Plot step response of transfer function

I am trying to plot the step function of a difference equation. The equation is given by y(n) + 1/4*y(n-1) + 1/2*y(n-2) = x(n) + 1/2*x(n-1). Where x(n) is supposed to be the input and y(n) is the output. The error is as shown:

Is there no way to plot it using the step function?

Code:

num = [1 -1/4 -1/2];
den = [1 1/2];
s = step(num,den);
stem(s);

[Ye Ken Kok]

Sorry fot not including the input signal for x(n). Here is the input signal.

F1 = 20;
F2 = 40;
F3 = 60;
Fs = 2*F3;
t = 0:0.001:2-0.001;
n = 0:100;

x = 10*sin(2*pi*F1*t)+10*sin(2*pi*F2*t)+10*sin(2*pi*F3*t);

xn = 10*sin(2*pi*(F1/Fs)*n)+10*sin(2*pi*(F2/Fs)*n)+10*sin(2*pi*(F3/Fs)*n);

Answer 1

[Mathieu NOE]

hello

you have 2 mistakes to correct

1 - how to get a z transfer function from the difference equation

your num and den are wrong (signs are wrong and you flipped num with den)

this might help

How can I find transfer function from a difference equation? - MATLAB Answers - MATLAB Central (mathworks.com)

2 - you have a discrete not a continuous time model so use dstep instead of step

num = [0 1 1/2];
den = [1 1/4 1/2];
s = dstep(num,den);
stem(s);

all the best

[Ye Ken Kok]

Thanks for your answer, I managed to solve it with your help

Answer 2

[Sam Chak]

Hi @Ye Ken Kok

It is a input-output difference equation. Thus, you cannot use the continuous-time Laplace transform.

Since the input is not provided, here is just a simple example.

dt = 0.001;
t  = 0:dt:20;   % sample times

ykm1 = 0;       % initial value of y(k - 1)
ykm2 = 0;       % initial value of y(k - 2)
xkm1 = 0;       % initial x(k - 1)
xk   = 0;       % initial x(k)
Y    = [];      % placeholder for y(k) array
X    = [];      % placeholder for x(k) array

for k = 1:length(t)
    % input-output difference equation
    % y(n) = - 1/4*y(n-1) - 1/2*y(n-2) + x(n) + 1/2*x(n-1)
    yk   = - 1/4*ykm1 - 1/2*ykm2 + 1*xk + 1/2*xkm1;
    ykm2 = ykm1;    % when time advances, y(k - 1) becomes y(k - 2)
    ykm1 = yk;      % when time advances, y(k) becomes y(k - 1)
    xkm1 = xk;
    xk   = sin(.05*pi*t(k));
    Y    = [Y yk];
end

plot(t, Y, 'linewidth', 1.5), grid on