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Difference between convolution and multiplication.

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dexel_uni

Newbie level 2
difference between convolution and multiplication

Hey,
I could not able to find the difference between convolution and multiplication.

difference between multiplication and convolution

The difference is huge. Convolution is an integral (in discrete a sum), you can find in every basic circuit book, systen book or maths book, convolution is useful in probability theory, as well.
Tha basic rule: in time domain convolution equals with multiplication in frequency domain.

Some basic information here:
https://en.wikipedia.org/wiki/Convolution

convolution and multiplication

convolution means if you want to find the system output when you have the input as well as the impulse response of system, then convolution will give you the system output. x*h=y... however the convolution in time domain is equal to the MULTIPLICATION in frequency domain... if you apply the unit impulse signals to the system, then you will get the system response.. it is same as if you apply onevolt to the amplifier then you will get the gain of the amplifier at the output that is similar to the impulse response.. not if you apply the intput and convolve the input with impulse response (like input X Gain) then you will get output of the system....

convolution vs multiplication

Hi
Convolution is indeed integration
But let me put it this way. Convolution is an addition of products of one constant and one time varying entity.

Hi
Convolution is indeed integration
But let me put it this way. Convolution is an addition of products of one constant and one time varying entity.

convolution multiplication

multiplication is usual multiplication one constant times another, convolution is polynomial multiplication which is multiplying 2 polynomials.

convolution multiplication different

hi

question to all........

Q: As in continous time impulse response has the amplitude equals to infinity, if we want to plot the convolution of this continous time impulse response with any of input signal x, in plot.......the problem will occur........

Please illustrate your answer ....if it is possible to plot in Matlab, with diagram, and if not possible , please give its reason with detail........

regards

convolution equal dirac

sorry
how had tell u that the impulse respose has infint amplitude, the impulse of dirac has this property

multiplication and convolution

I think you are completely confused .. there are continuous signals and discrete signals, then there are systems with finite or infinite impulse resonse. infinite impulse response does not mean infinite amplitude, it means that a certain system has an infinite response to an impulse.

now since you are trying to convolve x (which is usually the notation for a sampled signal; x(t) is a continuous signal) with an infinite duration signal, theoretically, you can do it. Even in matlab you can do it, but this would require you to sit in front of the plot, or require increasingly powerful computer, forever!

Now regarding convolution. I am sure that you have a polynomial expression which defines your impulse response. Also it will definitely have uncanceled poles.
The infinite impulse response system that you have can be of 3 types, converging, diverging and oscilatory. A diverging system is unstable and no realizable system should be like that. That leaves you with 2 scenarios; converging and oscilatory. An oscilatory system would keep on giving out the same output periodically so you will get the idea of how the outputis going to be. Lastly a convergent system, which is probably what you have, will give an output forever but the output signal after some time will be so small that you can neglect it for all practical purposes.

So decide a certain time duration for your output and stop the convolution after that point. This should give you a rough but sufficiently accurate response of your system to the input x. I hope this helps.

blooz

blooz

Points: 2
multiplication convolution wiki

No doubt, convolution and multiplication are different concerning their nature and physical and mathematical senses. All the distinguishing differences are underlined in the previous replies.

Still one coincedence exists. If you evaluate the linear (don't confuse it with circular convolution, which arises in DFT computing process) convolution of 2 discrete-time sequences you'll find out that the final result is the same as if you have multiplied 2 polynomials with coefficients, equal to sequences' samples. But it's the coincedence, nothing more. The sense of these 2 operations is quite different.

With respect,

Dmitrij

convulation - multiplication

hi every one,

ya i make mistake..in wrting the complete sentence..i appreciate for ur correction...

i mean the same ,what u have judge.."the dirac impulse", in continuse time...have its Amplitude , touches to infinity...am i correct or not ???

Q: my question is , i have the train of continous( dirac) impulses, and i want to convove it with x(t) and x?

i which case it is possible to plot in MAtlab ,with x or x(t)??????????

regards

unit impulse multiplication

Dmitrij said:
No doubt, convolution and multiplication are different concerning their nature and physical and mathematical senses. All the distinguishing differences are underlined in the previous replies.

Still one coincedence exists. If you evaluate the linear (don't confuse it with circular convolution, which arises in DFT computing process) convolution of 2 discrete-time sequences you'll find out that the final result is the same as if you have multiplied 2 polynomials with coefficients, equal to sequences' samples. But it's the coincedence, nothing more. The sense of these 2 operations is quite different.

With respect,

Dmitrij

I would like to differ here, if a sequence is written in its difference form then there is a one to one mapping between this difference equation and its z transform, z^-1 corresponds to a delay by one, if you extend it to the entire sequence then convolution does become a polynomial multiplication. So I'd say that instead of a coincidence its more a ramification of z transform.

vjfaisal said:
hi every one,

ya i make mistake..in wrting the complete sentence..i appreciate for ur correction...

i mean the same ,what u have judge.."the dirac impulse", in continuse time...have its Amplitude , touches to infinity...am i correct or not ???

Q: my question is , i have the train of continous( dirac) impulses, and i want to convove it with x(t) and x?

i which case it is possible to plot in MAtlab ,with x or x(t)??????????

regards

dirac impulse usually has an amplitude of 1 as far as i know. having said that, if you want to convolve this continuous pulse train there is absolutely no way to do this in continuous domain, because the moment you try to measure it, it becomes digitized or sampled. even matlab or any modern oscilloscope will measure in digital domain.
now keeping with the convention x is discrete, create a discrete dirac impulse train and then convolve it with discrete x.

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