# Convolution Sum [closed]

I understand convolution is linear combination of delayed impulses of decomposed signal.

$$\int_{-\infty}^{+\infty} x(\tau)h(t-\tau)\mathrm{d}\tau = g(t)$$

I want to know about these decomposed signals.

If I have my $g(t)$, can I decompose it in different ways? If yes what are those few decomposed signal? Else, I am sure that we decompose in one way for sure. But I am not able to think in reverse way.

Please guide me. If this way of thinking is correct.

I am novice in Signal Processing.

Thanks.

## closed as too broad by Stanley Pawlukiewicz, lennon310, A_A, Peter K.♦Jun 5 '18 at 15:42

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• I don't understand what the formula has to do with convolution in general? It's the convolution of some $g$ with an extremely special functional $\delta$... And: what decomposed signal are you referring to? can you give a bit of context? – Marcus Müller May 29 '18 at 9:25
• (also, I removed all the tags that seemed to be completely unrelated to your question – please add back what you think is really relevant, but if you do, please at least mention these terms in your question: Don't use tags randomly.) – Marcus Müller May 29 '18 at 9:27

I'm afraid you don't understand convolution

Let,
$x(t)$ : [1 2 3 4]
$h(t)$ : [1 2]

Your decomposed signals are now
[1 0 0 0]
[0 2 0 0]
[0 0 3 0]
[0 0 0 4]

If you were to individually apply each to the system, you'd end up with
[1 2]
[0 2 4]
[0 0 3 6]
[0 0 0 4 8]

Now a linear combination of these (which here is element-wise addition) yields
[1 4 7 10 8]

This is what your convolution equation gives you as well.

If I have my $g(t)$, can I decompose it in different ways?
Any way you like !
Could we write $g(t)$ above as a convolution of
$x(t)$ : [1 4 7 10 8], with
$h(t)$ : [1] ?
If yes, do you see how your decomposed signals are now different ?
Fourier transform does something similar as well, but, it decomposes signals into sinusoids.

If yes what are those few decomposed signal
Try to work out the answer above.

Being helpful (since you're starting off with DSP), there is usually a good depth in definitions and a quite some detail in wordings. Try to understand each in their appropriate context to get the complete picture ! Follow this OCW and good luck !

Disclaimer : I've liberally used terms like combination, decompose and linear. Like @Stanley points, they are very broad and only a narrow definition is used here.