Matlab examples
Matlab examples

## Example 1

Develop a code in MATLAB for one dimensional, discrete unit step function.

Result: Discrete unit step function

solution

SOLUTION

    t=-10:20;     %definition of time period
    step=heaviside(t);    %heaviside(x) is Matlab function

                           and has the value 0 for x < 0, 1 for x > 0,

                           and 0.5 for x = 0.
    step(t==0)=1;
    figure;      %command for drawn picture
    stem(t,step);
    grid on;
    xlabel('n');
    ylabel('f(n)');
    title('1D discrete step function');
    axis([-10 10 -1 3]);

## Example 2

Develop a code in MATLAB for sine wave generation.

Result: Two harmonic frequencies forming signal

solution

SOLUTION

    range=6*pi;             %max. time of the signal
    t=0:0.001:range;        %time points
    A=[1 0.13];             %vector of amplitudes
    w=[1 3];                %vector of frequencies [Hz]
    phi=[0 0];              %vector of phases
    sig1=A(1)*sin(w(1)*t+phi(1));  % definition of particular signals
    sig2=A(2)*sin(w(2)*t+phi(2));
    signal=sig1+sig2;
    figure;
    plot(t,sig1,':r','LineWidth',2);
    hold on;
    plot(t,sig2,'--g','LineWidth',2);
    hold on;
    plot(t,signal,'LineWidth',2);
    grid on;
    axis([0 rozsah -1.2*sum(A) 1.2*sum(A)]);
    xlabel('t [s]');
    ylabel('f(t)');
    title('Harmonic signals and their sum');

## Example 3

Develop a code in MATLAB for Discrete Fourier transformation and frequency characteristics.

Examples of transfer function of LDTI, magnitude and phase frequency characteristic

solution

SOLUTION

    count=32;
    Ts=4/count;   %sampling frequency
    per=4;        %number of periods
    syms k;       %symbol variable
    syms n;
    signal=[3.*ones(1,count/4) 2.*ones(1, count /4) ones(1, count /4) zeros(1, count /4)];
    fn=[];
    for n=1:per
        fn=[fn signal];
    end
    n=0:count*per-1;

    figure;
    stem(n,fn);
    title('Discrete signal');
    axis([0 length(fn) min(abs(fn))-0.5 max(abs(fn))+0.5]);
    grid on;

    figure;
    Xk=fft(signal);     %discrete Fourier transformation
    os=0:length(Xk)-1;
    stem(os,abs(Xk));   %magnitude frequency characteristic
    title('Magnitude frequency characteristic');
    grid on;

    figure;
    stem(os,angle(Xk));   %phase frequency characteristic
    title('Phase frequency characteristic');
    grid on;