[SOLVED] How to build a ramp signal equation?

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I need to set a ramp equation: y-axis is h(t), and x-axis is t (=time).
So I think of two different equations for this.

(Equation1)
h(t) = a1 * t
where a1 is a slope (or gain), and t is time.

(Equation2)
h(t) = a2 * u(t)
where a2 is a slope (or gain), and u(t) is an unit function.

Which one is correct to express a ramp signal? What's the reason for it?


Thanks.
 

the first one is correct and to be practical
h(t) = a1 * t where t>=0 ( there is no time less than zero )
 

Thanks, Mahmoud. Could you please explain the reason why the second one is not proper?

Thanks.
 

mmmmm i think the attached photo will explain it
in the first situation function = u(t)
it is only a step function which will equal 1 for all t >0 and zero otherwise

in the other figure
function = a2 * u(t) where a2=5
then the function will equal 5 for all t >0 and zero otherwise

i hope u got it ......sorry for the hand drawing figures
 

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I'm sorry for typo in Equation2. I missed 't' which needs to be multiplied by u(t) as follows.

(Equation2)
h(t) = a2 * t * u(t)
where a2 is a slope (or gain), and u(t) is an unit function.

In this case, which one of equation1 and the above updated equation2 is correct for a ramp equation?

Thanks.
 

The first equation represents a ramp starting in time from -infinity going to +infinity. The second equation is the same ramp (if a1=a2) but time limited from 0 to +infinity; in this case h(t)=0 if t<=0.
Usually real signals are starting from 0; think, for example, at a circuit that is switched on at a certain time instant (this is t=0).
 

Thank you both. It is clear!
 

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