Updated comments

2019-12-23 15:06:02 +02:00
parent f876a6a77a
commit 790c73cab6
2 changed files with 147 additions and 0 deletions
@@ -0,0 +1,144 @@
+%% FFT algoritm
+clear;                      % clears all previus values from memory 
+clc;                        % clear command window
+fs =  44100;                % samplinf freq.
+fftLength=512;              % windowlength 
+stage_num = log2(fftLength);
+% 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]);
+Length = length(comp3);
+% 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
+%data = comp3;
+
+% Grafika nobiides
+bin_vals = [0 : fftLength-1];
+N_2 = ceil(fftLength/2);
+fax_kHz = (bin_vals-N_2)*fs/fftLength/1000;
+
+freq3 = ceil(-(fftLength)/2:1:(fftLength)/2).*(fs/fftLength)/1000;
+
+figure(1)               % plots separete sin functions
+hold off,
+%plot ( comp1, '-');
+hold on;
+%plot ( comp2, '-');
+plot ( comp3, '-'), grid minor,;
+%xlim([1 50])
+title('Separete SIN functions') 
+ylabel('magnitude'), xlabel('time') 
+hold off;
+
+figure(2)               % plots signal for fft
+plot ( data), grid minor,;
+xlim([1 50])
+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); 
+ft1 = fftshift(ft);
+ftMag = abs(ft1); 
+plot (fax_kHz,ftMag), grid minor,
+title('Linear Magnitude FFT') 
+ylabel('magnitude'), xlabel('kHz') 
+
+figure(4)               % plots resultinf fft(in dB)  from Matlab functions
+ft = fft(data,fftLength+1); 
+ftMag = abs(ft(1:fftLength+1)); 
+plot (freq3,20*log10(ftMag)), grid minor,
+title('dB Magnitude') 
+ylabel('dB'), xlabel('kHz') 
+
+%% 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
+
+stage = 1;              %Do it here for stage #1 
+c = 0:fftLength-1;
+c_bin = de2bi(c);       % create binary table
+rev_bit_dec = bi2de(fliplr(circshift(c_bin',stage-1)'));    %Rotate binary table and convert to dec
+
+%  creating array
+%  create empty array to store values in reverse bit order
+stage = zeros(bits+1,fftLength);
+real_n = zeros(bits+1,fftLength);
+imag_n = zeros(bits+1,fftLength);
+
+Wn = zeros(1,fftLength/2);   % complex
+Wr = zeros(1,fftLength/2);    % real
+Wi = zeros(1,fftLength/2);    % imag
+
+%% New stages
+
+for st = 0 : stage_num;
+    if st == 0
+       for tmp=1:fftLength;
+            stage(st+1,tmp)  =  data(rev_bit_dec(tmp)+1);
+            real_n(st+1,tmp)  =  data(rev_bit_dec(tmp)+1);
+       end
+    else st > 0;
+        for n = 1 : fftLength/2;
+                Wn(n)  = exp(-j * (n-1) * 2 * pi/ 2^(st) );
+                Wr(n) = real(Wn(n));
+                Wi(n) = imag(Wn(n));
+        end
+        for i = 1 : 2^st : fftLength;
+                for k = 0 : 2^(st-1)-1;
+                    % Even
+                        stage(st+1,i+k) = stage(st,i+k) + Wn(k+1)*stage(st,i+k+2^(st-1));
+                        real_n(st+1,i+k) = real_n(st,i+k) + Wn(k+1)*real_n(st,i+k+2^(st-1));
+                        imag_n(st+1,i+k) = imag_n(st,i+k) + Wn(k+1)*imag_n(st,i+k+2^(st-1));
+                    % Odd
+                        stage(st+1,i+k+2^(st-1)) = stage(st,i+k) - Wn(k+1)*stage(st,i+k+2^(st-1));
+                        real_n(st+1,i+k+2^(st-1)) = real_n(st,i+k) - Wn(k+1)*real_n(st,i+k+2^(st-1));
+                        imag_n(st+1,i+k+2^(st-1)) = imag_n(st,i+k) - Wn(k+1)*imag_n(st,i+k+2^(st-1));
+                end
+        end
+    end
+end
+
+%% Ploting out
+% slowly plot result
+figure(5)
+for i = 1 : bits + 1;
+    %plot( abs( real_n(i, :) + j.*imag_n(i,  :) ) );
+    %plot( fax_kHz, abs( fftshift( real_n(i, :) + j.*imag_n(i,:) ) ) ), grid minor,;
+    plot( fax_kHz, abs( fftshift( stage(i,:) ) ) ), grid minor,;
+    %pause(1);
+end
+
+title('Linear Magnitude FFT') 
+ylabel('magnitude'), xlabel('kHz')
+
+figure(6)
+for i = 1 : bits + 1;
+    %plot( abs( real_n(i, :) + j.*imag_n(i,  :) ) );
+    plot( fax_kHz, abs( fftshift( real_n(i, :) + j.*imag_n(i,:) ) ) ), grid minor,;
+    %plot( fax_kHz, abs( fftshift( stage(i,:) ) ) ), grid minor,;
+    %pause(1);
+end
+
+title('Linear Magnitude FFT, ploted from Real + Imag') 
+ylabel('magnitude'), xlabel('kHz')