add matlab files
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Imants Pulkstenis
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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=16; % 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 = 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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% 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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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-1)*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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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-1)*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) ; % add 1 to match Matlab numbering
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end
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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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for i=1:fftLength
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stage(1,i) = data(rev_bit_dec(i)+1);
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end
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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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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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% 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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%% 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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% 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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%% 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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% 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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%% Ploting out
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% slowly plot result
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figure(5)
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for i = 1 : bits
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%plot( abs( real_n(i, :) + j.*imag_n(i, :) ) );
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plot( abs( stage(i,:) ) );
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pause(1);
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end
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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 ; % calculate new tick in kHz
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xticklabels(xtnew) % set new tick labels
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