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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[danadak]

Applet / utility - https://en.lntwww.de/Applets:Graphical_Convolution

https://ws.binghamton.edu/fowler/fowler%20personal%20page/EE301_files/Notes_11%20Sect%203-4%20Computing%20CT%20Conv.pdf

Linear Physical Systems - Erik Cheever

csv

lpsa.swarthmore.edu

https://eceweb1.rutgers.edu/~gajic/solmanual/slides/chapter6C.pdf

https://web.engr.oregonstate.edu/~karti/engr203/Convolution.pdf

 

[circuit975]

Applet / utility - https://en.lntwww.de/Applets:Graphical_Convolution

https://ws.binghamton.edu/fowler/fowler%20personal%20page/EE301_files/Notes_11%20Sect%203-4%20Computing%20CT%20Conv.pdf

Linear Physical Systems - Erik Cheever

csv

lpsa.swarthmore.edu

https://eceweb1.rutgers.edu/~gajic/solmanual/slides/chapter6C.pdf

https://web.engr.oregonstate.edu/~karti/engr203/Convolution.pdf

thank you for your valuable reply.

I can agree on signs similar to these, but in the signs I have shown you, one is on the up side and one is on the down side, so there can be no overlap. I'm trying to figure out how to do these things.

 

[circuit975]

Applet / utility - https://en.lntwww.de/Applets:Graphical_Convolution

https://ws.binghamton.edu/fowler/fowler%20personal%20page/EE301_files/Notes_11%20Sect%203-4%20Computing%20CT%20Conv.pdf

Linear Physical Systems - Erik Cheever

csv

lpsa.swarthmore.edu

https://eceweb1.rutgers.edu/~gajic/solmanual/slides/chapter6C.pdf

https://web.engr.oregonstate.edu/~karti/engr203/Convolution.pdf

My dear friend, first of all, I would like to express my gratitude for your valuable response.

However, what I was actually trying to say is this:

Under normal circumstances, in the first image I provided, I can visualize the convolution properly on the graph and see what aligns with what, and then perform the calculation accordingly.

But the point I was asking about — and the part I couldn't understand — was in the second image I shared: when the signal is pointing downward; in other words, when the two signals are in opposite directions, I don't know how to compute their convolution.

This is exactly where I get stuck and can't move forward, because they don't overlap in any way, and I can't take the convolution. This was precisely the part I was trying to ask about.
when I looked at the documents, I couldn't find anything similar there.

 

[rjenkinsgb]

If there is no overlap, the output is simply zero.

Convolution - Wikipedia

en.wikipedia.org

(From the Wikipedia article, the operation is similar to an FIR filter system, with one function being the signal and one the filter parameter).

 

[circuit975]

If there is no overlap, the output is simply zero.

Convolution - Wikipedia

en.wikipedia.org

(From the Wikipedia article, the operation is similar to an FIR filter system, with one function being the signal and one the filter parameter).

yes, I think so too, but is the example of the signs here correct?