Adding sine signal to dynamic signal

y(t) = x(t-10) + sin(t) I need to create the solution for this dynamic signal, I couldnt delay the signal that I have created randomly. Would you mind to help?

signal_length= 0:0.5:100;
rng(1);
xt=rand(1,length(signal_length));
plot(signal_length,xt,'color','r','linewidth',1.5)
grid on
xlabel('t','FontSize',10)
ylabel('x(t)', 'FontSize',10)
figure
t=0:0.5:100;
rng(1);
xt=rand(1,length(signal_length));
delayed_xt= delayseq(xt,10);
plot(t,delayed_xt,'color','r','linewidth',1.5)
grid on
xlabel('t','FontSize',10)
ylabel('x(t-10)', 'FontSize',10)

t=  -20:0.5:100;
w_sin= 2*pi/30;
sint= sin(w_sin*t);
figure
plot(t,sint,'color','r','LineWidth',1.5)
axis([0 100 -1 1])
grid on
xlabel('t','fontSize',10)
ylabel('sint(t)','FontSize',10)

grid on
t1=  0:0.5:100;
xlabel('t','fontSize',10)
ylabel('sint(t)','FontSize',10)
yt=delayed_xt+sint(41:length(sint));
figure
plot(t1,yt,'color','r','LineWidth',1.5)
xlabel('t','fontSize',10)
ylabel('y(t)','FontSize',10)
grid on

Answer 1

[William Rose]

@Nurullah Çetin,

dt=0.5;         %time step (s)
t=0:dt:100;     %time (s)
tlag=10;        %lag (s)
x=rand(1,length(t));
y=zeros(1,length(t));               %pre-allocate y
y(tlag/dt+1:end)=x(1:end-tlag/dt);  %y=x(t-tlag)
y=y+sin(t);  %add the sine wave
figure; 
plot(t,x,'-r.',t,y,'-b.');
grid on; legend('x','y'); xlabel('Time (s)');

Try it.

What would you expect the cross-correlation of x with y to look like? This is a way of checking to see if the script above worked as expected. Let's see:

[xc,lags] = xcorr(x,y,40,'normalized');
stem(lags*dt,xc)
xlabel('Time lag (s)'); title('CrossCorr(x,y)')

Interesting, and reassuring.

[Nurullah Çetin]

Thanks sir, it is like adding noise to the sine signal, should be like firslty noise, then shifted noise and then sine signal, after that adding shifted noise to the sine signal.

[William Rose]

@Nurullah Çetin,

I'm sorry that I do not understand your description of what you want x(t) and y(t) to be. My script computes x(t) and y(t) according to the equations

x(t) = noise

and

y(t) = x(t-10) + sin(t)

The second equation above is the equaiton you provided in your original posting. If either equation above is incorrect, please provide the correct equations.