There is a nonsense signal about Convolution and I couldn't understand what to do.

[circuit975]

First of all, I wholeheartedly greet my colleagues and the entire community!

I’ve set the signal as
m(t) = −t [ u(t) − u(t−2) ]
and the impulse response as
h(t) = 2 [ u(t−3) − u(t−4) ].

But while trying to find y(t), I ran into a small issue with the sketches.
Because there is no overlap, and thus they don’t convolve.
I just can’t figure out what I’m missing.

There is a topic I can't get my head around.
I have 2 signals. I’m going to convolve them, but even if I flip one of them, the other one lies horizontally on a different axis, so I can’t get them to overlap in any way — meaning I can’t convolve them.
In problems like this, how are we supposed to perform the convolution operation?
What’s the logic to solving these kinds of questions? What am I supposed to do?

I’ve attached an image of the graphs I drew below.
Any answer that helps me figure out how to proceed will be honored with sincere appreciation. I am grateful — thank you!


m(t) graphic ;

h(t) graphic ;

h(t−τ) graphic ;

 

[rjenkinsgb]

The last math class I took was over 50 years ago..
However, that look suspiciously like some form of digital filtering algorithm?

If that is the case, the output will vary at each stage (time step) as the input signal passes through; the output is dependant on that input signal.

Two signal chains would normally indicate an IIR type filter, which also needs feedback terms.

Without feedback, a single signal chain is used for an FIR-style filter (which is the type I have a fair bit of experience with).

More info

Difference Between FIR Filter and IIR Filter - GeeksforGeeks

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