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physical meaning of convolution

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deepa

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what is the physical meaning of convolution,
for eg,we know that integration means area under the curve,,similarly what does convoltuon mean
 

what is convolution

Physical meaning. You have a system whose impulse response is f(t). You give it a signal x(t). The output will be f(t)*x(t), where * represents convolution.

Geometrical meaning of convolution can be described with a "flip and drag" method. Some cartoons for the flip and drag method can be found here:
http://www-math.mit.edu/daimp/ConvFlipDrag.html
**broken link removed**
 

convolution meaning

hi,

convolution is just a operation. (like integration it too means something)

the physical importance could only be realized by taking a example.

consider a rectangular pulse fed to a low pass filter, what do u know about the output now?, i'd say if u know the impulse response of the system and the T and A of the rectangular pulse, u know the output.

the operation that links this rectangular pulse (in this case) and impulse response to its ouput, is the convolution (there are many other such operations using which i could represent a system and its output, like differential equations etc)

take different waves convolve them think of it.

mon
 

convolution physical meaning

Well again you have used the system's response to explain convolution ,forget a system for the time being.There are two signals X and Y with me,lets say i just know that some operation called X*Y and i do it ,what physical sense does the result of this give,does it give the area common to both the curves or i want to know what convolving a signal means.
 

physical significance of convolution

ya even i want the difference between convolution and filtering,

as both the equations are same, except the convolution's flipping, where are both used.

Can somebody tell me with example
 

meaning of convolution

convolution is physically expalined as shifting and multiplying of the sequences
to obtain correlation(in case of + shift) or aggreagtion of coefficients at that time (t)
in order to simplify the calculations
 

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explain convolution

Consider u have x(t) and h(t)... Break h(t) into a number of closely spaced impulses... Find out the response of each of these impulses with x(t)...{Just multiply it]... Do this for the "so many impulses" of the continuous wave h(t) and add all the outputs ntogether to obtain y(t)= x(t)*h(t)...
convolution is just multiplication of impulses of a signal with another signal...
 

what does convolution mean

hi mickey, is convolution deals only with multiplication no summation....

if u say summation is also included, then what about FIR filter.

ok, suppose i have h(n) now i do convolution with x(n) to get y(n) = x(n) * h(n)
if coefficeints of FIR filter is h(n), then output of FIR filter is y(n) = x(n) * h(n)

Now what is the difference, can u tell me where do we use convolution, as we know filters are used for filtering some signals.
 

physical significance convolution

"if coefficeints of FIR filter is h(n), then output of FIR filter is y(n) = x(n) * h(n)"

Really?

it is a sum of the h(n), each mutliplied with a delayed samples of x(n) and added up, which is ....convolution.

y(n) = sigma k=0 to N-1 (x(n-k) * h(n))

-b
 

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what is convolution?

deepa said:
what is the physical meaning of convolution,
for eg,we know that integration means area under the curve,,similarly what does convolution mean
Click to expand...
I like to think about convolution as how much two signal
look like each other, or how two signal belongs to each other.

There is an example on the DSP book from a Northeastern
University profesor that deals with it, in this example is
about a multiplication of two numbers, the product you can
interpreted it as how much two numbers "contain" each other.
 

convolution-physical significance

convolution is multiplying two signals.
 

meaning of convolutions

mutiplying two signals gives you an amplitude modulation of one with the other. Whether this modulation makes any sense is another thing, depending on frequency, wave shapes etc.

multiplication samples is not filtering.
-b
 

meaning convolution

convolution is common area under two curves which are interacting. so if u pass a signal through a system which has a certain response. then out put at any time will be the common area under the curves of both input as well as system.


Filtering is a physical application of convolution whereby we control output with the help of a known and self defined system

Added after 7 minutes:

have u ever doe polynomial multiplication in algebra.
polynomial multiplication is Convolution.. just think!!!
 

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physical meaning of integration

deepa,
Convolution can be though of as a process that determines the effect of current and past inputs (all the way back to the beginning of time) to the current output of a system.
Regards,
Kral
 

what is convolution

Convolution can be though of as a process that tells you how the past and present inputs ie related to the output.
 
the physics meaning of convolution

Let me explain it clearly !!

Let \[x(t)\;\&\;h(t)\] be the two signals which are to be convolved. We know that every signal is a scaled, continuous linear combination of shifted Dirac delta functions or in equation form,

\[h(t)=\int\limits_{-\infty}^{\infty}h(x)\delta(t-x)dx\]

The convolution operation is defined as

\[y(t)=\int\limits_{-\infty}^{\infty}x(t-\tau)h(\tau)d\tau\]

Substituting above equation for \[h(t)\] we get

\[y(t)=\int\limits_{-\infty}^{\infty}x(t-\tau)\left[\int\limits_{-\infty}^{\infty}h(x)\delta(\tau-x)dx\right]d\tau\]

or

\[y(t)=\int\limits_{-\infty}^{\infty}\int\limits_{-\infty}^{\infty}\left[x(t-\tau)h(x)\right]\delta(\tau-x)dxd\tau\]

Thus we see that \[y(t)\] is again linear combination of scaled, continuous linear combination of shifted Dirac delta functions except that the scaling factor changes from \[h(x)\] to \[x(t-\tau)h(x)\].

"Thus the conclusion is that the convolution operation is just the change of scaling factors of shifted Dirac delta functions!!!"
 

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significance of convolution

The physical meaning of convolution is the multiplication of two signal functions.

The convolution of two signals helps to delay, attenuate and accentuate signals.
 

meaning of convolution

I think this will expalin you better.
if you know the impulse response of any system then u can know the respone to any input by convolving the input and the impulse response.
 

geometrical meaning of convolution

Convolution or multiplication are just two faces of the same coin.

If you multiply to signals in the time domain you are really convolving them in the frequency domain. The opposite is also true. This is known.
Now the physical meaning of this is that convolution is the operation which gives you the interception of two or more signals; say in a certain frequency (frequency domain) or in a certain time (time domain) ie. it is the common area of the interacting signals.
 

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