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direct_2016_0202.m
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direct_2016_0202.m
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clear all
close all
clc
fs = 600;
f1 = 60;
f2 = 120;
f3 = 180;
f4 = 240;
F1 = f1/fs;
F2 = f2/fs;
F3 = f3/fs;
F4 = f4/fs;
N = 1024;
n = 0:N-1;
x = sin(2*pi*n*F1) + sin(2*pi*n*F2) + sin(2*pi*n*F3)+ sin(2*pi*n*F4);
x = x/(max([abs(min(x)) abs(max(x))])); % normalizacija
figure;
plot(n, x);
title('Input signal');
xlabel('n');
axis([0 100 min(x)-0.5 max(x)+0.5]);
fc = 60;
Aa = 40; Ap = 0.5;
[b, a] = power_line_noise_filter(fs, fc, Aa, Ap);
y = IIR_direct_II(b, a, x);
Nfreqz = 4096;
[H, w_in] = freqz(x, Nfreqz);
Ha = abs(H);
[H1, w_out] = freqz(y, Nfreqz);
Ha1 = abs(H1);
figure;
plot(w_in*fs/2/pi, Ha);
title('Input signal - amplitude');
xlabel('w');
ylabel('|H(e^(jW))|');
figure;
plot(w_out*fs/2/pi, Ha1);
title('Output signal - amplitude');
xlabel('w');
ylabel('|H(e^(jW))|');
%% 4.a
bit_length = 5;
frac_length = 10;
word_length = frac_length + bit_length;
while 1
FixedPointAttributes = fimath ( 'RoundingMethod', 'Floor', 'OverflowAction', 'Saturate', ...
'ProductMode', 'SpecifyPrecision', 'ProductWordLength', 2*word_length, 'ProductFractionLength', 2*frac_length, ...
'SumMode', 'SpecifyPrecision', 'SumWordLength', 2*word_length, 'SumFractionLength', 2*frac_length) ;
FI_a = fi(a, true, word_length, frac_length, FixedPointAttributes);
FixedPointAttributes.OverflowAction = 'Wrap';
FI_a = fi(FI_a, true, word_length, frac_length, FixedPointAttributes);
FI_zp = roots(double(FI_a));
max_pole = max(abs(double(FI_zp)));
if max_pole >= 1
frac_length = frac_length+1;
word_length = frac_length+bit_length;
else
disp('Potreban broj bita za razlomljeni deo: ')
disp(frac_length);
break
end
end
FI_a = fi (a, true, word_length, frac_length, FixedPointAttributes);
FI_b = fi (b, true, word_length, frac_length, FixedPointAttributes);
FI_zp = roots(double(FI_a));
FI_zo = roots(double(FI_b));
FI_a1 = fi (a, true, word_length-1, frac_length, FixedPointAttributes);
FI_b1 = fi (b, true, word_length-1, frac_length, FixedPointAttributes);
FI_zp1 = roots(double(FI_a1));
FI_zo1 = roots(double(FI_b1));
figure;
subplot(121);
[hz, hp, ht] = zplane(FI_zo, FI_zp);
title('zeros and poles');
xlabel('Re(z)');
ylabel('Im(z)');
subplot(122);
[hz1, hp1, ht1] = zplane(FI_zo1, FI_zp1);
title('zeros and poles - not stable');
xlabel('Re(z)');
ylabel('Im(z)');
%% 4.b
frac_length1 = 10;
bit_length1 = frac_length1+bit_length;
while 1
FixedPointAttributes = fimath ( 'RoundingMethod', 'Floor', 'OverflowAction', 'Saturate', ...
'ProductMode', 'SpecifyPrecision', 'ProductWordLength', 2*bit_length1, 'ProductFractionLength', 2*frac_length1, ...
'SumMode', 'SpecifyPrecision', 'SumWordLength', 2*bit_length1, 'SumFractionLength', 2*frac_length1) ;
FI_a = fi(a, true, bit_length1, frac_length1, FixedPointAttributes);
FI_b = fi(b, true, bit_length1, frac_length1, FixedPointAttributes);
FixedPointAttributes.OverflowAction = 'Wrap';
FI_a = fi(FI_a, true, bit_length1, frac_length1, FixedPointAttributes);
FI_b = fi(FI_b, true, bit_length1, frac_length1, FixedPointAttributes);
Nfreqz = 4096;
[H, w1] = freqz(b, a, Nfreqz);
Ha = abs(H);
[H1, w2] = freqz(double(FI_b), double(FI_a), Nfreqz);
Ha1 = abs(H1);
dHa = max(abs(Ha - Ha1));
if dHa >= 0.01
frac_length1 = frac_length1+1;
bit_length1 = frac_length1+bit_length;
else
disp('Minimalan broj bita za razlomljeni deo: ')
disp(frac_length1);
break
end
end
figure;
plot(w1, Ha);
title('Amplitude filter characteristics'), grid on, hold on
plot(w2, Ha1, 'r');
xlabel('w');
ylabel('|H(e^(jw))|');
ylim([0.85 1.05]);
xlim([0.5 0.75]);
%% 5
PWL = 63;
PFL = 46;
SWL = 63;
SFL = 46;
FCB = 28;
FCF = 23;
SB = 24;
SF = 23;
FixedPointAttributes = fimath ( 'RoundingMethod', 'Floor', 'OverflowAction', 'Saturate', ...
'ProductMode', 'SpecifyPrecision', 'ProductWordLength', PWL, 'ProductFractionLength', PFL, ...
'SumMode', 'SpecifyPrecision', 'SumWordLength', SWL, 'SumFractionLength', SFL) ;
fi_params = struct('FILTER_COEFITIENTS_BITLENGTH', FCB, 'FILTER_COEFITIENTS_FRAC', FCF, ...
'SIGNAL_BITLENGTH', SB, 'SIGNAL_FRAC', SF);
FI_a = fi(a, true, fi_params.FILTER_COEFITIENTS_BITLENGTH, fi_params.FILTER_COEFITIENTS_FRAC, FixedPointAttributes);
FI_b = fi(b, true, fi_params.FILTER_COEFITIENTS_BITLENGTH, fi_params.FILTER_COEFITIENTS_FRAC, FixedPointAttributes);
FI_x = fi(x, true, fi_params.SIGNAL_BITLENGTH, fi_params.SIGNAL_FRAC, FixedPointAttributes);
FixedPointAttributes.OverflowAction = 'Wrap';
FI_a = fi(FI_a, true, fi_params.FILTER_COEFITIENTS_BITLENGTH, fi_params.FILTER_COEFITIENTS_FRAC, FixedPointAttributes);
FI_b = fi(FI_b, true, fi_params.FILTER_COEFITIENTS_BITLENGTH, fi_params.FILTER_COEFITIENTS_FRAC, FixedPointAttributes);
FI_x = fi(FI_x, true, fi_params.SIGNAL_BITLENGTH, fi_params.SIGNAL_FRAC, FixedPointAttributes);
y = IIR_direct_II(b, a, x);
y_fixed_point = FI_IIR_direct_II(FI_b, FI_a, FI_x);
figure
subplot(411);
plot(n, x);
title('Ulazni signal');
xlabel('n');
xlim([0 1050]);
subplot(412);
plot(n, y);
title('Izlazni signal sa double preciznoscu');
xlabel('n');
xlim([0 1050]);
subplot(413);
plot(n, y_fixed_point);
title('Izlazni signal sa fixed-point preciznoscu');
xlabel('n');
xlim([0 1050]);
err = y - double(y_fixed_point);
subplot(414);
plot(n, err);
title('Razlika izlaznih signala');
xlabel('n');
xlim([0 1050]);