Works separately with Real & Imag parts
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Aleksejs Mirnijs
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%% FFT algoritm
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clear; % clears all previus values from memory
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clc; % clear command window
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fs = 44100; % samplinf freq.
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fftLength=512; % windowlength
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stage_num = log2(fftLength);
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% signal frequencies
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max = 2048 - 1 ;
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f1 = 430;
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a1 = 0;
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f2 = 4300;
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a2 = 0;
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f3 = 8000;
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a3 = max/2;
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% calculating signals
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comp1 = a1 * sin(2*pi*f1*[0:1/fs:1]);
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comp2 = a2 * sin(2*pi*f2*[0:1/fs:1]);
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comp3 = a3 * sin(2*pi*f3*[0:1/fs:1]);
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Length = length(comp3);
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% calculatin vector values for step function
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d1 = ones(1, 24);
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d2 = 0.*ones(1, 1000 );
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%data = [ d1 , d2]; % creates vector with step function
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data = comp1 + comp2 + comp3; % creates vector from 3 sin functions
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%data = comp3;
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% Grafika nobiides
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bin_vals = [0 : fftLength-1];
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N_2 = ceil(fftLength/2);
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fax_kHz = (bin_vals-N_2)*fs/fftLength/1000;
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freq3 = ceil(-(fftLength)/2:1:(fftLength)/2).*(fs/fftLength)/1000;
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figure(1) % plots separete sin functions
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hold off,
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%plot ( comp1, '-');
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hold on;
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%plot ( comp2, '-');
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plot ( comp3, '-'), grid minor,;
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%xlim([1 50])
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title('Separete SIN functions')
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ylabel('magnitude'), xlabel('time')
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hold off;
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figure(2) % plots signal for fft
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plot ( data), grid minor,;
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xlim([1 50])
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title('Signal for FFT analysis FFT')
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ylabel('magnitude'), xlabel('time')
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%xlim([1 100])
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figure(3) % plots resultinf fft from Matlab functions
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ft =fft(data,fftLength);
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ft1 = fftshift(ft);
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ftMag = abs(ft1);
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plot (fax_kHz,ftMag), grid minor,
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title('Linear Magnitude FFT')
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ylabel('magnitude'), xlabel('kHz')
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figure(4) % plots resultinf fft(in dB) from Matlab functions
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ft = fft(data,fftLength+1);
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ftMag = abs(ft(1:fftLength+1));
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plot (freq3,20*log10(ftMag)), grid minor,
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title('dB Magnitude')
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ylabel('dB'), xlabel('kHz')
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%% Data preparation for FFT
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% reverse bit calulation
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bits = length(dec2bin( fftLength - 1 )); % how many bits in binary number
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rev_bit_dec = zeros(1,fftLength); % create vektor size of fftlength
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stage = 1; %Do it here for stage #1
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c = 0:fftLength-1;
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c_bin = de2bi(c); % create binary table
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rev_bit_dec = bi2de(fliplr(circshift(c_bin',stage-1)')); %Rotate binary table and convert to dec
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% creating array
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% create empty array to store values in reverse bit order
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stage = zeros(bits+1,fftLength);
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real_n = zeros(bits+1,fftLength);
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imag_n = zeros(bits+1,fftLength);
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Wn = zeros(1,fftLength/2); % complex
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Wr = zeros(1,fftLength/2); % real
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Wi = zeros(1,fftLength/2); % imag
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%% New stages
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for st = 0 : stage_num;
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if st == 0
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for tmp=1:fftLength;
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stage(st+1,tmp) = data(rev_bit_dec(tmp)+1);
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real_n(st+1,tmp) = data(rev_bit_dec(tmp)+1);
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end
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else st > 0;
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for n = 1 : fftLength/2;
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Wn(n) = exp(-j * (n-1) * 2 * pi/ 2^(st) );
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Wr(n) = real(Wn(n));
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Wi(n) = imag(Wn(n));
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end
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for i = 1 : 2^st : fftLength;
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for k = 0 : 2^(st-1)-1;
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% Even
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stage(st+1,i+k) = stage(st,i+k) + Wn(k+1)*stage(st,i+k+2^(st-1));
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real_n(st+1,i+k) = real_n(st,i+k) + Wn(k+1)*real_n(st,i+k+2^(st-1));
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imag_n(st+1,i+k) = imag_n(st,i+k) + Wn(k+1)*imag_n(st,i+k+2^(st-1));
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% Odd
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stage(st+1,i+k+2^(st-1)) = stage(st,i+k) - Wn(k+1)*stage(st,i+k+2^(st-1));
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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));
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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));
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end
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end
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end
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end
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%% Ploting out
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% slowly plot result
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figure(5)
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for i = 1 : bits + 1;
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%plot( abs( real_n(i, :) + j.*imag_n(i, :) ) );
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%plot( fax_kHz, abs( fftshift( real_n(i, :) + j.*imag_n(i,:) ) ) ), grid minor,;
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plot( fax_kHz, abs( fftshift( stage(i,:) ) ) ), grid minor,;
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%pause(1);
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end
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title('Linear Magnitude FFT')
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ylabel('magnitude'), xlabel('kHz')
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figure(6)
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for i = 1 : bits + 1;
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%plot( abs( real_n(i, :) + j.*imag_n(i, :) ) );
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plot( fax_kHz, abs( fftshift( real_n(i, :) + j.*imag_n(i,:) ) ) ), grid minor,;
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%plot( fax_kHz, abs( fftshift( stage(i,:) ) ) ), grid minor,;
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%pause(1);
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end
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title('Linear Magnitude FFT, ploted from Real + Imag')
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ylabel('magnitude'), xlabel('kHz')
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