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experimenting with FFT algorithms

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Imants Pulkstenis
2019-10-20 23:04:38 +03:00
parent 7a8135bf30
commit 0a9e0301e1
1 changed files with 196 additions and 128 deletions
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matlab/myfft.m
+196 -128
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@@ -1,10 +1,11 @@
%% FFT algoritm %% FFT algoritm
clear; % clear all data from memmory
start_time = 0; start_time = 0;
number_of_samples = 16; number_of_samples = 8;
end_time = number_of_samples - 1; end_time = number_of_samples - 1;
n = linspace(start_time, end_time , number_of_samples ); n = linspace(start_time, end_time , number_of_samples );
f1 = 5; f1 = 1;
a1 = 0.2; a1 = 0.2;
f2 = 2; f2 = 2;
@@ -12,7 +13,7 @@ a2 = 00;
f3 = 1; f3 = 1;
a3 = 00; a3 = 00;
comp1 = a1 * sin( f1 *2*pi*n/number_of_samples); comp1 = a1 * cos( f1 *2*pi*n/number_of_samples);
comp2 = a2 * sin( f2 *2*pi*n/number_of_samples); comp2 = a2 * sin( f2 *2*pi*n/number_of_samples);
comp3 = a3 * sin( f3 *2*pi*n/number_of_samples); comp3 = a3 * sin( f3 *2*pi*n/number_of_samples);
@@ -61,165 +62,232 @@ end
% First stage of FFT % First stage of FFT
s_1_2 = zeros(1,number_of_samples);
stage = zeros(bits,number_of_samples); stage = zeros(bits,number_of_samples);
for i=1:number_of_samples for i=1:number_of_samples
if rem(i-1,2) == 0 % odd or even stage(1,i) = data((i));
stage(1,i) = data(rev_bit_dec(i)) + data(rev_bit_dec(i+1));
else
stage(1,i) = data(rev_bit_dec(i)) - data(rev_bit_dec(i-1));
end
end end
% s_1_2(1) = data(rev_bit_dec(1)) + data(rev_bit_dec(2));
% s_1_2(2) = data(rev_bit_dec(2)) - data(rev_bit_dec(1));
%
% s_1_2(3) = data(rev_bit_dec(3)) + data(rev_bit_dec(4));
% s_1_2(4) = data(rev_bit_dec(4)) - data(rev_bit_dec(3));
%
% s_1_2(5) = data(rev_bit_dec(5)) + data(rev_bit_dec(6));
% s_1_2(6) = data(rev_bit_dec(6)) - data(rev_bit_dec(5));
%
% s_1_2(7) = data(rev_bit_dec(7)) + data(rev_bit_dec(8));
% s_1_2(8) = data(rev_bit_dec(8)) - data(rev_bit_dec(7));
%
% s_1_2(9) = data(rev_bit_dec(9)) + data(rev_bit_dec(10));
% s_1_2(10) = data(rev_bit_dec(10)) - data(rev_bit_dec(9));
%
% s_1_2(11) = data(rev_bit_dec(11)) + data(rev_bit_dec(12));
% s_1_2(12) = data(rev_bit_dec(12)) - data(rev_bit_dec(11));
%
% s_1_2(13) = data(rev_bit_dec(13)) + data(rev_bit_dec(14));
% s_1_2(14) = data(rev_bit_dec(14)) - data(rev_bit_dec(13));
%
% s_1_2(15) = data(rev_bit_dec(15)) + data(rev_bit_dec(16));
% s_1_2(16) = data(rev_bit_dec(16)) - data(rev_bit_dec(15));
% s_1_2(1) = data(1) + data(5); stage(2,1) = stage(1,1) + stage(1,2);
% s_1_2(2) = data(5) - data(1); stage(2,2) = stage(1,1) - stage(1,2) ;
stage(2,3) = (stage(1,3) + stage(1,4)) * exp(-j * 0 * 2 * pi/ 4 );
stage(2,4) = (stage(1,3) - stage(1,4)) * exp(-j * 1 * 2 * pi/ 4 );
stage(2,5) = stage(1,5) + stage(1,6);
stage(2,6) = stage(1,5) - stage(1,6);
stage(2,7) = (stage(1,7) + stage(1,8)) * exp(-j * 0 * 2 * pi/ 4 );
stage(2,8) = (stage(1,7) - stage(1,8)) * exp(-j * 1 * 2 * pi/ 4 );
% stage(2,9) = stage(1,9) + stage(1,10);
% stage(2,10) = stage(1,9) - stage(1,10);
% %
% s_1_2(3) = data(3) + data(7); % stage(2,11) = (stage(1,11) + stage(1,12)) * exp(-j * 0 * 2 * pi/ 4 );
% s_1_2(4) = data(7) - data(3); % stage(2,12) = (stage(1,11) - stage(1,12)) * exp(-j * 1 * 2 * pi/ 4 );
% %
% s_1_2(5) = data(2) + data(6); % stage(2,13) = stage(1,13) + stage(1,14);
% s_1_2(6) = data(6) - data(2); % stage(2,14) = stage(1,13) - stage(1,14);
% %
% s_1_2(7) = data(4) + data(8); % stage(2,15) = (stage(1,15) + stage(1,16)) * exp(-j * 0 * 2 * pi/ 4 );
% s_1_2(8) = data(8) - data(4); % stage(2,16) = (stage(1,15) - stage(1,16)) * exp(-j * 1 * 2 * pi/ 4 );
% stage(2,17) = stage(1,17) + stage(1,18);
% stage(2,18) = stage(1,17) - stage(1,18)) * exp(-j * 1 * 2 * pi/ 4 );
%
% stage(2,19) = stage(1,19) + stage(1,20);
% stage(2,20) = stage(1,19) - stage(1,20)) * exp(-j * 1 * 2 * pi/ 4 );
%
% stage(2,21) = stage(1,21) + stage(1,22);
% stage(2,22) = stage(1,21) - stage(1,22);
%
% stage(2,23) = stage(1,23) + stage(1,24);
% stage(2,24) = stage(1,23) - stage(1,24);
%
% stage(2,25) = stage(1,25) + stage(1,26);
% stage(2,26) = stage(1,25) - stage(1,26);
%
% stage(2,27) = stage(1,27) + stage(1,28);
% stage(2,28) = stage(1,27) - stage(1,28);
%
% stage(2,29) = stage(1,29) + stage(1,30);
% stage(2,30) = stage(1,29) - stage(1,30);
%
% stage(2,31) = stage(1,31) + stage(1,32);
% stage(2,32) = stage(1,31) - stage(1,32);
% s_1_2,
% stage, % stage,
% Second stage % Second stage
s_2_3 = zeros(1,number_of_samples);
s_2_3(1) = s_1_2(1) + W(1) * s_1_2(3); stage(2,1) = stage(1,1) + stage(1,3);
s_2_3(2) = s_1_2(2) + W(3) * s_1_2(4); stage(2,2) = stage(1,2) + stage(1,4);
s_2_3(3) = s_1_2(3) + W(5) * s_1_2(1); stage(2,3) = stage(1,1) - stage(1,3);
s_2_3(4) = s_1_2(4) + W(7) * s_1_2(2); stage(2,4) = stage(1,2) - stage(1,4);
s_2_3(5) = s_1_2(5) + W(1) * s_1_2(7); stage(2,5) = (stage(1,5) + stage(1,7)) * exp(-j * 0 * 2 * pi/ 8 );
s_2_3(6) = s_1_2(6) + W(3) * s_1_2(8); stage(2,6) = (stage(1,6) + stage(1,8)) * exp(-j * 1 * 2 * pi/ 8 );
s_2_3(7) = s_1_2(7) + W(5) * s_1_2(5); stage(2,7) = (stage(1,5) - stage(1,7)) * exp(-j * 2 * 2 * pi/ 8 );
s_2_3(8) = s_1_2(8) + W(7) * s_1_2(6); stage(2,8) = (stage(1,6) - stage(1,8)) * exp(-j * 3 * 2 * pi/ 8 );
% stage(2,9) = stage(1,9) + stage(1,11);
% stage(2,10) = stage(1,10) + stage(1,12);
% stage(2,11) = stage(1,9) - stage(1,11);
% stage(2,12) = stage(1,10) - stage(1,12);
%
% stage(2,13) = (stage(1,13) + stage(1,15)) * exp(-j * 0 * 2 * pi/ 8 );
% stage(2,14) = (stage(1,14) + stage(1,16)) * exp(-j * 1 * 2 * pi/ 8 );
% stage(2,15) = (stage(1,13) - stage(1,15)) * exp(-j * 2 * 2 * pi/ 8 );
% stage(2,16) = (stage(1,14) - stage(1,16)) * exp(-j * 3 * 2 * pi/ 8 );
W1 = zeros(1,4); % complex % stage(2,17) = stage(1,17) + 1 * stage(1,19);
for i = 1 : 4 % stage(2,18) = stage(1,18) + 1 * stage(1,20);
W1(i) = exp(-j * (i-1) * 2 * pi/ 4 ); % stage(2,19) = stage(1,19) - W1(1) * stage(1,17);
end % stage(2,20) = stage(1,20) - W1(2) * stage(1,18);
%
stage(2,1) = stage(1,1) + W1(1) * stage(1,3); % stage(2,21) = stage(1,21) + 1 * stage(1,23);
stage(2,2) = stage(1,2) + W1(2) * stage(1,4); % stage(2,22) = stage(1,22) + 1 * stage(1,24);
stage(2,3) = stage(1,3) - W1(1) * stage(1,1); % stage(2,23) = stage(1,23) - W1(1) * stage(1,21);
stage(2,4) = stage(1,4) - W1(2) * stage(1,2); % stage(2,24) = stage(1,24) - W1(2) * stage(1,22);
%
stage(2,5) = stage(1,5) + W1(1) * stage(1,7); % stage(2,25) = stage(1,25) + 1 * stage(1,27);
stage(2,6) = stage(1,6) + W1(2) * stage(1,8); % stage(2,26) = stage(1,26) + 1 * stage(1,28);
stage(2,7) = stage(1,7) - W1(1) * stage(1,5); % stage(2,27) = stage(1,27) - W1(1) * stage(1,25);
stage(2,8) = stage(1,8) - W1(2) * stage(1,6); % stage(2,28) = stage(1,28) - W1(2) * stage(1,26);
%
stage(2,9) = stage(1,9) + W1(1) * stage(1,11); % stage(2,29) = stage(1,29) + 1 * stage(1,31);
stage(2,10) = stage(1,10) + W1(2) * stage(1,12); % stage(2,30) = stage(1,30) + 1 * stage(1,32);
stage(2,11) = stage(1,11) - W1(1) * stage(1,9); % stage(2,31) = stage(1,31) - W1(1) * stage(1,29);
stage(2,12) = stage(1,12) - W1(2) * stage(1,10); % stage(2,32) = stage(1,32) - W1(2) * stage(1,30);
stage(2,13) = stage(1,13) + W1(1) * stage(1,15);
stage(2,14) = stage(1,14) + W1(2) * stage(1,16);
stage(2,15) = stage(1,15) - W1(1) * stage(1,13);
stage(2,16) = stage(1,16) - W1(2) * stage(1,14);
% theard stage % theard stage
s_3_4 = zeros(1,number_of_samples);
s_3_4(1) = s_2_3(1) + W(1) * s_2_3(5); stage(3,1) = stage(2,1) + stage(2,5);
s_3_4(2) = s_2_3(2) + W(2) * s_2_3(6); stage(3,2) = stage(2,2) + stage(2,6);
stage(3,3) = stage(2,3) + stage(2,7);
stage(3,4) = stage(2,4) + stage(2,8);
stage(3,5) = stage(2,1) - stage(2,5);
stage(3,6) = stage(2,2) - stage(2,6);
stage(3,7) = stage(2,3) - stage(2,7);
stage(3,8) = stage(2,4) - stage(2,8);
s_3_4(3) = s_2_3(3) + W(3) * s_2_3(7); % stage(3,9) = (stage(2,9) + stage(2,13)) * exp(-j * 0 * 2 * pi/ 16 );
s_3_4(4) = s_2_3(4) + W(4) * s_2_3(8); % stage(3,10) = (stage(2,10) + stage(2,14)) * exp(-j * 1 * 2 * pi/ 16 );
% stage(3,11) = (stage(2,11) + stage(2,15)) * exp(-j * 2 * 2 * pi/ 16 );
% stage(3,12) = (stage(2,12) + stage(2,16)) * exp(-j * 3 * 2 * pi/ 16 );
% stage(3,13) = (stage(2,9) - stage(2,13)) * exp(-j * 4 * 2 * pi/ 16 );
% stage(3,14) = (stage(2,10) - stage(2,14)) * exp(-j * 5 * 2 * pi/ 16 );
% stage(3,15) = (stage(2,11) - stage(2,15)) * exp(-j * 6 * 2 * pi/ 16 );
% stage(3,16) = (stage(2,12) - stage(2,16)) * exp(-j * 7 * 2 * pi/ 16 );
s_3_4(5) = s_2_3(5) + W(5) * s_2_3(1);
s_3_4(6) = s_2_3(6) + W(6) * s_2_3(2);
s_3_4(7) = s_2_3(7) + W(7) * s_2_3(3); % stage(3,17) = stage(2,17) + W2(1) * stage(2,21);
s_3_4(8) = s_2_3(8) + W(8) * s_2_3(4); % stage(3,18) = stage(2,18) + W2(2) * stage(2,22);
% stage(3,19) = stage(2,19) + W2(3) * stage(2,23);
W2 = zeros(1,8); % complex % stage(3,20) = stage(2,20) + W2(4) * stage(2,24);
for i = 1 : 8 % stage(3,21) = stage(2,21) - W2(1) * stage(2,17);
W2(i) = exp(-j * (i-1) * 2 * pi/ 8 ); % stage(3,22) = stage(2,22) - W2(2) * stage(2,18);
end % stage(3,23) = stage(2,23) - W2(3) * stage(2,19);
% stage(3,24) = stage(2,24) - W2(4) * stage(2,20);
stage(3,1) = stage(2,1) + W2(1) * stage(2,5); %
stage(3,2) = stage(2,2) + W2(2) * stage(2,6); % stage(3,25) = stage(2,25) + W2(1) * stage(2,29);
stage(3,3) = stage(2,3) + W2(3) * stage(2,7); % stage(3,26) = stage(2,26) + W2(2) * stage(2,30);
stage(3,4) = stage(2,4) + W2(4) * stage(2,8); % stage(3,27) = stage(2,27) + W2(3) * stage(2,31);
stage(3,5) = stage(2,5) - W2(1) * stage(2,1); % stage(3,28) = stage(2,28) + W2(4) * stage(2,32);
stage(3,6) = stage(2,6) - W2(2) * stage(2,2); % stage(3,29) = stage(2,29) - W2(1) * stage(2,25);
stage(3,7) = stage(2,7) - W2(3) * stage(2,3); % stage(3,30) = stage(2,30) - W2(2) * stage(2,26);
stage(3,8) = stage(2,8) - W2(4) * stage(2,4); % stage(3,31) = stage(2,31) - W2(3) * stage(2,27);
% stage(3,32) = stage(2,32) - W2(4) * stage(2,28);
stage(3,9) = stage(2,9) + W2(1) * stage(2,13);
stage(3,10) = stage(2,10) + W2(2) * stage(2,14);
stage(3,11) = stage(2,11) + W2(3) * stage(2,15);
stage(3,12) = stage(2,12) + W2(4) * stage(2,16);
stage(3,13) = stage(2,13) - W2(1) * stage(2,9);
stage(3,14) = stage(2,14) - W2(2) * stage(2,10);
stage(3,15) = stage(2,15) - W2(3) * stage(2,11);
stage(3,16) = stage(2,16) - W2(4) * stage(2,12);
% Fourt stage % Fourt stage
W3 = zeros(1,16); % complex %
for i = 1 : 16 % stage(4,1) = stage(3,1) + stage(3,9);
W3(i) = exp(-j * (i-1) * 2 * pi/ 16 ); % stage(4,2) = stage(3,2) + stage(3,10);
end % stage(4,3) = stage(3,3) + stage(3,11);
% stage(4,4) = stage(3,4) + stage(3,12);
% stage(4,5) = stage(3,5) + stage(3,13);
% stage(4,6) = stage(3,6) + stage(3,14);
% stage(4,7) = stage(3,7) + stage(3,15);
% stage(4,8) = stage(3,8) + stage(3,16);
% stage(4,9) = stage(3,1) - stage(3,9);
% stage(4,10) = stage(3,2) - stage(3,10);
% stage(4,11) = stage(3,3) - stage(3,11);
% stage(4,12) = stage(3,4) - stage(3,12);
% stage(4,13) = stage(3,5) - stage(3,13);
% stage(4,14) = stage(3,6) - stage(3,14);
% stage(4,15) = stage(3,7) - stage(3,15);
% stage(4,16) = stage(3,8) - stage(3,16);
% stage(4,17) = stage(3,17) + W3(1) * stage(3,25);
% stage(4,18) = stage(3,18) + W3(2) * stage(3,26);
% stage(4,19) = stage(3,19) + W3(3) * stage(3,27);
% stage(4,20) = stage(3,20) + W3(4) * stage(3,28);
% stage(4,21) = stage(3,21) + W3(5) * stage(3,29);
% stage(4,22) = stage(3,22) + W3(6) * stage(3,30);
% stage(4,23) = stage(3,23) + W3(7) * stage(3,31);
% stage(4,24) = stage(3,24) + W3(8) * stage(3,32);
% stage(4,25) = stage(3,25) - W3(1) * stage(3,17);
% stage(4,26) = stage(3,26) - W3(2) * stage(3,18);
% stage(4,27) = stage(3,27) - W3(3) * stage(3,19);
% stage(4,28) = stage(3,28) - W3(4) * stage(3,20);
% stage(4,29) = stage(3,29) - W3(5) * stage(3,21);
% stage(4,30) = stage(3,30) - W3(6) * stage(3,22);
% stage(4,31) = stage(3,31) - W3(7) * stage(3,23);
% stage(4,32) = stage(3,32) - W3(8) * stage(3,24);
% Fifth stage
% W4 = zeros(1,32); % complex
% for i = 1 : 32
% W4(i) = exp(-j * (i-1) * 2 * pi/ 32 );
% end
%
% stage(5,1) = stage(4,1) + W4(1) * stage(4,17);
% stage(5,2) = stage(4,2) + W4(2) * stage(4,18);
% stage(5,3) = stage(4,3) + W4(3) * stage(4,19);
% stage(5,4) = stage(4,4) + W4(4) * stage(4,20);
% stage(5,5) = stage(4,5) + W4(5) * stage(4,21);
% stage(5,6) = stage(4,6) + W4(6) * stage(4,22);
% stage(5,7) = stage(4,7) + W4(7) * stage(4,23);
% stage(5,8) = stage(4,8) + W4(8) * stage(4,24);
% stage(5,9) = stage(4,9) + W4(9) * stage(4,25);
% stage(5,10) = stage(4,10) + W4(10) * stage(4,26);
% stage(5,11) = stage(4,11) + W4(11) * stage(4,27);
% stage(5,12) = stage(4,12) + W4(12) * stage(4,28);
% stage(5,13) = stage(4,13) + W4(13) * stage(4,29);
% stage(5,14) = stage(4,14) + W4(14) * stage(4,30);
% stage(5,15) = stage(4,15) + W4(15) * stage(4,31);
% stage(5,16) = stage(4,16) + W4(16) * stage(4,32);
% stage(5,17) = stage(4,17) - W4(1) * stage(4,1);
% stage(5,18) = stage(4,18) - W4(2) * stage(4,2);
% stage(5,19) = stage(4,19) - W4(3) * stage(4,3);
% stage(5,20) = stage(4,20) - W4(4) * stage(4,4);
% stage(5,21) = stage(4,21) - W4(5) * stage(4,5);
% stage(5,22) = stage(4,22) - W4(6) * stage(4,6);
% stage(5,23) = stage(4,23) - W4(7) * stage(4,7);
% stage(5,24) = stage(4,24) - W4(8) * stage(4,8);
% stage(5,25) = stage(4,25) - W4(9) * stage(4,9);
% stage(5,26) = stage(4,26) - W4(10) * stage(4,10);
% stage(5,27) = stage(4,27) - W4(11) * stage(4,11);
% stage(5,28) = stage(4,28) - W4(12) * stage(4,12);
% stage(5,29) = stage(4,29) - W4(13) * stage(4,13);
% stage(5,30) = stage(4,30) - W4(14) * stage(4,14);
% stage(5,31) = stage(4,31) - W4(15) * stage(4,15);
% stage(5,32) = stage(4,32) - W4(16) * stage(4,16);
stage(4,1) = stage(3,1) + W3(1) * stage(3,9);
stage(4,2) = stage(3,2) + W3(2) * stage(3,10);
stage(4,3) = stage(3,3) + W3(3) * stage(3,11);
stage(4,4) = stage(3,4) + W3(4) * stage(3,12);
stage(4,5) = stage(3,5) + W3(5) * stage(3,13);
stage(4,6) = stage(3,6) + W3(6) * stage(3,14);
stage(4,7) = stage(3,7) + W3(7) * stage(3,15);
stage(4,8) = stage(3,8) + W3(8) * stage(3,16);
stage(4,9) = stage(3,9) - W3(1) * stage(3,1);
stage(4,10) = stage(3,10) - W3(2) * stage(3,2);
stage(4,11) = stage(3,11) - W3(3) * stage(3,3);
stage(4,12) = stage(3,12) - W3(4) * stage(3,4);
stage(4,13) = stage(3,13) - W3(5) * stage(3,5);
stage(4,14) = stage(3,14) - W3(6) * stage(3,6);
stage(4,15) = stage(3,15) - W3(7) * stage(3,7);
stage(4,16) = stage(3,16) - W3(8) * stage(3,8);
figure(4) figure(4)
stem(n, abs( stage(4,:) ) ) stem(n, abs( stage(bits,:) ) )