semestralka

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/1.m

@@ -0,0 +1,21 @@
+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)
+freq = (0:n-1)/n
+
+figure;
+plot(double(data));
+figure;
+plot(freq, X)
+figure;
+plot(freq, abs(X))
+figure;
+plot(freq, angle(X))