Generate user-defined signal

I want to generate a user-defined signal (either with Matlab and / or Simulink):

In the diagram above, you can see two plots. The upper signal represents the "trigger" for the lower signal. As soon as the trigger changes from 0 to 1, the desired output-signal should also change from 0 to 1. In contrast to the trigger-signal, the output-signal changes with some time delay. As drawn in the diagram, the change between 0 and 1 can be simple straight-line equation (f(t) = mt + y). However, it would be great if the trigger-signal could also initiate some non-linear transition (e.g. a parabolic function).

As the trigger changes from 1 to 0, the output-signal should change with the same specific transition (e.g. a linear or non-linear).

I know the time that it takes to change from state 0 to state 1 in the signal-plot. Furthermore, I know the formula which describes the transition from 0 to 1 (and from 1 to 0). However, I am not able to bring everything together in order to recieve the desired output-signal.

Can you please help me?

Regards, Phil

[Jan]

In which form is your initial signal available? As vector with a certain frequency?

Answer 1

[Jan]

signal = [0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0];
t      = 1:length(signal);
d      = diff(signal);
on     = find(d == 1);
off    = find(d == -1);

f = zeros(1, length(signal));
f(on:on + 3)      = linspace(0, 1, 4);       % Linear ascend
f(on + 4:off - 1) = 1; 
f(off:off + 3)    = linspace(1, 0, 4) .^ 2;  % Quadratic descent
plot(t, f, 'r', t, signal, 'b')