Hi there,
I am not entirely sure i understand your question 100 percent, but one thing you can do that is very informative is to sit down and start with a simple filter like a resistor and capacitor (low pass filter) and a simple forcing function like the unit step function, or whatever you choose really.
Start by finding the time domain representation for the filter (impulse response), then knowing that the output of the filter is the convolution of the input function and the filter function, try to arrange the convolution integral until you get the right answer for the output. As you know, the output will be an increasing exponential that starts at Vout=0 and ends at Vout=1.
If you like after that you can change the forcing function to a ramp (whatever slope you want) and see that the output looks right, which you can check with the circuit simulator of your choice.
It also helps to draw a graph of this process.
Also, for real physical systems the integral is often changed to:
y(t)=Integral[0 to +inf] x(t-z)h(z) dz
where it may be a little easier to spot that the variable of integration is z, not t.
Here's a discrete form that makes it a little easier to see too:
y(n)=Sum[k=-inf to +inf] x(k)h(n-k)
where we see we are summing an awful lot just for one n.
It's also very illustrative to convert the low pass filter impulse response into a discrete form (as well as the step or ramp function) and then go through the summation for each n. The result is the discrete form of the output and all this is very easy to graph.