296 lines
9.7 KiB
Matlab
296 lines
9.7 KiB
Matlab
%% FFT algoritm
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clear; % clear all data from memmory
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start_time = 0;
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number_of_samples = 8;
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end_time = number_of_samples - 1;
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n = linspace(start_time, end_time , number_of_samples );
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f1 = 1;
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a1 = 0.2;
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f2 = 2;
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a2 = 00;
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f3 = 1;
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a3 = 00;
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comp1 = a1 * cos( f1 *2*pi*n/number_of_samples);
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comp2 = a2 * sin( f2 *2*pi*n/number_of_samples);
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comp3 = a3 * sin( f3 *2*pi*n/number_of_samples);
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data = comp1 + comp2 + comp3;
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figure(1)
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plot (n, comp1, '-');
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hold on;
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plot (n, comp2, '-');
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plot (n, comp3, '-');
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hold off;
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figure(2)
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plot (n, data);
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figure(3)
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X_matlab = fft(data, number_of_samples);
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stem (n,abs(X_matlab))
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%% My FFT
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% W_N vector calculation
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% W = zeros(1,number_of_samples); % complex
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% Wr = zeros(1,number_of_samples); % real
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% Wi = zeros(1,number_of_samples); % imag
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% for i = 1 : number_of_samples
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% W(i) = exp(-j * (i-1) * 2 * pi/ number_of_samples );
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% Wr(i) = real(W(i));
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% Wi(i) = imag(W(i));
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% end
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% reverse bit calulation
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bits = length(dec2bin( number_of_samples - 1 ));
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rev_bit_dec = zeros(1,number_of_samples);
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for i=1:number_of_samples
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bin_num = dec2bin(i-1 , bits);
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rev_bit = [];
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for k=bits:-1:1
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rev_bit = [rev_bit , bin_num(k)];
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end
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rev_bit_dec(i) = bin2dec(rev_bit) + 1; % add 1 to match Matlab numbering
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end
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% First stage of FFT
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stage = zeros(bits,number_of_samples);
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for i=1:number_of_samples
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stage(1,i) = data((i));
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end
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stage(2,1) = stage(1,1) + stage(1,2);
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stage(2,2) = stage(1,1) - stage(1,2) ;
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stage(2,3) = (stage(1,3) + stage(1,4)) * exp(-j * 0 * 2 * pi/ 4 );
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stage(2,4) = (stage(1,3) - stage(1,4)) * exp(-j * 1 * 2 * pi/ 4 );
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stage(2,5) = stage(1,5) + stage(1,6);
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stage(2,6) = stage(1,5) - stage(1,6);
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stage(2,7) = (stage(1,7) + stage(1,8)) * exp(-j * 0 * 2 * pi/ 4 );
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stage(2,8) = (stage(1,7) - stage(1,8)) * exp(-j * 1 * 2 * pi/ 4 );
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% stage(2,9) = stage(1,9) + stage(1,10);
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% stage(2,10) = stage(1,9) - stage(1,10);
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%
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% stage(2,11) = (stage(1,11) + stage(1,12)) * exp(-j * 0 * 2 * pi/ 4 );
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% stage(2,12) = (stage(1,11) - stage(1,12)) * exp(-j * 1 * 2 * pi/ 4 );
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%
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% stage(2,13) = stage(1,13) + stage(1,14);
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% stage(2,14) = stage(1,13) - stage(1,14);
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%
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% stage(2,15) = (stage(1,15) + stage(1,16)) * exp(-j * 0 * 2 * pi/ 4 );
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% stage(2,16) = (stage(1,15) - stage(1,16)) * exp(-j * 1 * 2 * pi/ 4 );
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% stage(2,17) = stage(1,17) + stage(1,18);
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% stage(2,18) = stage(1,17) - stage(1,18)) * exp(-j * 1 * 2 * pi/ 4 );
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%
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% stage(2,19) = stage(1,19) + stage(1,20);
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% stage(2,20) = stage(1,19) - stage(1,20)) * exp(-j * 1 * 2 * pi/ 4 );
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%
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% stage(2,21) = stage(1,21) + stage(1,22);
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% stage(2,22) = stage(1,21) - stage(1,22);
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%
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% stage(2,23) = stage(1,23) + stage(1,24);
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% stage(2,24) = stage(1,23) - stage(1,24);
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%
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% stage(2,25) = stage(1,25) + stage(1,26);
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% stage(2,26) = stage(1,25) - stage(1,26);
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%
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% stage(2,27) = stage(1,27) + stage(1,28);
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% stage(2,28) = stage(1,27) - stage(1,28);
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%
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% stage(2,29) = stage(1,29) + stage(1,30);
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% stage(2,30) = stage(1,29) - stage(1,30);
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%
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% stage(2,31) = stage(1,31) + stage(1,32);
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% stage(2,32) = stage(1,31) - stage(1,32);
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% stage,
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% Second stage
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stage(2,1) = stage(1,1) + stage(1,3);
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stage(2,2) = stage(1,2) + stage(1,4);
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stage(2,3) = stage(1,1) - stage(1,3);
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stage(2,4) = stage(1,2) - stage(1,4);
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stage(2,5) = (stage(1,5) + stage(1,7)) * exp(-j * 0 * 2 * pi/ 8 );
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stage(2,6) = (stage(1,6) + stage(1,8)) * exp(-j * 1 * 2 * pi/ 8 );
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stage(2,7) = (stage(1,5) - stage(1,7)) * exp(-j * 2 * 2 * pi/ 8 );
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stage(2,8) = (stage(1,6) - stage(1,8)) * exp(-j * 3 * 2 * pi/ 8 );
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% stage(2,9) = stage(1,9) + stage(1,11);
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% stage(2,10) = stage(1,10) + stage(1,12);
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% stage(2,11) = stage(1,9) - stage(1,11);
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% stage(2,12) = stage(1,10) - stage(1,12);
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%
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% stage(2,13) = (stage(1,13) + stage(1,15)) * exp(-j * 0 * 2 * pi/ 8 );
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% stage(2,14) = (stage(1,14) + stage(1,16)) * exp(-j * 1 * 2 * pi/ 8 );
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% stage(2,15) = (stage(1,13) - stage(1,15)) * exp(-j * 2 * 2 * pi/ 8 );
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% stage(2,16) = (stage(1,14) - stage(1,16)) * exp(-j * 3 * 2 * pi/ 8 );
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% stage(2,17) = stage(1,17) + 1 * stage(1,19);
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% stage(2,18) = stage(1,18) + 1 * stage(1,20);
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% stage(2,19) = stage(1,19) - W1(1) * stage(1,17);
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% stage(2,20) = stage(1,20) - W1(2) * stage(1,18);
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%
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% stage(2,21) = stage(1,21) + 1 * stage(1,23);
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% stage(2,22) = stage(1,22) + 1 * stage(1,24);
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% stage(2,23) = stage(1,23) - W1(1) * stage(1,21);
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% stage(2,24) = stage(1,24) - W1(2) * stage(1,22);
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%
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% stage(2,25) = stage(1,25) + 1 * stage(1,27);
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% stage(2,26) = stage(1,26) + 1 * stage(1,28);
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% stage(2,27) = stage(1,27) - W1(1) * stage(1,25);
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% stage(2,28) = stage(1,28) - W1(2) * stage(1,26);
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%
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% stage(2,29) = stage(1,29) + 1 * stage(1,31);
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% stage(2,30) = stage(1,30) + 1 * stage(1,32);
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% stage(2,31) = stage(1,31) - W1(1) * stage(1,29);
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% stage(2,32) = stage(1,32) - W1(2) * stage(1,30);
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% theard stage
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stage(3,1) = stage(2,1) + stage(2,5);
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stage(3,2) = stage(2,2) + stage(2,6);
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stage(3,3) = stage(2,3) + stage(2,7);
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stage(3,4) = stage(2,4) + stage(2,8);
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stage(3,5) = stage(2,1) - stage(2,5);
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stage(3,6) = stage(2,2) - stage(2,6);
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stage(3,7) = stage(2,3) - stage(2,7);
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stage(3,8) = stage(2,4) - stage(2,8);
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% stage(3,9) = (stage(2,9) + stage(2,13)) * exp(-j * 0 * 2 * pi/ 16 );
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% stage(3,10) = (stage(2,10) + stage(2,14)) * exp(-j * 1 * 2 * pi/ 16 );
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% stage(3,11) = (stage(2,11) + stage(2,15)) * exp(-j * 2 * 2 * pi/ 16 );
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% stage(3,12) = (stage(2,12) + stage(2,16)) * exp(-j * 3 * 2 * pi/ 16 );
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% stage(3,13) = (stage(2,9) - stage(2,13)) * exp(-j * 4 * 2 * pi/ 16 );
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% stage(3,14) = (stage(2,10) - stage(2,14)) * exp(-j * 5 * 2 * pi/ 16 );
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% stage(3,15) = (stage(2,11) - stage(2,15)) * exp(-j * 6 * 2 * pi/ 16 );
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% stage(3,16) = (stage(2,12) - stage(2,16)) * exp(-j * 7 * 2 * pi/ 16 );
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% stage(3,17) = stage(2,17) + W2(1) * stage(2,21);
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% stage(3,18) = stage(2,18) + W2(2) * stage(2,22);
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% stage(3,19) = stage(2,19) + W2(3) * stage(2,23);
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% stage(3,20) = stage(2,20) + W2(4) * stage(2,24);
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% stage(3,21) = stage(2,21) - W2(1) * stage(2,17);
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% stage(3,22) = stage(2,22) - W2(2) * stage(2,18);
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% stage(3,23) = stage(2,23) - W2(3) * stage(2,19);
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% stage(3,24) = stage(2,24) - W2(4) * stage(2,20);
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%
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% stage(3,25) = stage(2,25) + W2(1) * stage(2,29);
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% stage(3,26) = stage(2,26) + W2(2) * stage(2,30);
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% stage(3,27) = stage(2,27) + W2(3) * stage(2,31);
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% stage(3,28) = stage(2,28) + W2(4) * stage(2,32);
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% stage(3,29) = stage(2,29) - W2(1) * stage(2,25);
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% stage(3,30) = stage(2,30) - W2(2) * stage(2,26);
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% stage(3,31) = stage(2,31) - W2(3) * stage(2,27);
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% stage(3,32) = stage(2,32) - W2(4) * stage(2,28);
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% Fourt stage
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%
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% stage(4,1) = stage(3,1) + stage(3,9);
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% stage(4,2) = stage(3,2) + stage(3,10);
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% stage(4,3) = stage(3,3) + stage(3,11);
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% stage(4,4) = stage(3,4) + stage(3,12);
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% stage(4,5) = stage(3,5) + stage(3,13);
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% stage(4,6) = stage(3,6) + stage(3,14);
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% stage(4,7) = stage(3,7) + stage(3,15);
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% stage(4,8) = stage(3,8) + stage(3,16);
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% stage(4,9) = stage(3,1) - stage(3,9);
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% stage(4,10) = stage(3,2) - stage(3,10);
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% stage(4,11) = stage(3,3) - stage(3,11);
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% stage(4,12) = stage(3,4) - stage(3,12);
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% stage(4,13) = stage(3,5) - stage(3,13);
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% stage(4,14) = stage(3,6) - stage(3,14);
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% stage(4,15) = stage(3,7) - stage(3,15);
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% stage(4,16) = stage(3,8) - stage(3,16);
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% stage(4,17) = stage(3,17) + W3(1) * stage(3,25);
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% stage(4,18) = stage(3,18) + W3(2) * stage(3,26);
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% stage(4,19) = stage(3,19) + W3(3) * stage(3,27);
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% stage(4,20) = stage(3,20) + W3(4) * stage(3,28);
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% stage(4,21) = stage(3,21) + W3(5) * stage(3,29);
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% stage(4,22) = stage(3,22) + W3(6) * stage(3,30);
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% stage(4,23) = stage(3,23) + W3(7) * stage(3,31);
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% stage(4,24) = stage(3,24) + W3(8) * stage(3,32);
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% stage(4,25) = stage(3,25) - W3(1) * stage(3,17);
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% stage(4,26) = stage(3,26) - W3(2) * stage(3,18);
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% stage(4,27) = stage(3,27) - W3(3) * stage(3,19);
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% stage(4,28) = stage(3,28) - W3(4) * stage(3,20);
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% stage(4,29) = stage(3,29) - W3(5) * stage(3,21);
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% stage(4,30) = stage(3,30) - W3(6) * stage(3,22);
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% stage(4,31) = stage(3,31) - W3(7) * stage(3,23);
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% stage(4,32) = stage(3,32) - W3(8) * stage(3,24);
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% Fifth stage
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% W4 = zeros(1,32); % complex
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% for i = 1 : 32
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% W4(i) = exp(-j * (i-1) * 2 * pi/ 32 );
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% end
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%
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% stage(5,1) = stage(4,1) + W4(1) * stage(4,17);
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% stage(5,2) = stage(4,2) + W4(2) * stage(4,18);
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% stage(5,3) = stage(4,3) + W4(3) * stage(4,19);
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% stage(5,4) = stage(4,4) + W4(4) * stage(4,20);
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% stage(5,5) = stage(4,5) + W4(5) * stage(4,21);
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% stage(5,6) = stage(4,6) + W4(6) * stage(4,22);
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% stage(5,7) = stage(4,7) + W4(7) * stage(4,23);
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% stage(5,8) = stage(4,8) + W4(8) * stage(4,24);
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% stage(5,9) = stage(4,9) + W4(9) * stage(4,25);
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% stage(5,10) = stage(4,10) + W4(10) * stage(4,26);
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% stage(5,11) = stage(4,11) + W4(11) * stage(4,27);
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% stage(5,12) = stage(4,12) + W4(12) * stage(4,28);
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% stage(5,13) = stage(4,13) + W4(13) * stage(4,29);
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% stage(5,14) = stage(4,14) + W4(14) * stage(4,30);
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% stage(5,15) = stage(4,15) + W4(15) * stage(4,31);
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% stage(5,16) = stage(4,16) + W4(16) * stage(4,32);
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% stage(5,17) = stage(4,17) - W4(1) * stage(4,1);
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% stage(5,18) = stage(4,18) - W4(2) * stage(4,2);
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% stage(5,19) = stage(4,19) - W4(3) * stage(4,3);
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% stage(5,20) = stage(4,20) - W4(4) * stage(4,4);
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% stage(5,21) = stage(4,21) - W4(5) * stage(4,5);
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% stage(5,22) = stage(4,22) - W4(6) * stage(4,6);
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% stage(5,23) = stage(4,23) - W4(7) * stage(4,7);
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% stage(5,24) = stage(4,24) - W4(8) * stage(4,8);
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% stage(5,25) = stage(4,25) - W4(9) * stage(4,9);
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% stage(5,26) = stage(4,26) - W4(10) * stage(4,10);
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% stage(5,27) = stage(4,27) - W4(11) * stage(4,11);
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% stage(5,28) = stage(4,28) - W4(12) * stage(4,12);
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% stage(5,29) = stage(4,29) - W4(13) * stage(4,13);
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% stage(5,30) = stage(4,30) - W4(14) * stage(4,14);
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% stage(5,31) = stage(4,31) - W4(15) * stage(4,15);
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% stage(5,32) = stage(4,32) - W4(16) * stage(4,16);
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figure(4)
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stem(n, abs( stage(bits,:) ) )
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