = 1.0000;
tc1 = 0.9239 - 0.3827我;
tc2 = 0.7071 - 0.7071我;
tc3 = 0.3827 - 0.9239我;
tc4 = 0.0000 - 1.0000我;
tc5 = -0.3827 - 0.9239我;
tc6 = -0.7071 - 0.7071我;
tc7 = -0.9239 - 0.3827我;
%抚弄因素
% 2阶段
tb0 = 1.0000;
tb1 = 0.7071 - 0.7071我;
tb2 = 0.0000 - 1.0000我;
tb3 = -0.7071 - 0.7071我;
% 1阶段
ta0 = 1.0000;
ta1 = 0.0000 - 1.0000我;
% %第三阶段输出
s3_0 = x0 +的混合体;
s3_1 = x1 + x9;
s3_2 = x2 + x10;
s3_3 = x3 + x11;
s3_4 = x4 + x12;
s3_5 = * + * 13;
s3_6 = x6 + x14;
s3_7 = x7 +连接;
s3_8 = (x0 -×8) * tc0;
s3_9 = (x1 - x9) * tc1;
s3_10 = (x2 - x10) * tc2;
s3_11 = (x3 (x11) * tc3;
s3_12 = (x4 - x12) * tc4;
s3_13 = (x5 - * 13) * tc5;
s3_14 = (x6 - x14英寸)* tc6;
s3_15 = (x7 - x15) * tc7;
Stage3 = [s3_0; s3_1; s3_2 s3_3; s3_4;
s3_5; s3_6 s3_7; s3_8 s3_9;
s3_10; s3_11 s3_12;
s3_13; s3_14 s3_15];
% %第二阶段输出
s2_0 = s3_0 + s3_4;
s2_1 = s3_1 + s3_5;
s2_2 = s3_2 + s3_6;
s2_3 = s3_3 + s3_7;
s2_4 = (s3_0 - s3_4) * tb0;
s2_5 = (s3_1 - s3_5) * tb1;
s2_6 = (s3_2 - s3_6) * tb2;
s2_7 = (s3_3 - s3_7) * tb3;
s2_8 = s3_8 + s3_12;
s2_9 = s3_9 + s3_13;
s2_10 = s3_10 + s3_14;
s2_11 = s3_11 + s3_15;
s2_12 = (s3_8 - s3_12) * tb0;
s2_13 = (s3_9 - s3_13) * tb1;
s2_14 = (s3_10 - s3_14) * tb2;
s2_15 = (s3_11 - s3_15) * tb3;
Stage2 = [s2_0; s2_1; s2_2 s2_3; s2_4;
s2_5; s2_6 s2_7; s2_8 s2_9;
s2_10; s2_11 s2_12;
s2_13; s2_14 s2_15];
% %第一阶段
s1_0 = s2_0 + s2_2;
s1_1 = s2_1 + s2_3;
s1_2 = (s2_0 - s2_2) * ta0;
s1_3 = (s2_1 - s2_3) * ta1;
s1_4 = s2_4 + s2_6;
s1_5 = s2_5 + s2_7;
s1_6 = (s2_4 - s2_6) * ta0;
s1_7 = (s2_5 - s2_7) * ta1;
s1_8 = s2_8 + s2_10;
s1_9 = s2_9 + s2_11;
s1_10 = (s2_8 - s2_10) * ta0;
s1_11 = (s2_9 - s2_11) * ta1;
s1_12 = s2_12 + s2_14;
s1_13 = s2_13 + s2_15;
s1_14 = (s2_12 - s2_14) * ta0;
s1_15 = (s2_13 - s2_15) * ta1;
% % 0阶段
s0_0 = s1_0 + s1_1;
s0_1 = s1_0 - s1_1;
s0_2 = s1_2 + s1_3;
s0_3 = s1_2 - s1_3;
s0_4 = s1_4 + s1_5;
s0_5 = s1_4 - s1_5;
s0_6 = s1_6 + s1_7;
s0_7 = s1_6 - s1_7;
s0_8 = s1_8 + s1_9;
s0_9 = s1_8 - s1_9;
s0_10 = s1_10 + s1_11;
s0_11 = s1_10 - s1_11;
s0_12 = s1_12 + s1_13;
s0_13 = s1_12 - s1_13;
s0_14 = s1_14 + s1_15;
s0_15 = s1_14 - s1_15;
Y = [s0_0; s0_1; s0_2 s0_3; s0_4;
s0_5; s0_6 s0_7; s0_8 s0_9;
s0_10; s0_11 s0_12; s0_13;
s0_14; s0_15);
% i = 0:15;
% de2bi(我);
% D = bi2de (ans left-msb);
% D1 = D + 1;
Y = [(1); Y (9); Y (5); Y (13), Y (3);
(11);Y (7); Y (15); Y (2);
(10);Y (6); Y (14);
(4);Y (12); Y (8); Y (16)];
人物,情节(abs (Y));标题(我们的FFT结果);%绘制我的FFT
%反转输出....
%大量毁灭的频率
清除所有;
关闭所有;
clc;
%输入系数
x0 = 1 + i * 1;
x1 = 2 + i * 1;
x2 = 1 - i * 2;
x3 = 2——我* 1;
x4 = 2 + i * 3;
x5 = 3 + i * 2;
x6 = 1 + i * 3;
x7 = 3 + i * 1;
×8 = 3 + i * 3;
x9 = 3 -我* 3;
x10 = 1 - i * 1;
x11 = 3 -我* 3;
x12 = 3 -我* 3;
* 13 = 1 - i * 1;
= 3,我* 3;
连接= 1 + i * 1;
x = (x0, x1, x2, x3, x4, x5;
x6;x7;的混合体;x9;x10;x11;
x12; * 13;x14; x15];
%抚弄因素
%第三阶段
tc0 = 1.0000;
tc1 = 0.9239 - 0.3827我;
tc2 = 0.7071 - 0.7071我;
tc3 = 0.3827 - 0.9239我;
tc4 = 0.0000 - 1.0000我;
tc5 = -0.3827 - 0.9239我;
tc6 = -0.7071 - 0.7071我;
tc7 = -0.9239 - 0.3827我;
%抚弄因素
% 2阶段
tb0 = 1.0000;
tb1 = 0.7071 - 0.7071我;
tb2 = 0.0000 - 1.0000我;
tb3 = -0.7071 - 0.7071我;
% 1阶段
ta0 = 1.0000;
ta1 = 0.0000 - 1.0000我;
% %第三阶段输出
s3_0 = x0 +的混合体;
s3_1 = x1 + x9;
s3_2 = x2 + x10;
s3_3 = x3 + x11;
s3_4 = x4 + x12;
s3_5 = * + * 13;
s3_6 = x6 + x14;
s3_7 = x7 +连接;
s3_8 = (x0 -×8) * tc0;
s3_9 = (x1 - x9) * tc1;
s3_10 = (x2 - x10) * tc2;
s3_11 = (x3 (x11) * tc3;
s3_12 = (x4 - x12) * tc4;
s3_13 = (x5 - * 13) * tc5;
s3_14 = (x6 - x14英寸)* tc6;
s3_15 = (x7 - x15) * tc7;
Stage3 = [s3_0; s3_1; s3_2 s3_3; s3_4;
s3_5; s3_6 s3_7; s3_8 s3_9;
s3_10; s3_11 s3_12;
s3_13; s3_14 s3_15];
% %第二阶段输出
s2_0 = s3_0 + s3_4;
s2_1 = s3_1 + s3_5;
s2_2 = s3_2 + s3_6;
s2_3 = s3_3 + s3_7;
s2_4 = (s3_0 - s3_4) * tb0;
s2_5 = (s3_1 - s3_5) * tb1;
s2_6 = (s3_2 - s3_6) * tb2;
s2_7 = (s3_3 - s3_7) * tb3;
s2_8 = s3_8 + s3_12;
s2_9 = s3_9 + s3_13;
s2_10 = s3_10 + s3_14;
s2_11 = s3_11 + s3_15;
s2_12 = (s3_8 - s3_12) * tb0;
s2_13 = (s3_9 - s3_13) * tb1;
s2_14 = (s3_10 - s3_14) * tb2;
s2_15 = (s3_11 - s3_15) * tb3;
Stage2 = [s2_0; s2_1; s2_2 s2_3; s2_4;
s2_5; s2_6 s2_7; s2_8 s2_9;
s2_10; s2_11 s2_12;
s2_13; s2_14 s2_15];
% %第一阶段
s1_0 = s2_0 + s2_2;
s1_1 = s2_1 + s2_3;
s1_2 = (s2_0 - s2_2) * ta0;
s1_3 = (s2_1 - s2_3) * ta1;
s1_4 = s2_4 + s2_6;
s1_5 = s2_5 + s2_7;
s1_6 = (s2_4 - s2_6) * ta0;
s1_7 = (s2_5 - s2_7) * ta1;
s1_8 = s2_8 + s2_10;
s1_9 = s2_9 + s2_11;
s1_10 = (s2_8 - s2_10) * ta0;
s1_11 = (s2_9 - s2_11) * ta1;
s1_12 = s2_12 + s2_14;
s1_13 = s2_13 + s2_15;
s1_14 = (s2_12 - s2_14) * ta0;
s1_15 = (s2_13 - s2_15) * ta1;
% % 0阶段
s0_0 = s1_0 + s1_1;
s0_1 = s1_0 - s1_1;
s0_2 = s1_2 + s1_3;
s0_3 = s1_2 - s1_3;
s0_4 = s1_4 + s1_5;
s0_5 = s1_4 - s1_5;
s0_6 = s1_6 + s1_7;
s0_7 = s1_6 - s1_7;
s0_8 = s1_8 + s1_9;
s0_9 = s1_8 - s1_9;
s0_10 = s1_10 + s1_11;
s0_11 = s1_10 - s1_11;
s0_12 = s1_12 + s1_13;
s0_13 = s1_12 - s1_13;
s0_14 = s1_14 + s1_15;
s0_15 = s1_14 - s1_15;
Y = [s0_0; s0_1; s0_2 s0_3; s0_4;
s0_5; s0_6 s0_7; s0_8 s0_9;
s0_10; s0_11 s0_12; s0_13;
s0_14; s0_15);
% i = 0:15;
% de2bi(我);
% D = bi2de (ans left-msb);
% D1 = D + 1;
Y = [(1); Y (9); Y (5); Y (13), Y (3);
(11);Y (7); Y (15); Y (2);
(10);Y (6); Y (14);
(4);Y (12); Y (8); Y (16)];
人物,情节(abs (Y));标题(我们的FFT结果);%绘制我的FFT
MATLAB内置FFT MATLAB函数
Y_fft = fft (x, 16);
图;情节(abs (Y_fft));标题(“MATLAB函数FFT结果”);%绘制matlab的FFT建成的
图;情节(abs (Y_fft));标题(“MATLAB函数FFT结果”);%绘制matlab的FFT建成的
16点FFT MATLAB输出

16点FFT matlab函数输出

MATLAB的有用链接代码
参考以下以及链接提到左侧面板上有用的MATLAB代码。
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