storiing sem2

hod2/1.m

@@ -0,0 +1,27 @@
+% X(k)=1/N \sum_{n=0}^{N-1} x(n)*e^{-j*2*\pi*n*k/N}
+% x(n)=\sum_{n=0}^{N-1} X(k)e^{j*2*\pi*n*k/N}
+
+x = [8,8,8,8,8,8,8,8]
+X = []
+N = length(x)
+
+for k = 0:(N - 1)
+  Xk = 0;
+  for n = 0:(N - 1)
+    Xk = Xk + ( x(n + 1) .* exp(-1j * 2 * pi * n * k / N) );
+  end
+  X(end + 1) =  Xk;
+end
+X = 1/N * X
+
+temp = 1/N * fft(x)
+
+y = [];
+for n = 0:(N - 1)
+  xn = 0;
+  for k = 0:(N - 1)
+    xn = xn + ( X(k + 1) .* exp(1j * 2 * pi * n * k / N) );
+  end
+  y(end + 1) =  xn;
+end
+y

hod2/2.m

@@ -0,0 +1,8 @@
+% X(k)=1/N \sum_{n=0}^{N-1} x(n)*e^{-j*2*\pi*n*k/N}
+% x(n)=\sum_{n=0}^{N-1} X(k)e^{j*2*\pi*n*k/N}
+
+
+x = [8,8,8,8,8,8,8,8]
+X = DFT_priama(x)
+
+x = DFT_spatna(X)

hod2/DFT_priama.m

@@ -0,0 +1,13 @@
+% priama X(k) z x(n)
+function X = DFT_priama(x)
+  N = length(x);
+  X = zeros(1,N);
+  for k = 0:(N - 1)
+    Xk = 0;
+    for n = 0:(N - 1)
+      Xk = Xk + ( x(n + 1) .* exp(-1j * 2 * pi * n * k / N) );
+    end
+    X(k + 1) =  Xk;
+  end
+  X = 1/N * X;
+end

hod2/DFT_spatna.m

@@ -0,0 +1,13 @@
+% spatna x(n) z X(k)
+function x = DFT_spatna(X)
+  N = length(X);
+  x = zeros(1,N);
+  for n = 0:(N - 1)
+    xn = 0;
+    for k = 0:(N - 1)
+      xn = xn + ( X(k + 1) .* exp(1j * 2 * pi * n * k / N) );
+    end
+    x(n + 1) =  xn;
+  end
+end
+

hod3/1.m

@@ -0,0 +1,32 @@
+clc;
+close all;
+
+max_val = 99
+n = 0:max_val
+f = 0.05
+% x = (x^5-x^3+x^2-1)*(x^6-2);
+%
+% Konvolucia
+a = sin(2*pi*f*n)
+
+b = sin(2*pi*f*n+0.5)
+c = conv(a,b)
+
+
+figure;
+stem(a)
+hold on;
+stem(b)
+
+figure;
+stem(c)
+
+figure;
+% Korelacia
+R = xcorr(a,b)
+stem(R)
+
+figure;
+% AutoKorelacia
+T = autocorr(a)
+stem(T)

hod3/2.m

@@ -0,0 +1,33 @@
+clc;
+close all;
+
+max_val = 99
+n = 0:max_val
+f = 0.05
+% x = (x^5-x^3+x^2-1)*(x^6-2);
+%
+% Konvolucia
+a = sin(2*pi*f*n)
+
+b = sin(2*pi*f*n+0.5)
+c = conv(a,b)
+
+
+figure;
+stem(a)
+hold on;
+stem(b)
+
+figure;
+stem(c)
+
+figure;
+% Korelacia
+R = xcorr(a,b)
+stem(R)
+
+figure;
+% AutoKorelacia
+T = autocorr(a)
+stem(T)
+

hod4/1.m

@@ -0,0 +1,30 @@
+% y(n)=(3/4)*y(n-1) + (1/6)*y(n-2) + x(n)+(1/2)*x(n-1)
+clc;
+clear all;
+close all;
+
+cit = [1, 0.5]
+men = [1, -0.75, -1/6]
+roots(men)
+figure;
+zplane(cit, men)
+figure;
+freqz(cit, men, 'whole')
+
+z = roots(cit);
+p = roots(men);
+theta = pi/4;
+r = 0.99;
+new_zero_pair = [0;0];
+new_pole_pair = [r*exp(1j*theta); r*exp(-1j*theta)];
+filter_cit = poly(new_zero_pair)
+filter_men = poly(new_pole_pair)
+z_new = [z; new_zero_pair];
+p_new = [p; new_pole_pair];
+cit_new = poly(z_new)
+men_new = poly(p_new) 
+figure;
+zplane(cit_new, men_new)
+figure;
+freqz(cit_new, men_new, 'whole')
+

hod4/2.m

@@ -0,0 +1,28 @@
+% y(n)=(3/4)*y(n-1) + (1/6)*y(n-2) + x(n)+(1/2)*x(n-1)
+clc;
+clear all;
+close all;
+
+cit = [1, 0.5]
+men = [1, -0.75, -1/6]
+roots(men)
+figure;
+zplane(cit, men);
+figure;
+freqz(cit, men, 'whole');
+
+x = [zeros(1, 10), 1, zeros(1, 100)]
+y = zeros(size(x));
+for n = 3:length(x)
+    y(n) = 0.75*y(n-1) + (1/6)*y(n-2) + x(n) + 0.5*x(n-1)
+
+    stem(0:length(x)-1, y, 'filled');     % plot discrete-time sequence
+    title(['System output up to sample n = ' num2str(n)]);
+    xlabel('n');
+    ylabel('y(n)');
+    ylim([-0.5 1.5]);                     % fixed axis for stability
+    grid on;
+    pause(0.25);
+end
+
+

semestralka/FIR.m

@@ -0,0 +1,61 @@
+clc;
+close all;
+clear all;
+
+f0_ohranicene = [25, 20, 10, 12.5];
+% semestralka
+rawText = fileread('data6.dat');
+nums = regexp(rawText, '[-+]?\d+', 'match');
+data = int16(str2double(nums));
+
+Fs = 200;
+N = 3000;
+notch_hw = 0.08;
+trans_bw = 0.08;
+f0_sorted = sort(f0_ohranicene);
+F = [];
+A = [];
+prev_end = 0;
+
+for k = 1:length(f0_sorted)
+    f0 = f0_sorted(k);
+    notch_start = (f0 - notch_hw) / (Fs/2);
+    notch_end = (f0 + notch_hw) / (Fs/2);
+    trans_start = max(prev_end + 0.001, (f0 - notch_hw - trans_bw) / (Fs/2));
+    trans_end = (f0 + notch_hw + trans_bw) / (Fs/2);
+    if trans_start > prev_end + 0.001
+        F = [F, prev_end, trans_start];
+        A = [A, 1, 1];
+    end
+    F = [F, notch_start, notch_end];
+    A = [A, 0, 0];
+    prev_end = trans_end;
+end
+
+if prev_end < 1
+    F = [F, prev_end, 1];
+    A = [A, 1, 1];
+end
+
+F = max(0, min(1, F));
+b = firls(N, F, A);
+a = 1;
+
+b = real(b);
+figure;
+zplane(b, a);
+figure;
+freqz(b, a);
+set(gcf, 'Color', 'none');
+set(gca, 'Color', 'none');
+print('-depsc', 'fig1_semD.eps');
+figure;
+freqz(b, a);
+filtered_data = filtfilt(b, a, double(data));
+title('Filtrovaný signál');
+xlabel('Vzorky');
+ylabel('Amplitúda');
+set(gcf, 'Color', 'none');
+set(gca, 'Color', 'none');
+plot(filtered_data);
+print('-depsc', 'fig2_semD.eps');

semestralka/IIR_SOS.m

@@ -0,0 +1,56 @@
+clc;
+close all;
+clear all;
+
+f0_ohranicene = [25, 20, 10, 12.5];
+rawText = fileread('data6.dat');
+nums = regexp(rawText, '[-+]?\d+', 'match');
+data = int16(str2double(nums));
+
+Fs = 200;
+r = 0.98;
+
+% predalokovana SOS matica pre vsetky filtrovane zlozky
+% 6 lebo koeficienty [b0, b1, b2, a0, a1, a2]
+sos = zeros(length(f0_ohranicene), 6);
+
+for k = 1:length(f0_ohranicene)
+    theta = 2 * pi * (f0_ohranicene(k) / Fs);
+    b = [1, -2*cos(theta), 1];
+    a = [1, -2*r*cos(theta), r^2];
+    sos(k, :) = [b, a]
+end
+
+figure;
+[z, p, k_gain] = sos2zp(sos);
+
+figure;
+zplane(z, p);
+title('Nuly a póly filtra');
+xlabel('Reálna časť');
+ylabel('Imaginárna časť');
+set(gcf, 'Color', 'none');
+set(gca, 'Color', 'none');
+print('-depsc', 'fig2_semE.eps');
+
+figure;
+freqz(sos, 4096, Fs);
+title('Frekvenčná charakteristika SOS filtra');
+xlabel('Frekvencia [Hz]');
+ylabel('Zosilnenie [dB]');
+set(gcf, 'Color', 'none');
+set(gca, 'Color', 'none');
+print('-depsc', 'fig3_semE.eps');
+
+filtered_data = sosfilt(sos, double(data));
+figure;
+plot(filtered_data);
+title('Filtrovaný signál');
+xlabel('Vzorky');
+ylabel('Amplitúda');
+grid on;
+set(gcf, 'Color', 'none');
+set(gca, 'Color', 'none');
+set(gcf, 'PaperPosition', [0 0 1.7*6 0.75*4.2]);
+set(gcf, 'PaperSize', [1.7*6 0.75*4.2]);
+print('-depsc', 'fig4_semE.eps');

semestralka/docs.txt

@@ -0,0 +1,2 @@
+https://en.wikipedia.org/wiki/Infinite_impulse_response
+https://courses.physics.illinois.edu/ece401/fa2020/slides/lec15.pdf

semestralka/full_IIR.m

@@ -0,0 +1,102 @@
+clc;
+close all;
+clear all;
+
+% semestralka
+rawText = fileread('data6.dat');
+nums = regexp(rawText, '[-+]?\d+', 'match');
+data = int16(str2double(nums));
+
+X = DFT_priama(double(data));
+n = length(X);
+Fs = 200;
+freq = (0:n-1)*Fs/n;
+
+figure;
+plot(double(data));
+figure;
+plot(freq, X)
+%3
+figure;
+magX = abs(X);
+plot(freq, magX)
+%4
+% freq shift pre -Fs/2 po Fs/2
+freq_shift = (-n/2:n/2-1)*(Fs/n);
+figure;
+subplot(2,1,1);
+plot(freq_shift, real(fftshift(X)));
+title('Reálna časť posunutého spektra');
+xlabel('Frekvencia [Hz]');
+ylabel('Reálna hodnota');
+subplot(2,1,2);
+plot(freq_shift, imag(fftshift(X)), 'r');
+title('Imaginárna časť posunutého spektra');
+xlabel('Frekvencia [Hz]');
+ylabel('Imaginárna hodnota');
+set(gcf, 'PaperPosition', [0 0 1.7*6 0.75*4.2]);
+set(gcf, 'PaperSize', [1.7*6 0.75*4.2]);
+set(gcf, 'Color', 'none'); set(gca, 'Color', 'none');
+print('-depsc', 'fig_im_real_semC.eps');
+%5
+figure;
+plot(freq, imag(X), 'r');
+%6
+figure;
+plot(freq, real(X));
+%7
+figure;
+% fazove spektrum
+plot(freq, angle(X))
+
+[pks, locs] = findpeaks(magX, 'NPeaks', 10, 'SortStr', 'descend');
+f0 = freq(locs)
+f0b = f0(f0 < 100); % nyquistov teorem
+f0_ohranicene = f0b
+
+f0_ohranicene(f0_ohranicene < 2) = [];
+r = 0.975;
+b = 1;
+a = 1;
+
+for k = 1:length(f0_ohranicene)
+    theta = 2*pi*(f0_ohranicene(k)/Fs);
+    b = conv(b, [1, -2*cos(theta), 1]);
+    a = conv(a, [1, -2*r*cos(theta), r^2]);
+end
+
+figure;
+zplane(b, a);
+title('Nuly a póly filtra');
+xlabel('Reálna časť');
+ylabel('Imaginárna časť');
+set(gcf, 'Color', 'none'); set(gca, 'Color', 'none');
+print('-depsc', 'fig1_semC.eps');
+
+figure;
+freqz(b, a);
+title('Frekvenčná charakteristika (1)');
+xlabel('Frekvencia [Hz]');
+ylabel('Zosilnenie [dB]');
+set(gcf, 'Color', 'none'); set(gca, 'Color', 'none');
+print('-depsc', 'fig2_semC.eps');
+
+figure;
+freqz(b, a);
+title('Frekvenčná charakteristika (2)');
+xlabel('Frekvencia [Hz]');
+ylabel('Zosilnenie [dB]');
+set(gcf, 'Color', 'none'); set(gca, 'Color', 'none');
+print('-depsc', 'fig3_semC.eps');
+
+filtered_data = filter(b, a, double(data));
+figure;
+plot(filtered_data);
+title('Filtrovaný signál');
+xlabel('Vzorky');
+ylabel('Amplitúda');
+grid on;
+set(gcf, 'Color', 'none'); set(gca, 'Color', 'none');
+set(gcf, 'PaperPosition', [0 0 1.7*6 0.75*4.2]);
+set(gcf, 'PaperSize', [1.7*6 0.75*4.2]);
+print('-depsc', 'fig4_semC.eps');

semestralka2/analyza.m

@@ -0,0 +1,72 @@
+clc;
+close all;
+clear all;
+
+[y, Fs] = audioread('sem2.wav');
+t = (0:length(y)-1) / Fs;
+
+figure; %1
+plot(t, y);
+xlabel('Time');
+ylabel('Amplitude');
+title('Waveform sem2.wav');
+grid on;
+
+[y1, Fs1] = audioread('flac.wav');
+[y2, Fs2] = audioread('flac2.wav');
+
+t1 = (0:length(y1)-1) / Fs1;
+t2 = (0:length(y2)-1) / Fs2;
+
+figure; %2
+plot(t1, y1);
+xlabel('Time [s]');
+ylabel('Amplitude');
+title('Waveform flac.wav');
+grid on;
+
+figure; %3
+plot(t2, y2);
+xlabel('Time [s]');
+ylabel('Amplitude');
+title('Waveform flac2.wav');
+grid on;
+
+N1 = length(y1);
+N2 = length(y2);
+
+X1 = fft(y1);
+X2 = fft(y2);
+
+freq_shift1 = (-N1/2 : N1/2 - 1) * (Fs1 / N1);
+freq_shift2 = (-N2/2 : N2/2 - 1) * (Fs2 / N2);
+
+figure; %4
+subplot(2,1,1);
+plot(freq_shift1, real(fftshift(X1)), 'b');
+title('Reálna časť posunutého spektra flac.wav');
+xlabel('Frekvencia [Hz]');
+ylabel('Reálna hodnota');
+grid on;
+subplot(2,1,2);
+plot(freq_shift1, imag(fftshift(X1)), 'r');
+title('Imaginárna časť posunutého spektra flac.wav');
+xlabel('Frekvencia [Hz]');
+ylabel('Imaginárna hodnota');
+grid on;
+set(gcf, 'Color', 'none'); set(gca, 'Color', 'none');
+
+figure; %5
+subplot(2,1,1);
+plot(freq_shift2, real(fftshift(X2)), 'b');
+title('Reálna časť posunutého spektra flac2.wav');
+xlabel('Frekvencia [Hz]');
+ylabel('Reálna hodnota');
+grid on;
+subplot(2,1,2);
+plot(freq_shift2, imag(fftshift(X2)), 'r');
+title('Imaginárna časť posunutého spektra flac2.wav');
+xlabel('Frekvencia [Hz]');
+ylabel('Imaginárna hodnota');
+grid on;
+set(gcf, 'Color', 'none'); set(gca, 'Color', 'none');

semestralka2/analyza_b.m

@@ -0,0 +1,114 @@
+clc;
+close all;
+clear all;
+
+[y, Fs] = audioread('sem2.wav');
+t = (0:length(y)-1) / Fs;
+
+figure; %1
+plot(t, y);
+xlabel('Time');
+ylabel('Amplitude');
+title('Waveform sem2.wav');
+grid on;
+
+[y1, Fs1] = audioread('flac.wav');
+[y2, Fs2] = audioread('flac2.wav');
+
+t1 = (0:length(y1)-1) / Fs1;
+t2 = (0:length(y2)-1) / Fs2;
+
+figure; %2
+plot(t1, y1);
+xlabel('Time [s]');
+ylabel('Amplitude');
+title('Waveform flac.wav');
+grid on;
+
+figure; %3
+plot(t2, y2);
+xlabel('Time [s]');
+ylabel('Amplitude');
+title('Waveform flac2.wav');
+grid on;
+
+N1 = length(y1);
+N2 = length(y2);
+
+X1 = fft(y1);
+X2 = fft(y2);
+
+freq_shift1 = (-N1/2 : N1/2 - 1) * (Fs1 / N1);
+freq_shift2 = (-N2/2 : N2/2 - 1) * (Fs2 / N2);
+
+figure; %4
+subplot(2,1,1);
+plot(freq_shift1, real(fftshift(X1)), 'b');
+title('Reálna časť posunutého spektra flac.wav');
+xlabel('Frekvencia [Hz]');
+ylabel('Reálna hodnota');
+grid on;
+subplot(2,1,2);
+plot(freq_shift1, imag(fftshift(X1)), 'r');
+title('Imaginárna časť posunutého spektra flac.wav');
+xlabel('Frekvencia [Hz]');
+ylabel('Imaginárna hodnota');
+grid on;
+set(gcf, 'Color', 'none'); set(gca, 'Color', 'none');
+
+figure; %5
+subplot(2,1,1);
+plot(freq_shift2, real(fftshift(X2)), 'b');
+title('Reálna časť posunutého spektra flac2.wav');
+xlabel('Frekvencia [Hz]');
+ylabel('Reálna hodnota');
+grid on;
+subplot(2,1,2);
+plot(freq_shift2, imag(fftshift(X2)), 'r');
+title('Imaginárna časť posunutého spektra flac2.wav');
+xlabel('Frekvencia [Hz]');
+ylabel('Imaginárna hodnota');
+grid on;
+set(gcf, 'Color', 'none'); set(gca, 'Color', 'none');
+
+% === Najdenie špičiek len v prvej polovici spektra ===
+halfN1 = floor(N1/2);
+halfN2 = floor(N2/2);
+
+magX1 = abs(X1(1:halfN1));
+magX2 = abs(X2(1:halfN2));
+realX2 = real(X2(1:halfN2));
+imagX2 = imag(X2(1:halfN2));
+
+freq1 = (0:halfN1-1)*(Fs1/N1);
+freq2 = (0:halfN2-1)*(Fs2/N2);
+
+% ---- flac.wav (10 peaks from magnitude) ----
+[pks1, locs1] = findpeaks(magX1, 'NPeaks', 10, 'SortStr', 'descend');
+f0_1 = freq1(locs1);
+f0_1(f0_1 < 2) = []; % ignore DC and very low freq
+
+% ---- flac2.wav (4 peaks from real, 6 peaks from imag) ----
+[pks2r, locs2r] = findpeaks(abs(realX2), 'NPeaks', 4, 'SortStr', 'descend');
+f0_2r = freq2(locs2r);
+f0_2r(f0_2r < 2) = [];
+
+[pks2i, locs2i] = findpeaks(abs(imagX2), 'NPeaks', 6, 'SortStr', 'descend');
+f0_2i = freq2(locs2i);
+f0_2i(f0_2i < 2) = [];
+
+% ---- Výpis výsledkov ----
+disp('Najvýraznejšie frekvenčné zložky flac.wav (10, len 1/2 spektra):');
+disp(f0_1');
+
+disp('Najvýraznejšie frekvenčné zložky flac2.wav - reálna časť (4, len 1/2 spektra):');
+disp(f0_2r');
+
+disp('Najvýraznejšie frekvenčné zložky flac2.wav - imaginárna časť (6, len 1/2 spektra):');
+disp(f0_2i');
+
+
+
+
+% // NOTCH FILTER
+