add matlab files
This commit is contained in:
Imants Pulkstenis
+158
-159
@@ -1,11 +1,11 @@
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%% 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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number_of_samples = 32;
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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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f1 = 2;
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a1 = 0.2;
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f2 = 2;
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@@ -66,7 +66,6 @@ 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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@@ -82,41 +81,41 @@ 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(2,9) = stage(1,9) + stage(1,10);
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stage(2,10) = stage(1,9) - stage(1,10);
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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(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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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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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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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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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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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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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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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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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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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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@@ -134,35 +133,35 @@ 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(2,9) = 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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% 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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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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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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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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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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@@ -176,112 +175,112 @@ 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(3,9) = (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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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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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(4,1) = 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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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);
|
||||
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);
|
||||
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);
|
||||
|
||||
|
||||
|
||||
|
||||
+510
@@ -0,0 +1,510 @@
|
||||
%% FFT algoritm
|
||||
clear; % clears all previus values from memory
|
||||
clc; % clear command window
|
||||
fs = 44100; % samplinf freq.
|
||||
fftLength=512; % windowlength
|
||||
% signal frequencies
|
||||
max = 2048 - 1 ;
|
||||
|
||||
f1 = 430;
|
||||
a1 = 0;
|
||||
|
||||
f2 = 8000;
|
||||
a2 = 0;
|
||||
|
||||
f3 = 8000;
|
||||
a3 = max/2;
|
||||
|
||||
% calculating signals
|
||||
comp1 = a1 * sin(2*pi*f1*[0:1/fs:1]);
|
||||
comp2 = a2 * sin(2*pi*f2*[0:1/fs:1]);
|
||||
comp3 = a3 * sin(2*pi*f3*[0:1/fs:1]);
|
||||
|
||||
% calculatin vector values for step function
|
||||
d1 = ones(1, 24);
|
||||
d2 = 0.*ones(1, 1000 );
|
||||
|
||||
%data = [ d1 , d2]; % creates vector with step function
|
||||
data = comp1 + comp2 + comp3; % creates vector from 3 sin functions
|
||||
|
||||
figure(1) % plots separete sin functions
|
||||
plot ( comp1, '-');
|
||||
hold on;
|
||||
plot ( comp2, '-');
|
||||
plot ( comp3, '-');
|
||||
xlim([1 50])
|
||||
title('Separete SIN functions')
|
||||
ylabel('magnitude'), xlabel('time')
|
||||
hold off;
|
||||
|
||||
figure(2) % plots signal for fft
|
||||
plot ( data);
|
||||
title('Signal for FFT analysis FFT')
|
||||
ylabel('magnitude'), xlabel('time')
|
||||
xlim([1 100])
|
||||
|
||||
figure(3) % plots resultinf fft from Matlab functions
|
||||
ft =fft(data,fftLength);
|
||||
%ftMag=abs(ft(1:fftLength/2));
|
||||
ftMag=abs(ft);
|
||||
plot (ftMag)
|
||||
title('Linear Magnitude FFT')
|
||||
ylabel('magnitude'), xlabel('kHz')
|
||||
|
||||
xt = xticks; % returns the current x-axis tick values as a vector
|
||||
fstep = fs/fftLength; % tick of f axis in f domain
|
||||
xtnew = round(xt*fstep/1000, 1) ; % calculate new tick in kHz
|
||||
xticklabels(xtnew) % set new tick labels
|
||||
|
||||
figure(4) % plots resultinf fft(in dB) from Matlab functions
|
||||
ft =fft(data,fftLength);
|
||||
%ftMag=abs(ft(1:fftLength/2));
|
||||
ftMag=abs(ft);
|
||||
plot (20*log10(ftMag))
|
||||
title('dB Magnitude')
|
||||
ylabel('dB'), xlabel('kHz')
|
||||
|
||||
xt = xticks; % returns the current x-axis tick values as a vector
|
||||
fstep = fs/fftLength; % tick of f axis in f domain
|
||||
xtnew = round(xt*fstep/1000, 1) ; % calculate new tick in kHz
|
||||
xticklabels(xtnew) % set new tick labels
|
||||
|
||||
%% Data preparation for FFT
|
||||
|
||||
% reverse bit calulation
|
||||
bits = length(dec2bin( fftLength - 1 )); % how many bits in binary number
|
||||
rev_bit_dec = zeros(1,fftLength); % create vektor size of fftlength
|
||||
|
||||
for i=1:fftLength
|
||||
bin_num = dec2bin(i-1 , bits); % converting to binary number
|
||||
rev_bit = []; % create empty vector
|
||||
for k=bits:-1:1
|
||||
rev_bit = [rev_bit , bin_num(k)];
|
||||
end
|
||||
rev_bit_dec(i) = bin2dec(rev_bit) + 1; % add 1 to match Matlab numbering
|
||||
end
|
||||
|
||||
% creating array
|
||||
|
||||
real_n = zeros(bits+1,fftLength); % create empty array to store values in reverse bit order
|
||||
imag_n = zeros(bits+1,fftLength);
|
||||
stage = zeros(bits+1,fftLength);
|
||||
%sfi_data = sfi(data,16,0);
|
||||
for i=1:fftLength
|
||||
real_n(1,i) = data(rev_bit_dec(i)+1);
|
||||
stage(1,i) = data(rev_bit_dec(i)+1);
|
||||
end
|
||||
|
||||
|
||||
% % W_N vector calculation
|
||||
% W = zeros(1,fftLength); % complex
|
||||
% Wr = zeros(1,fftLength); % real
|
||||
% Wi = zeros(1,fftLength); % imag
|
||||
% for i = 1 : fftLength
|
||||
% W(i) = exp(-j * (i-1) * 2 * pi/ fftLength );
|
||||
% Wr(i) = sfi(real(W(i)),16,15);
|
||||
% Wi(i) = sfi(imag(W(i)),16,15);
|
||||
% end
|
||||
%
|
||||
% % W(30) = - W(30+256)
|
||||
% % or
|
||||
% % W(x) = - W(x + fftLength/2)
|
||||
|
||||
% new W_N vector calculation this time only half
|
||||
|
||||
W = zeros(1,fftLength/2); % complex
|
||||
Wr = zeros(1,fftLength/2); % real
|
||||
Wi = zeros(1,fftLength/2); % imag
|
||||
for i = 1 : fftLength/2
|
||||
W(i) = exp(-j * (i-1) * 2 * pi/ fftLength );
|
||||
Wr(i) = real(W(i));%sfi(real(W(i)),16,15);
|
||||
Wi(i) = imag(W(i));%sfi(imag(W(i)),16,15);
|
||||
end
|
||||
|
||||
|
||||
%% FFT FSM
|
||||
|
||||
%% First stage
|
||||
|
||||
for i = 1 : 2^1 : fftLength
|
||||
% % % Even
|
||||
% % stage(2,i) = stage(1,i) + stage(1,i+1);
|
||||
% % % Odd
|
||||
% % stage(2,i+1) = stage(1,i) - stage(1,i+1);
|
||||
|
||||
% Even
|
||||
real_n(2,i) = real_n(1,i) + real_n(1,i+1);
|
||||
% Odd
|
||||
real_n(2,i+1) = real_n(1,i) - real_n(1,i+1);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%% Second stage
|
||||
|
||||
% % % Calculating W twiddling factor
|
||||
% % for i = 1 : 2
|
||||
% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 4 );
|
||||
% % end
|
||||
% %
|
||||
% % % calculate next stage values
|
||||
% % for i = 1 : 2^2 : fftLength
|
||||
% % % Even pair
|
||||
% % stage(3,i+0) = stage(2,i+0) + Wn(1)*stage(2,i+2);
|
||||
% % stage(3,i+1) = stage(2,i+1) + Wn(2)*stage(2,i+3);
|
||||
% % % Odd par
|
||||
% % stage(3,i+2) = stage(2,i+0) - Wn(1)*stage(2,i+2);
|
||||
% % stage(3,i+3) = stage(2,i+1) - Wn(2)*stage(2,i+3);
|
||||
% % end
|
||||
|
||||
% Multiply odd pairs with W twiddling factor
|
||||
for i = 1 : 1 : fftLength
|
||||
i_bin = dec2bin(i-1, bits); % calculates "i" in binary
|
||||
|
||||
if i_bin(bits - 1:bits) == '11' % Odd pair odd number(every fourth)
|
||||
|
||||
imag_n(2,i) = -real_n(2,i);
|
||||
real_n(2,i) = 0;
|
||||
% c= real_n(2,i) + j * imag_n(2,i),
|
||||
end
|
||||
end
|
||||
% calculate next stage values
|
||||
for i = 1 : 2^2 : fftLength
|
||||
% Even pair
|
||||
real_n(3,i+0) = real_n(2,i+0) + real_n(2,i+2);
|
||||
real_n(3,i+1) = real_n(2,i+1) + real_n(2,i+3);
|
||||
imag_n(3,i+0) = imag_n(2,i+0) + imag_n(2,i+2);
|
||||
imag_n(3,i+1) = imag_n(2,i+1) + imag_n(2,i+3);
|
||||
% Odd par
|
||||
real_n(3,i+2) = real_n(2,i+0) - real_n(2,i+2);
|
||||
real_n(3,i+3) = real_n(2,i+1) - real_n(2,i+3);
|
||||
imag_n(3,i+2) = imag_n(2,i+0) - imag_n(2,i+2);
|
||||
imag_n(3,i+3) = imag_n(2,i+1) - imag_n(2,i+3);
|
||||
end
|
||||
|
||||
%% Therd stage
|
||||
|
||||
% % % Calculating W twiddling factor
|
||||
% % for i = 1 : 4
|
||||
% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 8 );
|
||||
% % end
|
||||
% %
|
||||
% % % calculate next stage values
|
||||
% % for i = 1 : 2^3 : fftLength
|
||||
% % for k = 0 : 3
|
||||
% % % Even pair
|
||||
% % stage(4,i+k) = stage(3,i+k) + Wn(k+1)*stage(3,i+k+4);
|
||||
% % % Odd par
|
||||
% % stage(4,i+k+4) = stage(3,i+k) - Wn(k+1)*stage(3,i+k+4);
|
||||
% % end
|
||||
% % end
|
||||
|
||||
% Multiply odd pairs with W twiddling factor
|
||||
for i = 1 : 1 : fftLength
|
||||
i_bin = dec2bin(i-1, bits); % calculates "i" in binary
|
||||
|
||||
if i_bin(bits - 2) == '1' %
|
||||
if i_bin(bits - 1: bits) == '00'
|
||||
% real_n(3,i) = real_n(3,i);
|
||||
% imag_n(3,i) = imag_n(3,i);
|
||||
end
|
||||
if i_bin(bits - 1: bits) == '01'
|
||||
real_x = real_n(3,i)*Wr(65) - imag_n(3,i)*Wi(65);
|
||||
imag_x = real_n(3,i)*Wi(65) + Wr(65)*imag_n(3,i);
|
||||
real_n(3,i) = real_x;
|
||||
imag_n(3,i) = imag_x;
|
||||
end
|
||||
if i_bin(bits - 1: bits) == '10'
|
||||
real_x = real_n(3,i)*Wr(129) - imag_n(3,i)*Wi(129);
|
||||
imag_x = real_n(3,i)*Wi(129) + Wr(129)*imag_n(3,i);
|
||||
real_n(3,i) = real_x;
|
||||
imag_n(3,i) = imag_x;
|
||||
end
|
||||
if i_bin(bits - 1: bits) == '11'
|
||||
real_x = real_n(3,i)*Wr(193) - imag_n(3,i)*Wi(193);
|
||||
imag_x = real_n(3,i)*Wi(193) + Wr(193)*imag_n(3,i);
|
||||
real_n(3,i) = real_x;
|
||||
imag_n(3,i) = imag_x;
|
||||
end
|
||||
end
|
||||
end
|
||||
% calculate next stage values
|
||||
for i = 1 : 2^3 : fftLength
|
||||
for k = 0 : 3
|
||||
% Even pair
|
||||
real_n(4,i+k) = real_n(3,i+k) + real_n(3,i+k+4);
|
||||
imag_n(4,i+k) = imag_n(3,i+k) + imag_n(3,i+k+4);
|
||||
% Odd par
|
||||
real_n(4,i+k+4) = real_n(3,i+k) - real_n(3,i+k+4);
|
||||
imag_n(4,i+k+4) = imag_n(3,i+k) - imag_n(3,i+k+4);
|
||||
end
|
||||
end
|
||||
|
||||
%% 4th stage
|
||||
|
||||
% % % Calculating W twiddling factor
|
||||
% % for i = 1 : 8
|
||||
% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 16 );
|
||||
% % end
|
||||
% %
|
||||
% % % calculate next stage values
|
||||
% % for i = 1 : 2^4 : fftLength
|
||||
% % for k = 0 : 7
|
||||
% % % Even pair
|
||||
% % stage(5,i+k) = stage(4,i+k) + Wn(k+1)*stage(4,i+k+8);
|
||||
% % % Odd par
|
||||
% % stage(5,i+k+8) = stage(4,i+k) - Wn(k+1)*stage(4,i+k+8);
|
||||
% % end
|
||||
% % end
|
||||
|
||||
% Multiply odd pairs with W twiddling factor
|
||||
for i = 1 : 1 : fftLength
|
||||
i_bin = dec2bin(i-1, bits); % calculates "i" in binary
|
||||
|
||||
if i_bin(bits - 3) == '1' %
|
||||
n = bin2dec(i_bin(bits - 2:bits)); % converting last 3 bits to decimal
|
||||
real_x = real_n(4,i)*Wr(n*32+1) - imag_n(4,i)*Wi(n*32+1);
|
||||
imag_x = real_n(4,i)*Wi(n*32+1) + imag_n(4,i)*Wr(n*32+1);
|
||||
real_n(4,i) = real_x;
|
||||
imag_n(4,i) = imag_x;
|
||||
end
|
||||
end
|
||||
|
||||
% calculate next stage values
|
||||
for i = 1 : 2^4 : fftLength
|
||||
for k = 0 : 7
|
||||
%Even pair
|
||||
real_n(5,i+k) = real_n(4,i+k) + real_n(4,i+k+8);
|
||||
imag_n(5,i+k) = imag_n(4,i+k) + imag_n(4,i+k+8);
|
||||
%Odd par
|
||||
real_n(5,i+k+8) = real_n(4,i+k) - real_n(4,i+k+8);
|
||||
imag_n(5,i+k+8) = imag_n(4,i+k) - imag_n(4,i+k+8);
|
||||
end
|
||||
end
|
||||
|
||||
%% 5th stage
|
||||
|
||||
% % % Calculating W twiddling factor
|
||||
% % for i = 1 : 16
|
||||
% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 32 );
|
||||
% % end
|
||||
% %
|
||||
% % % calculate next stage values
|
||||
% % for i = 1 : 2^5 : fftLength
|
||||
% % for k = 0 : 15
|
||||
% % % Even pair
|
||||
% % stage(6,i+k) = stage(5,i+k) + Wn(k+1)*stage(5,i+k+16);
|
||||
% % % Odd par
|
||||
% % stage(6,i+k+16) = stage(5,i+k) - Wn(k+1)*stage(5,i+k+16);
|
||||
% % end
|
||||
% % end
|
||||
|
||||
% Multiply odd pairs with W twiddling factor
|
||||
for i = 1 : 1 : fftLength
|
||||
i_bin = dec2bin(i-1, bits); % calculates "i" in binary
|
||||
|
||||
if i_bin(bits - 4) == '1' %
|
||||
n = bin2dec(i_bin(bits - 3:bits)); % converting last 4 bits to decimal
|
||||
real_x = real_n(5,i)*Wr(n*16+1) - imag_n(5,i)*Wi(n*16+1);
|
||||
imag_x = real_n(5,i)*Wi(n*16+1) + imag_n(5,i)*Wr(n*16+1);
|
||||
real_n(5,i) = real_x;
|
||||
imag_n(5,i) = imag_x;
|
||||
end
|
||||
end
|
||||
|
||||
% calculate next stage values
|
||||
for i = 1 : 2^5 : fftLength
|
||||
for k = 0 : 15
|
||||
% Even pair
|
||||
real_n(6,i+k) = real_n(5,i+k) + real_n(5,i+k+16);
|
||||
imag_n(6,i+k) = imag_n(5,i+k) + imag_n(5,i+k+16);
|
||||
% Odd par
|
||||
real_n(6,i+k+16)= real_n(5,i+k) - real_n(5,i+k+16);
|
||||
imag_n(6,i+k+16)= imag_n(5,i+k) - imag_n(5,i+k+16);
|
||||
end
|
||||
end
|
||||
|
||||
%% 6th stage
|
||||
|
||||
% % % Calculating W twiddling factor
|
||||
% % for i = 1 : 32
|
||||
% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 64 );
|
||||
% % end
|
||||
% %
|
||||
% % % calculate next stage values
|
||||
% % for i = 1 : 2^6 : fftLength
|
||||
% % for k = 0 : 31
|
||||
% % % Even pair
|
||||
% % stage(7,i+k) = stage(6,i+k) + Wn(k+1)*stage(6,i+k+32);
|
||||
% % % Odd par
|
||||
% % stage(7,i+k+32) = stage(6,i+k) - Wn(k+1)*stage(6,i+k+32);
|
||||
% % end
|
||||
% % end
|
||||
|
||||
% Multiply odd pairs with W twiddling factor
|
||||
for i = 1 : 1 : fftLength
|
||||
i_bin = dec2bin(i-1, bits); % calculates "i" in binary
|
||||
|
||||
if i_bin(bits - 5) == '1' %
|
||||
n = bin2dec(i_bin(bits - 4:bits)); % converting last 5 bits to decimal
|
||||
real_x = real_n(6,i)*Wr(n*8+1) - imag_n(6,i)*Wi(n*8+1);
|
||||
imag_x = real_n(6,i)*Wi(n*8+1) + imag_n(6,i)*Wr(n*8+1);
|
||||
real_n(6,i) = real_x;
|
||||
imag_n(6,i) = imag_x;
|
||||
end
|
||||
end
|
||||
|
||||
% calculate next stage values
|
||||
for i = 1 : 2^6 : fftLength
|
||||
for k = 0 : 31
|
||||
% Even pair
|
||||
real_n(7,i+k) = real_n(6,i+k) + real_n(6,i+k+32);
|
||||
imag_n(7,i+k) = imag_n(6,i+k) + imag_n(6,i+k+32);
|
||||
% Odd par
|
||||
real_n(7,i+k+32)= real_n(6,i+k) - real_n(6,i+k+32);
|
||||
imag_n(7,i+k+32)= imag_n(6,i+k) - imag_n(6,i+k+32);
|
||||
end
|
||||
end
|
||||
|
||||
%% 7th stage
|
||||
|
||||
% % % Calculating W twiddling factor
|
||||
% % for i = 1 : 64
|
||||
% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 128 );
|
||||
% % end
|
||||
% %
|
||||
% % % calculate next stage values
|
||||
% % for i = 1 : 2^7 : fftLength
|
||||
% % for k = 0 : 63
|
||||
% % % Even pair
|
||||
% % stage(8,i+k) = stage(7,i+k) + Wn(k+1)*stage(7,i+k+64);
|
||||
% % % Odd par
|
||||
% % stage(8,i+k+64) = stage(7,i+k) - Wn(k+1)*stage(7,i+k+64);
|
||||
% % end
|
||||
% % end
|
||||
|
||||
% Multiply odd pairs with W twiddling factor
|
||||
for i = 1 : 1 : fftLength
|
||||
i_bin = dec2bin(i-1, bits); % calculates "i" in binary
|
||||
|
||||
if i_bin(bits - 6) == '1' %
|
||||
n = bin2dec(i_bin(bits - 5:bits)); % converting last 6 bits to decimal
|
||||
real_x = real_n(7,i)*Wr(n*4+1) - imag_n(7,i)*Wi(n*4+1);
|
||||
imag_x = real_n(7,i)*Wi(n*4+1) + imag_n(7,i)*Wr(n*4+1);
|
||||
real_n(7,i) = real_x;
|
||||
imag_n(7,i) = imag_x;
|
||||
end
|
||||
end
|
||||
|
||||
% calculate next stage values
|
||||
for i = 1 : 2^7 : fftLength
|
||||
for k = 0 : 63
|
||||
% Even pair
|
||||
real_n(8,i+k) = real_n(7,i+k) + real_n(7,i+k+64);
|
||||
imag_n(8,i+k) = imag_n(7,i+k) + imag_n(7,i+k+64);
|
||||
% Odd par
|
||||
real_n(8,i+k+64)= real_n(7,i+k) - real_n(7,i+k+64);
|
||||
imag_n(8,i+k+64)= imag_n(7,i+k) - imag_n(7,i+k+64);
|
||||
end
|
||||
end
|
||||
|
||||
%% 8th stage
|
||||
|
||||
|
||||
% % % Calculating W twiddling factor
|
||||
% % for i = 1 : 128
|
||||
% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 256 );
|
||||
% % end
|
||||
% %
|
||||
% % % calculate next stage values
|
||||
% % for i = 1 : 2^8 : fftLength
|
||||
% % for k = 0 : 127
|
||||
% % % Even pair
|
||||
% % stage(9,i+k) = stage(8,i+k) + Wn(k+1)*stage(8,i+k+128);
|
||||
% % % Odd par
|
||||
% % stage(9,i+k+128) = stage(8,i+k) - Wn(k+1)*stage(8,i+k+128);
|
||||
% % end
|
||||
% % end
|
||||
|
||||
|
||||
% Multiply odd pairs with W twiddling factor
|
||||
for i = 1 : 1 : fftLength
|
||||
i_bin = dec2bin(i-1, bits); % calculates "i" in binary
|
||||
|
||||
if i_bin(bits - 7) == '1' %
|
||||
n = bin2dec(i_bin(bits - 6:bits)); % converting last 7 bits to decimal
|
||||
real_x = real_n(8,i)*Wr(n*2+1) - imag_n(8,i)*Wi(n*2+1);
|
||||
imag_x = real_n(8,i)*Wi(n*2+1) + imag_n(8,i)*Wr(n*2+1);
|
||||
real_n(8,i) = real_x;
|
||||
imag_n(8,i) = imag_x;
|
||||
end
|
||||
end
|
||||
|
||||
% calculate next stage values
|
||||
for i = 1 : 2^8 : fftLength
|
||||
for k = 0 : 127
|
||||
% Even pair
|
||||
real_n(9,i+k) = real_n(8,i+k) + real_n(8,i+k+128);
|
||||
imag_n(9,i+k) = imag_n(8,i+k) + imag_n(8,i+k+128);
|
||||
% Odd par
|
||||
real_n(9,i+k+128)= real_n(8,i+k) - real_n(8,i+k+128);
|
||||
imag_n(9,i+k+128)= imag_n(8,i+k) - imag_n(8,i+k+128);
|
||||
end
|
||||
end
|
||||
|
||||
%% 9th stage
|
||||
|
||||
|
||||
% % % Calculating W twiddling factor
|
||||
% % for i = 1 : 256
|
||||
% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 512 );
|
||||
% % end
|
||||
% %
|
||||
% % % calculate next stage values
|
||||
% % for i = 1 : 2^9 : fftLength
|
||||
% % for k = 0 : 255
|
||||
% % % Even pair
|
||||
% % stage(10,i+k) = stage(9,i+k) + Wn(k+1)*stage(9,i+k+256);
|
||||
% % % Odd par
|
||||
% % stage(10,i+k+256) = stage(9,i+k) - Wn(k+1)*stage(9,i+k+256);
|
||||
% % end
|
||||
% % end
|
||||
|
||||
% Multiply odd pairs with W twiddling factor
|
||||
for i = 1 : 1 : fftLength
|
||||
i_bin = dec2bin(i-1, bits); % calculates "i" in binary
|
||||
|
||||
if i_bin(bits - 8) == '1' %
|
||||
n = bin2dec(i_bin(bits - 7:bits)); % converting last 8 bits to decimal
|
||||
real_x = real_n(8,i)*Wr(n*1+1) - imag_n(8,i)*Wi(n*1+1);
|
||||
imag_x = real_n(8,i)*Wi(n*1+1) + imag_n(8,i)*Wr(n*1+1);
|
||||
real_n(8,i) = real_x;
|
||||
imag_n(8,i) = imag_x;
|
||||
end
|
||||
end
|
||||
|
||||
% calculate next stage values
|
||||
i = 1;
|
||||
for k = 0 : 255
|
||||
% Even pair
|
||||
real_n(10,i+k) = real_n(9,i+k) + real_n(9,i+k+255);
|
||||
imag_n(10,i+k) = imag_n(9,i+k) + imag_n(9,i+k+255);
|
||||
% Odd par
|
||||
real_n(10,i+k+255)= real_n(9,i+k) - real_n(9,i+k+255);
|
||||
imag_n(10,i+k+255)= imag_n(9,i+k) - imag_n(9,i+k+255);
|
||||
end
|
||||
|
||||
|
||||
|
||||
%% Ploting out
|
||||
% slowly plot result
|
||||
figure(5)
|
||||
for i = bits : bits
|
||||
plot( abs( real_n(i, :) + j.*imag_n(i, :) ) );
|
||||
% plot( abs( stage(i,:) ) );
|
||||
% pause(1);
|
||||
end
|
||||
xt = xticks; % returns the current x-axis tick values as a vector
|
||||
fstep = fs/fftLength; % tick of f axis in f domain
|
||||
xtnew = round(xt*fstep)/1000 ; % calculate new tick in kHz
|
||||
xticklabels(xtnew) % set new tick labels
|
||||
+165
@@ -0,0 +1,165 @@
|
||||
%% FFT algoritm
|
||||
clear; % clears all previus values from memory
|
||||
clc; % clear command window
|
||||
fs = 44100; % samplinf freq.
|
||||
fftLength=16; % windowlength
|
||||
% signal frequencies
|
||||
max = 2048 - 1 ;
|
||||
|
||||
f1 = 430;
|
||||
a1 = 0;
|
||||
|
||||
f2 = 4300;
|
||||
a2 = 0;
|
||||
|
||||
f3 = 8000;
|
||||
a3 = max/2;
|
||||
|
||||
% calculating signals
|
||||
comp1 = a1 * sin(2*pi*f1*[0:1/fs:1]);
|
||||
comp2 = a2 * sin(2*pi*f2*[0:1/fs:1]);
|
||||
comp3 = a3 * sin(2*pi*f3*[0:1/fs:1]);
|
||||
|
||||
% calculatin vector values for step function
|
||||
d1 = ones(1, 24);
|
||||
d2 = 0.*ones(1, 1000 );
|
||||
|
||||
%data = [ d1 , d2]; % creates vector with step function
|
||||
data = comp1 + comp2 + comp3; % creates vector from 3 sin functions
|
||||
|
||||
figure(1) % plots separete sin functions
|
||||
plot ( comp1, '-');
|
||||
hold on;
|
||||
plot ( comp2, '-');
|
||||
plot ( comp3, '-');
|
||||
xlim([1 50])
|
||||
title('Separete SIN functions')
|
||||
ylabel('magnitude'), xlabel('time')
|
||||
hold off;
|
||||
|
||||
figure(2) % plots signal for fft
|
||||
plot ( data);
|
||||
title('Signal for FFT analysis FFT')
|
||||
ylabel('magnitude'), xlabel('time')
|
||||
xlim([1 100])
|
||||
|
||||
figure(3) % plots resultinf fft from Matlab functions
|
||||
ft =fft(data,fftLength);
|
||||
ftMag=abs(ft(1:fftLength/2));
|
||||
plot (ftMag)
|
||||
title('Linear Magnitude FFT')
|
||||
ylabel('magnitude'), xlabel('kHz')
|
||||
|
||||
xt = xticks; % returns the current x-axis tick values as a vector
|
||||
fstep = fs/fftLength; % tick of f axis in f domain
|
||||
xtnew = round((xt-1)*fstep/1000, 1) ; % calculate new tick in kHz
|
||||
xticklabels(xtnew) % set new tick labels
|
||||
|
||||
figure(4) % plots resultinf fft(in dB) from Matlab functions
|
||||
ft =fft(data,fftLength);
|
||||
ftMag=abs(ft(1:fftLength/2));
|
||||
plot (20*log10(ftMag))
|
||||
title('dB Magnitude')
|
||||
ylabel('dB'), xlabel('kHz')
|
||||
|
||||
xt = xticks; % returns the current x-axis tick values as a vector
|
||||
fstep = fs/fftLength; % tick of f axis in f domain
|
||||
xtnew = round((xt-1)*fstep/1000, 1) ; % calculate new tick in kHz
|
||||
xticklabels(xtnew) % set new tick labels
|
||||
|
||||
%% Data preparation for FFT
|
||||
|
||||
% reverse bit calulation
|
||||
bits = length(dec2bin( fftLength - 1 )); % how many bits in binary number
|
||||
rev_bit_dec = zeros(1,fftLength); % create vektor size of fftlength
|
||||
|
||||
for i=1:fftLength
|
||||
bin_num = dec2bin(i-1 , bits); % converting to binary number
|
||||
rev_bit = []; % create empty vector
|
||||
for k=bits:-1:1
|
||||
rev_bit = [rev_bit , bin_num(k)];
|
||||
end
|
||||
rev_bit_dec(i) = bin2dec(rev_bit) ; % add 1 to match Matlab numbering
|
||||
end
|
||||
|
||||
% creating array
|
||||
% create empty array to store values in reverse bit order
|
||||
stage = zeros(bits + 1,fftLength);
|
||||
|
||||
for i=1:fftLength
|
||||
stage(1,i) = data(rev_bit_dec(i)+1);
|
||||
end
|
||||
|
||||
%% First stage
|
||||
|
||||
for i = 1 : 2^1 : fftLength
|
||||
% Even
|
||||
stage(2,i) = stage(1,i) + stage(1,i+1);
|
||||
% Odd
|
||||
stage(2,i+1) = stage(1,i) - stage(1,i+1);
|
||||
|
||||
end
|
||||
|
||||
%% Second stage
|
||||
|
||||
% Calculating W twiddling factor
|
||||
for i = 1 : 2
|
||||
Wn(i) = exp(-j * (i-1) * 2 * pi/ 4 );
|
||||
end
|
||||
|
||||
% calculate next stage values
|
||||
for i = 1 : 2^2 : fftLength
|
||||
% Even pair
|
||||
stage(3,i+0) = stage(2,i+0) + Wn(1)*stage(2,i+2);
|
||||
stage(3,i+1) = stage(2,i+1) + Wn(2)*stage(2,i+3);
|
||||
% Odd par
|
||||
stage(3,i+2) = stage(2,i+0) - Wn(1)*stage(2,i+2);
|
||||
stage(3,i+3) = stage(2,i+1) - Wn(2)*stage(2,i+3);
|
||||
end
|
||||
|
||||
%% Therd stage
|
||||
|
||||
% Calculating W twiddling factor
|
||||
for i = 1 : 4
|
||||
Wn(i) = exp(-j * (i-1) * 2 * pi/ 8 );
|
||||
end
|
||||
|
||||
% calculate next stage values
|
||||
for i = 1 : 2^3 : fftLength
|
||||
for k = 0 : 3
|
||||
% Even pair
|
||||
stage(4,i+k) = stage(3,i+k) + Wn(k+1)*stage(3,i+k+4);
|
||||
% Odd par
|
||||
stage(4,i+k+4) = stage(3,i+k) - Wn(k+1)*stage(3,i+k+4);
|
||||
end
|
||||
end
|
||||
|
||||
%% 4th stage
|
||||
|
||||
% Calculating W twiddling factor
|
||||
for i = 1 : 8
|
||||
Wn(i) = exp(-j * (i-1) * 2 * pi/ 16 );
|
||||
end
|
||||
|
||||
% calculate next stage values
|
||||
for i = 1 : 2^4 : fftLength
|
||||
for k = 0 : 7
|
||||
% Even pair
|
||||
stage(5,i+k) = stage(4,i+k) + Wn(k+1)*stage(4,i+k+8);
|
||||
% Odd par
|
||||
stage(5,i+k+8) = stage(4,i+k) - Wn(k+1)*stage(4,i+k+8);
|
||||
end
|
||||
end
|
||||
|
||||
%% Ploting out
|
||||
% slowly plot result
|
||||
figure(5)
|
||||
for i = 1 : bits
|
||||
%plot( abs( real_n(i, :) + j.*imag_n(i, :) ) );
|
||||
plot( abs( stage(i,:) ) );
|
||||
pause(1);
|
||||
end
|
||||
xt = xticks; % returns the current x-axis tick values as a vector
|
||||
fstep = fs/fftLength; % tick of f axis in f domain
|
||||
xtnew = round(xt*fstep)/1000 ; % calculate new tick in kHz
|
||||
xticklabels(xtnew) % set new tick labels
|
||||
@@ -1,16 +1,28 @@
|
||||
f = 4000;
|
||||
fs = 22050;
|
||||
fftLength=1024; %windowlength
|
||||
x =sin(2*pi*f*[0:1/fs:1]); %makethesinewave
|
||||
ft =fft(x,fftLength); %doFFT,userect.window
|
||||
ftMag=abs(ft); %computemagnitude
|
||||
f = 4300;
|
||||
fs = 44100;
|
||||
fftLength=512; % windowlength
|
||||
x =sin(2*pi*1000*[0:1/fs:1]) + sin(2*pi*f*[0:1/fs:1]) + sin(2*pi*20000*[0:1/fs:1]); % makethesinewave
|
||||
ft =fft(x,fftLength); % doFFT,userect.window
|
||||
ftMag=abs(ft(1:fftLength/2)); % computemagnitude ( half )
|
||||
|
||||
% plot the results both in linear and dB magnitudes
|
||||
|
||||
subplot(2, 1, 1), plot(ftMag)
|
||||
title('Linear Magnitude')
|
||||
ylabel('magnitude'), xlabel('bins')
|
||||
ylabel('magnitude'), xlabel('kHz')
|
||||
|
||||
xt = xticks; % returns the current x-axis tick values as a vector
|
||||
fstep = fs/fftLength; % tick of f axis in f domain
|
||||
xtnew = round(xt*fstep)/1000 ; % calculate new tick in kHz
|
||||
xticklabels(xtnew) % set new tick labels
|
||||
|
||||
subplot(2, 1, 2), plot(20*log10(ftMag))
|
||||
title('dB Magnitude')
|
||||
ylabel('dB'), xlabel('bins')
|
||||
ylabel('dB'), xlabel('kHz')
|
||||
|
||||
xt = xticks; % returns the current x-axis tick values as a vector
|
||||
fstep = (fs/fftLength); % tick of f axis in f domain
|
||||
xtnew = round(xt*fstep)/1000; % calculate new tick in kHz
|
||||
xticklabels(xtnew) % set new tick labels
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user