convolution

hi guys.....i am beginner in dsp.....
Can somebody tell me the physical meaning of convolution.....wht does
it do actually??

lee wrote:
> hi guys.....i am beginner in dsp.....
> Can somebody tell me the physical meaning of convolution.....wht does
> it do actually??
> 
The dictionary says convolving means rolling together. I love convolving 
with my wife. :-)

I guess what it actually does it to make Swiss rolls.

Steve

Steve Underwood wrote:
> lee wrote:
>> hi guys.....i am beginner in dsp.....
>> Can somebody tell me the physical meaning of convolution.....wht does
>> it do actually??
>>
> The dictionary says convolving means rolling together. I love convolving 
> with my wife. :-)
> 
> I guess what it actually does it to make Swiss rolls.
> 
> Steve

Ah, OK, a more meaningful answer. Consider the following pattern on the 
surface of a piece of piezo electric material (e.g. lithium niobate):

   |                                           |
   |                                           |
+-+-+   +-------------------------------+   +-+-+
|   |   |                               |   |   |
| | |   |                               |   | | |
| | |   |                               |   | | |
| | |   |                               |   | | |
| | |   |                               |   | | |
| | |   |                               |   | | |
| | |   |                               |   | | |
| | |   |                               |   | | |
| | |   |                               |   | | |
| | |   +---------------+---------------+   | | |
   |                     |                     |
   |                     |                     |

Port A                Port C                Port B

If you apply a signal to the interdigital pattern labelled port A, 
surface acoustic waves will be created going left and right. Ignore the 
one going left, and assume it ends in oblivion.

Similarly, if you apply a signal to the interdigital pattern labelled 
port B, surface acoustic waves will be created going left and right. 
Ignore the one going right, and assume it ends in oblivion.

Now, we have two waves traveling in opposite directions under the large 
metal plate labelled port C. This plate is basically integrating the two 
waves over its area - hardly an integration over all time, but a 
reasonable approximation. The signal coming out at port C is the 
convolution of the two signals going into A and B.

Is that physical enough?

Steve

On Aug 12, 5:05 pm, lee <libi...@gmail.com> wrote:
> hi guys.....i am beginner in dsp.....
> Can somebody tell me the physical meaning of convolution.....wht does
> it do actually??

It's the process that a linear system has to perform in order to get
an output from a given input.
In fact it's the classical solution to ode's. The impulse response (or
kernal) is 'mixed' in a special way with the input. Look in the books
and you will see follding shifting and adding.

I like to think of it stepwise:

One starts with two functions and proceeds to ask the question: "How similar 
are these two functions?"

We immediately realize that there's no scale reference for when the 
similarity might occur so the question gets expanded to "when are these two 
functions the most similar and by how much?"  This implies sliding one past 
the other and making a measurement of similarity at each point along the 
slide.

Then, we realize that if the two functions are identical, and if they are 
aligned, that the integral of their product is maximum.  The result is the 
integral of the magnitude squared - for real functions at least.

So, we might decide to slide one function past another, and, at each 
position of the slide, multiply them together and integrate the product. 
The more similar two functions, the greater the integral.  And a plot of 
those products with the slide being the independent variable is a 
convolution.

That's not a "physical" description yet of course.  But perhaps it was what 
you were driving at.

Then, for a physical description you need to accept that the output of a 
linear system is the convolution of the impulse response of the system and 
the input.

Think of some familiar linear systems:

A very narrow bandpass filter has an impulse response that is a sinusoid at 
the center frequency.  When a sinusoid of that frequency is the input, 
there's a maximum output.
Convolving two sinusoids of the same frequency yield a maximum output that 
is also a sinousoid at the same frequency.

Put in a different frequency and the output is very low - the similarity 
between the impluse response function and the input function is low.  The 
correlation is low.

Does that help?

Fred 

On 12 Aug, 07:05, lee <libi...@gmail.com> wrote:
> hi guys.....i am beginner in dsp.....
> Can somebody tell me the physical meaning of convolution.....wht does
> it do actually??

I don't think it is possible to explain better than what Dilip Sarwate
did
some time ago:

http://groups.google.no/group/comp.dsp/msg/f99bcd270cc776d8?hl=no&

Rune

Rune Allnor wrote:
> On 12 Aug, 07:05, lee <libi...@gmail.com> wrote:
> 
>>hi guys.....i am beginner in dsp.....
>>Can somebody tell me the physical meaning of convolution.....wht does
>>it do actually??
> 
> 
> I don't think it is possible to explain better than what Dilip Sarwate
> did
> some time ago:
> 
> http://groups.google.no/group/comp.dsp/msg/f99bcd270cc776d8?hl=no&
> 
> Rune
> 

Not really a "physical" explanation though. For that, the example of a 
reverberant space is enough. The cathedral is one example, the "sound of 
the sea" in a conch shell held to the ear is another. The sound we hear 
is the convolution of the source sound with the responding space (hence, 
modern "convolving reverb" software).



Richard Dobson

lee wrote:
> hi guys.....i am beginner in dsp.....
> Can somebody tell me the physical meaning of convolution.....wht does
> it do actually??


Consider long multiplication. Multiply two numbers is the same as 
convolving their digits.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Aug 12, 1:16 am, gyansor...@gmail.com wrote:
> On Aug 12, 5:05 pm, lee <libi...@gmail.com> wrote:
>
> > hi guys.....i am beginner in dsp.....
> > Can somebody tell me the physical meaning of convolution.....wht does
> > it do actually??
>
> It's the process that a linear system has to perform in order to get
> an output from a given input.
> In fact it's the classical solution to ode's. The impulse response (or
> kernal) is 'mixed' in a special way with the input. Look in the books
> and you will see follding shifting and adding.

To add to Gyansor's answer, it's the way that input-output
relationships are computed for linear, time-invariant systems.
Break down the input signal into delta impulse functions, and
then you can compute the result of each impulse, using
linearity and time-invariance.

But damn, for continuous-time signals, there's infinitely many
such deltas.  So then you try to be smart and compute more
efficiently.  And voila, it's what "convolution" is.

So to me, it's a computational technique that is a consequence
of linearity and time-invariance.

It's easier to understand in discrete-time, too.

Julius

Jerry Avins wrote:
> lee wrote:
>> hi guys.....i am beginner in dsp.....
>> Can somebody tell me the physical meaning of convolution.....wht does
>> it do actually??
> 
> 
> Consider long multiplication. Multiply two numbers is the same as 
> convolving their digits.

46 x 26

Juxtapose:

  46
   26

Record product of overlaps

20 x 6 = 120

Shift and repeat:

  46
  26

6 x  6 =  36
20 x 40 = 800

Shift and repeat:

  46
26

6 x 40 = 240

Sum the products: 1196

Correction! That isn't exactly convolution because there's no 
end-for-end reversal.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯