add matlab files
This commit is contained in:
Imants Pulkstenis
+510
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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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% 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 = 8000;
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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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% 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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figure(1) % plots separete sin functions
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plot ( comp1, '-');
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hold on;
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plot ( comp2, '-');
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plot ( comp3, '-');
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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);
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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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%ftMag=abs(ft(1:fftLength/2));
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ftMag=abs(ft);
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plot (ftMag)
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title('Linear Magnitude FFT')
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ylabel('magnitude'), xlabel('kHz')
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xt = xticks; % returns the current x-axis tick values as a vector
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fstep = fs/fftLength; % tick of f axis in f domain
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xtnew = round(xt*fstep/1000, 1) ; % calculate new tick in kHz
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xticklabels(xtnew) % set new tick labels
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figure(4) % plots resultinf fft(in dB) from Matlab functions
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ft =fft(data,fftLength);
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%ftMag=abs(ft(1:fftLength/2));
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ftMag=abs(ft);
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plot (20*log10(ftMag))
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title('dB Magnitude')
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ylabel('dB'), xlabel('kHz')
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xt = xticks; % returns the current x-axis tick values as a vector
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fstep = fs/fftLength; % tick of f axis in f domain
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xtnew = round(xt*fstep/1000, 1) ; % calculate new tick in kHz
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xticklabels(xtnew) % set new tick labels
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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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for i=1:fftLength
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bin_num = dec2bin(i-1 , bits); % converting to binary number
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rev_bit = []; % create empty vector
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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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% creating array
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real_n = zeros(bits+1,fftLength); % create empty array to store values in reverse bit order
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imag_n = zeros(bits+1,fftLength);
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stage = zeros(bits+1,fftLength);
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%sfi_data = sfi(data,16,0);
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for i=1:fftLength
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real_n(1,i) = data(rev_bit_dec(i)+1);
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stage(1,i) = data(rev_bit_dec(i)+1);
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end
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% % W_N vector calculation
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% W = zeros(1,fftLength); % complex
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% Wr = zeros(1,fftLength); % real
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% Wi = zeros(1,fftLength); % imag
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% for i = 1 : fftLength
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% W(i) = exp(-j * (i-1) * 2 * pi/ fftLength );
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% Wr(i) = sfi(real(W(i)),16,15);
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% Wi(i) = sfi(imag(W(i)),16,15);
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% end
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%
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% % W(30) = - W(30+256)
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% % or
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% % W(x) = - W(x + fftLength/2)
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% new W_N vector calculation this time only half
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W = 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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for i = 1 : fftLength/2
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W(i) = exp(-j * (i-1) * 2 * pi/ fftLength );
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Wr(i) = real(W(i));%sfi(real(W(i)),16,15);
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Wi(i) = imag(W(i));%sfi(imag(W(i)),16,15);
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end
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%% FFT FSM
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%% First stage
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for i = 1 : 2^1 : fftLength
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% % % Even
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% % stage(2,i) = stage(1,i) + stage(1,i+1);
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% % % Odd
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% % stage(2,i+1) = stage(1,i) - stage(1,i+1);
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% Even
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real_n(2,i) = real_n(1,i) + real_n(1,i+1);
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% Odd
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real_n(2,i+1) = real_n(1,i) - real_n(1,i+1);
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end
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%% Second stage
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% % % Calculating W twiddling factor
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% % for i = 1 : 2
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% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 4 );
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% % end
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% %
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% % % calculate next stage values
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% % for i = 1 : 2^2 : fftLength
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% % % Even pair
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% % stage(3,i+0) = stage(2,i+0) + Wn(1)*stage(2,i+2);
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% % stage(3,i+1) = stage(2,i+1) + Wn(2)*stage(2,i+3);
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% % % Odd par
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% % stage(3,i+2) = stage(2,i+0) - Wn(1)*stage(2,i+2);
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% % stage(3,i+3) = stage(2,i+1) - Wn(2)*stage(2,i+3);
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% % end
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% Multiply odd pairs with W twiddling factor
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for i = 1 : 1 : fftLength
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i_bin = dec2bin(i-1, bits); % calculates "i" in binary
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if i_bin(bits - 1:bits) == '11' % Odd pair odd number(every fourth)
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imag_n(2,i) = -real_n(2,i);
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real_n(2,i) = 0;
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% c= real_n(2,i) + j * imag_n(2,i),
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end
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end
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% calculate next stage values
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for i = 1 : 2^2 : fftLength
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% Even pair
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real_n(3,i+0) = real_n(2,i+0) + real_n(2,i+2);
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real_n(3,i+1) = real_n(2,i+1) + real_n(2,i+3);
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imag_n(3,i+0) = imag_n(2,i+0) + imag_n(2,i+2);
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imag_n(3,i+1) = imag_n(2,i+1) + imag_n(2,i+3);
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% Odd par
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real_n(3,i+2) = real_n(2,i+0) - real_n(2,i+2);
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real_n(3,i+3) = real_n(2,i+1) - real_n(2,i+3);
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imag_n(3,i+2) = imag_n(2,i+0) - imag_n(2,i+2);
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imag_n(3,i+3) = imag_n(2,i+1) - imag_n(2,i+3);
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end
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%% Therd stage
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% % % Calculating W twiddling factor
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% % for i = 1 : 4
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% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 8 );
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% % end
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% %
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% % % calculate next stage values
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% % for i = 1 : 2^3 : fftLength
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% % for k = 0 : 3
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% % % Even pair
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% % stage(4,i+k) = stage(3,i+k) + Wn(k+1)*stage(3,i+k+4);
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% % % Odd par
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% % stage(4,i+k+4) = stage(3,i+k) - Wn(k+1)*stage(3,i+k+4);
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% % end
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% % end
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% Multiply odd pairs with W twiddling factor
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for i = 1 : 1 : fftLength
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i_bin = dec2bin(i-1, bits); % calculates "i" in binary
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if i_bin(bits - 2) == '1' %
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if i_bin(bits - 1: bits) == '00'
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% real_n(3,i) = real_n(3,i);
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% imag_n(3,i) = imag_n(3,i);
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end
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if i_bin(bits - 1: bits) == '01'
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real_x = real_n(3,i)*Wr(65) - imag_n(3,i)*Wi(65);
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imag_x = real_n(3,i)*Wi(65) + Wr(65)*imag_n(3,i);
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real_n(3,i) = real_x;
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imag_n(3,i) = imag_x;
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end
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if i_bin(bits - 1: bits) == '10'
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real_x = real_n(3,i)*Wr(129) - imag_n(3,i)*Wi(129);
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imag_x = real_n(3,i)*Wi(129) + Wr(129)*imag_n(3,i);
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real_n(3,i) = real_x;
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imag_n(3,i) = imag_x;
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end
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if i_bin(bits - 1: bits) == '11'
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real_x = real_n(3,i)*Wr(193) - imag_n(3,i)*Wi(193);
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imag_x = real_n(3,i)*Wi(193) + Wr(193)*imag_n(3,i);
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real_n(3,i) = real_x;
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imag_n(3,i) = imag_x;
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end
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end
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end
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% calculate next stage values
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for i = 1 : 2^3 : fftLength
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for k = 0 : 3
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% Even pair
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real_n(4,i+k) = real_n(3,i+k) + real_n(3,i+k+4);
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imag_n(4,i+k) = imag_n(3,i+k) + imag_n(3,i+k+4);
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% Odd par
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real_n(4,i+k+4) = real_n(3,i+k) - real_n(3,i+k+4);
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imag_n(4,i+k+4) = imag_n(3,i+k) - imag_n(3,i+k+4);
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end
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end
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%% 4th stage
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% % % Calculating W twiddling factor
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% % for i = 1 : 8
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% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 16 );
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% % end
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% %
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% % % calculate next stage values
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% % for i = 1 : 2^4 : fftLength
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% % for k = 0 : 7
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% % % Even pair
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% % stage(5,i+k) = stage(4,i+k) + Wn(k+1)*stage(4,i+k+8);
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% % % Odd par
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% % stage(5,i+k+8) = stage(4,i+k) - Wn(k+1)*stage(4,i+k+8);
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% % end
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% % end
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% Multiply odd pairs with W twiddling factor
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for i = 1 : 1 : fftLength
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i_bin = dec2bin(i-1, bits); % calculates "i" in binary
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if i_bin(bits - 3) == '1' %
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n = bin2dec(i_bin(bits - 2:bits)); % converting last 3 bits to decimal
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real_x = real_n(4,i)*Wr(n*32+1) - imag_n(4,i)*Wi(n*32+1);
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imag_x = real_n(4,i)*Wi(n*32+1) + imag_n(4,i)*Wr(n*32+1);
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real_n(4,i) = real_x;
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imag_n(4,i) = imag_x;
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end
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end
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% calculate next stage values
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for i = 1 : 2^4 : fftLength
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for k = 0 : 7
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%Even pair
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real_n(5,i+k) = real_n(4,i+k) + real_n(4,i+k+8);
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imag_n(5,i+k) = imag_n(4,i+k) + imag_n(4,i+k+8);
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%Odd par
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real_n(5,i+k+8) = real_n(4,i+k) - real_n(4,i+k+8);
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imag_n(5,i+k+8) = imag_n(4,i+k) - imag_n(4,i+k+8);
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end
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end
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%% 5th stage
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% % % Calculating W twiddling factor
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% % for i = 1 : 16
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% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 32 );
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% % end
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% %
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% % % calculate next stage values
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% % for i = 1 : 2^5 : fftLength
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% % for k = 0 : 15
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% % % Even pair
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% % stage(6,i+k) = stage(5,i+k) + Wn(k+1)*stage(5,i+k+16);
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% % % Odd par
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% % stage(6,i+k+16) = stage(5,i+k) - Wn(k+1)*stage(5,i+k+16);
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% % end
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% % end
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% Multiply odd pairs with W twiddling factor
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for i = 1 : 1 : fftLength
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i_bin = dec2bin(i-1, bits); % calculates "i" in binary
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if i_bin(bits - 4) == '1' %
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n = bin2dec(i_bin(bits - 3:bits)); % converting last 4 bits to decimal
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real_x = real_n(5,i)*Wr(n*16+1) - imag_n(5,i)*Wi(n*16+1);
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imag_x = real_n(5,i)*Wi(n*16+1) + imag_n(5,i)*Wr(n*16+1);
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real_n(5,i) = real_x;
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imag_n(5,i) = imag_x;
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end
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end
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% calculate next stage values
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for i = 1 : 2^5 : fftLength
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for k = 0 : 15
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% Even pair
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real_n(6,i+k) = real_n(5,i+k) + real_n(5,i+k+16);
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imag_n(6,i+k) = imag_n(5,i+k) + imag_n(5,i+k+16);
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% Odd par
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real_n(6,i+k+16)= real_n(5,i+k) - real_n(5,i+k+16);
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imag_n(6,i+k+16)= imag_n(5,i+k) - imag_n(5,i+k+16);
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end
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end
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%% 6th stage
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% % % Calculating W twiddling factor
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% % for i = 1 : 32
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% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 64 );
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% % end
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% %
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% % % calculate next stage values
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% % for i = 1 : 2^6 : fftLength
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% % for k = 0 : 31
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% % % Even pair
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% % stage(7,i+k) = stage(6,i+k) + Wn(k+1)*stage(6,i+k+32);
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% % % Odd par
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% % stage(7,i+k+32) = stage(6,i+k) - Wn(k+1)*stage(6,i+k+32);
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% % end
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% % end
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% Multiply odd pairs with W twiddling factor
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for i = 1 : 1 : fftLength
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i_bin = dec2bin(i-1, bits); % calculates "i" in binary
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if i_bin(bits - 5) == '1' %
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n = bin2dec(i_bin(bits - 4:bits)); % converting last 5 bits to decimal
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real_x = real_n(6,i)*Wr(n*8+1) - imag_n(6,i)*Wi(n*8+1);
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imag_x = real_n(6,i)*Wi(n*8+1) + imag_n(6,i)*Wr(n*8+1);
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real_n(6,i) = real_x;
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imag_n(6,i) = imag_x;
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end
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end
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% calculate next stage values
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for i = 1 : 2^6 : fftLength
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for k = 0 : 31
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% Even pair
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real_n(7,i+k) = real_n(6,i+k) + real_n(6,i+k+32);
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imag_n(7,i+k) = imag_n(6,i+k) + imag_n(6,i+k+32);
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% Odd par
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real_n(7,i+k+32)= real_n(6,i+k) - real_n(6,i+k+32);
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imag_n(7,i+k+32)= imag_n(6,i+k) - imag_n(6,i+k+32);
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end
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end
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%% 7th stage
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% % % Calculating W twiddling factor
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% % for i = 1 : 64
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% % Wn(i) = exp(-j * (i-1) * 2 * pi/ 128 );
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% % end
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% %
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% % % calculate next stage values
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% % for i = 1 : 2^7 : fftLength
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% % for k = 0 : 63
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% % % Even pair
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% % stage(8,i+k) = stage(7,i+k) + Wn(k+1)*stage(7,i+k+64);
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% % % Odd par
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% % stage(8,i+k+64) = stage(7,i+k) - Wn(k+1)*stage(7,i+k+64);
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% % end
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% % end
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% Multiply odd pairs with W twiddling factor
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for i = 1 : 1 : fftLength
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i_bin = dec2bin(i-1, bits); % calculates "i" in binary
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if i_bin(bits - 6) == '1' %
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n = bin2dec(i_bin(bits - 5:bits)); % converting last 6 bits to decimal
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real_x = real_n(7,i)*Wr(n*4+1) - imag_n(7,i)*Wi(n*4+1);
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imag_x = real_n(7,i)*Wi(n*4+1) + imag_n(7,i)*Wr(n*4+1);
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real_n(7,i) = real_x;
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imag_n(7,i) = imag_x;
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end
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end
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% calculate next stage values
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for i = 1 : 2^7 : fftLength
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for k = 0 : 63
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% 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
|
||||
Reference in New Issue
Block a user