Updated myfft3 file. Add calculations using fixed point integers and seperatly calculated real and imaginary numbers
This commit is contained in:
Imants Pulkstenis
+173
-50
@@ -2,17 +2,19 @@
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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=32; % windowlength
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fftLength=32; % windowlength
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% signal frequencies
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max = 2048 - 1 ; % max aplitude
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data_length = 8; % data length in FPGA calculations
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max = 2^(data_length-1) - 1 ; % max aplitude 2^n /2
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f1 = 1000;
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a1 = max/5;
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a1 = max/2;
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f2 = 0;
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a2 = max/4;
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f3 = 9600;
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f3 = 8000;
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a3 = max/2;
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% calculating signals
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@@ -46,7 +48,7 @@ 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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stem (ftMag)
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title('Linear Magnitude FFT')
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ylabel('magnitude'), xlabel('kHz')
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@@ -55,17 +57,17 @@ 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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% 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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%
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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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@@ -73,111 +75,232 @@ xticklabels(xtnew) % set new tick labels
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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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for n=1:fftLength
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bin_num = dec2bin(n-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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rev_bit_dec(n) = 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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for n=1:fftLength
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stage(1,n) = data(rev_bit_dec(n)+1);
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end
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% Calculating W twiddling factor for all stages
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for n = 1 : fftLength/2
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W(n) = exp(-1i * (n-1) * 2 * pi/ fftLength );
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end
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% convert to fixed point mumber -> sfi(v,w,f) returns a signed fixed-point object with value v, word length w, and fraction length f.
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Wr = sfi(real(W),data_length,data_length-2);
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Wi = sfi(imag(W),data_length,data_length-2);
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st_real = sfi(real(stage) , data_length + 3 , 0);
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st_imag = sfi(imag(stage) , data_length + 3 , 0);
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% temp values for multiplaying with W twiddling factor
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st_real_tmp = sfi(real(zeros(bits + 1,fftLength)) , data_length + 3 , 0);
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st_imag_tmp = sfi(imag(zeros(bits + 1,fftLength)) , data_length + 3 , 0);
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%% First stage
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for i = 1 : 2^1 : fftLength
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for n = 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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stage(2,n) = stage(1,n) + stage(1,n+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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stage(2,n+1) = stage(1,n) - stage(1,n+1);
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end
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% calculations using separate real and imaginary numbers
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for n = 1 : 2^1 : fftLength
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% Even
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st_real(2,n) = st_real(1,n) + st_real(1,n+1);
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% imag is 0
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% Odd
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st_real(2,n+1) = st_real(1,n) - st_real(1,n+1);
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% imag is 0
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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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for n = 1 : 2
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Wn(n) = exp(-1i * (n-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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for n = 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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stage(3,n+0) = stage(2,n+0) + Wn(1)*stage(2,n+2);
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stage(3,n+1) = stage(2,n+1) + Wn(2)*stage(2,n+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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stage(3,n+2) = stage(2,n+0) - Wn(1)*stage(2,n+2);
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stage(3,n+3) = stage(2,n+1) - Wn(2)*stage(2,n+3);
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end
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% calculations using separate real and imaginary numbers
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for n = 1 : 2^2 : fftLength
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% Even pair
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st_real(3,n+0) = st_real(2,n+0) + st_real(2,n+2);
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% imag is 0
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st_real(3,n+1) = st_real(2,n+1) ; % real is 0
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st_imag(3,n+1) = -1 * st_real(2,n+3); % mult -j
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% Odd par
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st_real(3,n+2) = st_real(2,n+0) - st_real(2,n+2);
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% imag is 0
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st_real(3,n+3) = st_real(2,n+1) ; % real is 0
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st_imag(3,n+3) = st_real(2,n+3); % mult -j
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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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for n = 1 : 4
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Wn(n) = exp(-1i * (n-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 n = 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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stage(4,n+k) = stage(3,n+k) + Wn(k+1)*stage(3,n+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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stage(4,n+k+4) = stage(3,n+k) - Wn(k+1)*stage(3,n+k+4);
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end
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end
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% calculations using separate real and imaginary numbers
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for n = 1 : 2^3 : fftLength
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for k = 0 : 3
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st_real_tmp(3,n+k+4) = ( Wr(k*4+1) * st_real(3,n+k+4) ) - ( Wi(k*4+1) * st_imag(3,n+k+4) );
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st_imag_tmp(3,n+k+4) = ( Wi(k*4+1) * st_real(3,n+k+4) ) + ( Wr(k*4+1) * st_imag(3,n+k+4) );
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end
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end
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for n = 1 : 2^3 : fftLength
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for k = 0 : 3
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% Even pair
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st_real(4,n+k) = st_real(3,n+k) + st_real_tmp(3,n+k+4);
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st_imag(4,n+k) = st_imag(3,n+k) + st_imag_tmp(3,n+k+4);
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% Odd par
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st_real(4,n+k+4) = st_real(3,n+k) - st_real_tmp(3,n+k+4);
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st_imag(4,n+k+4) = st_imag(3,n+k) - st_imag_tmp(3,n+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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for n = 1 : 8
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Wn(n) = exp(-1i * (n-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 n = 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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stage(5,n+k) = stage(4,n+k) + Wn(k+1)*stage(4,n+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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stage(5,n+k+8) = stage(4,n+k) - Wn(k+1)*stage(4,n+k+8);
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end
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end
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% calculations using separate real and imaginary numbers
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for n = 1 : 2^4 : fftLength
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for k = 0 : 7
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st_real_tmp(4,n+k+8) = ( Wr(k*2+1) * st_real(4,n+k+8) ) - ( Wi(k*2+1) * st_imag(4,n+k+8) );
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st_imag_tmp(4,n+k+8) = ( Wi(k*2+1) * st_real(4,n+k+8) ) + ( Wr(k*2+1) * st_imag(4,n+k+8) );
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end
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end
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for n = 1 : 2^4 : fftLength
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for k = 0 : 7
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% Even pair
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st_real(5,n+k) = st_real(4,n+k) + st_real_tmp(4,n+k+8);
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st_imag(5,n+k) = st_imag(4,n+k) + st_imag_tmp(4,n+k+8);
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% Odd par
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st_real(5,n+k+8) = st_real(4,n+k) - st_real_tmp(4,n+k+8);
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st_imag(5,n+k+8) = st_imag(4,n+k) - st_imag_tmp(4,n+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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for n = 1 : 16
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Wn(n) = exp(-1i * (n-1) * 2 * pi/ 32 );
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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 n = 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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stage(6,n+k) = stage(5,n+k) + Wn(k+1)*stage(5,n+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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stage(6,n+k+16) = stage(5,n+k) - Wn(k+1)*stage(5,n+k+16);
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end
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end
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% calculations using separate real and imaginary numbers
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for n = 1 : 2^5 : fftLength
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for k = 0 : 15
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st_real_tmp(5,n+k+16) = ( Wr(k*1+1) * st_real(5,n+k+16) ) - ( Wi(k*1+1) * st_imag(5,n+k+16) );
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st_imag_tmp(5,n+k+16) = ( Wi(k*1+1) * st_real(5,n+k+16) ) + ( Wr(k*1+1) * st_imag(5,n+k+16) );
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end
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end
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for n = 1 : 2^5 : fftLength
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for k = 0 : 15
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% Even pair
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st_real(6,n+k) = st_real(5,n+k) + st_real_tmp(5,n+k+16);
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st_imag(6,n+k) = st_imag(5,n+k) + st_imag_tmp(5,n+k+16);
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% Odd par
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st_real(6,n+k+16) = st_real(5,n+k) - st_real_tmp(5,n+k+16);
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st_imag(6,n+k+16) = st_imag(5,n+k) - st_imag_tmp(5,n+k+16);
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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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for n = 1 : bits +1
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%plot( abs( real_n(i, :) + j.*imag_n(i, :) ) );
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plot( abs( stage(i,1:fftLength/2) ) );
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pause(1);
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stem( abs( stage(n,1:fftLength/2) ) );
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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-1)*fstep/1000, 1) ; % calculate new tick in kHz
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xticklabels(xtnew) % set new tick labels
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title('FFT using custom function')
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ylabel('magnitude'), xlabel('kHz')
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figure(6)
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for n = 1 : bits +1
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%plot( abs( real_n(i, :) + j.*imag_n(i, :) ) );
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temp = st_real + 1i * st_imag;
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stem( abs( temp(n,1:fftLength/2) ) );
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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-1)*fstep/1000, 1) ; % calculate new tick in kHz
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xticklabels(xtnew) % set new tick labels
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title('FFT using custom function real/imag separate')
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ylabel('magnitude'), xlabel('kHz')
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figure(7)
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dif2 = 100* abs(temp(bits +1,1:fftLength/2) - ft(1:fftLength/2))./abs(ft(1:fftLength/2)) ;
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plot(dif2, 'blue')
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title('Difference in calculations')
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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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ylabel('percents, %'), xlabel('kHz')
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