MATLAB - Delay sine wave

I have a damped sine wave as below:

N=250;

Fs=20;

Ts=1/Fs;

t=(0:N-1)*Ts;

A = 3;

f = 1;

x = A*exp(-t).*sin(2*pi*f*t);

How can I generate a delay signal from the damped sine wave x, so that:

y(n) = a*x(n-k)+b(n),

Where a is the attenuation coefficient, b(n) is the noise and k is a delay

Answer 1

[Alan Stevens]

Like this?

N=250; 
Fs=20; 
Ts=1/Fs; 
t=(0:N-1)*Ts;
A = 3; 
f = 1;
signal = @(t) A*exp(-t).*sin(2*pi*f*t);
x = signal(t);

a = 0.7;    % attenuation coefficient
k = 10*Ts;  % delay time
b = 0.1*randn(1,numel(t));  % normally distributed noise 
y = a*signal(t-k) + b;

plot(t,x,t,y),grid
xlabel('t'),ylabel('signal')
legend('signal','delayed signal')

[long le]

Thank you.

But I think that the length/time of the emitted signal should be shorter than the received one because of the delay?

The received signal should be longer

[Alan Stevens]

I wouldn't know! But doesn't it just mean you define a different timespan for the delayed signal?