> 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.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by julius●August 12, 20072007-08-12
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
Reply by Jerry Avins●August 12, 20072007-08-12
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.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by Richard Dobson●August 12, 20072007-08-12
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
Reply by Rune Allnor●August 12, 20072007-08-12
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 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
Reply by ●August 12, 20072007-08-12
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.
Reply by Steve Underwood●August 12, 20072007-08-12
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
Reply by Steve Underwood●August 12, 20072007-08-12
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
Reply by lee●August 12, 20072007-08-12
hi guys.....i am beginner in dsp.....
Can somebody tell me the physical meaning of convolution.....wht does
it do actually??