[sage-support] Convolution and sine integral

[Tobias Katz]

Hi,
I am trying to use sage for signal analysis and didn't find a solution
to perform symbolic convolution. Is there a way to do this?
Has anybody done something similar in sage before?

Is there a way to work with the sine integral?
I tried to get it by integrating a sinc-function but I didn't get
anything usable.

Would be great if anybody could give me a hint.

Thanks,
Tobias

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[David Joyner]

On Wed, May 19, 2010 at 6:46 AM, Tobias Katz <tob...@web.de> wrote:
> Hi,
> I am trying to use sage for signal analysis and didn't find a solution
> to perform symbolic convolution. Is there a way to do this?
> Has anybody done something similar in sage before?

Do you mean this, for example?


sage: x,t = var("x,t")
sage: assume(t>0)
sage: f = function("f",x)
sage: g(t) = integral(f(x)*sin(t-x),x,0,t)
sage: g
t |--> -integrate(sin(-t + x)*f(x), x, 0, t)

[kcrisman]

On May 19, 7:41 am, David Joyner <wdjoy...@gmail.com> wrote:

> On Wed, May 19, 2010 at 6:46 AM, Tobias Katz <tobi...@web.de> wrote:
> > Hi,
> > I am trying to use sage for signal analysis and didn't find a solution
> > to perform symbolic convolution. Is there a way to do this?
> > Has anybody done something similar in sage before?
>
> Do you mean this, for example?
>
> sage: x,t = var("x,t")
> sage: assume(t>0)
> sage: f = function("f",x)
> sage: g(t) = integral(f(x)*sin(t-x),x,0,t)
> sage: g
> t |--> -integrate(sin(-t + x)*f(x), x, 0, t)
>

But perhaps the OP wishes functionality like

sage: g(t) = convolve(f,sin) # doesn't exist!

which I've wanted to implement for a long time for arithmetic
functions, but haven't quite figured out how to get Python to do
consistently for some reason (it being low on the priority list).

Does Maxima have a convolution?

- kcrisman

> > Is there a way to work with the sine integral?
> > I tried to get it by integrating a sinc-function but I didn't get
> > anything usable.
>
> > Would be great if anybody could give me a hint.
>
> > Thanks,
> > Tobias
>
> > --
> > To post to this group, send email to sage-s...@googlegroups.com
> > To unsubscribe from this group, send email to sage-support...@googlegroups.com

> > For more options, visit this group athttp://groups.google.com/group/sage-support

> > URL:http://www.sagemath.org
>
> --
> To post to this group, send email to sage-s...@googlegroups.com
> To unsubscribe from this group, send email to sage-support...@googlegroups.com

> For more options, visit this group athttp://groups.google.com/group/sage-support

[Tobias Katz]

Hi,
Indeed I am looking for s.th. like

g(t) = convolve(f,sin)

I am not familiar with Maxima - I had a short look at it but I didn't
find a function like this.

Is the best way to convolve numerically?

Does anybody know a way in Maxima or another CAS?

Tobias

[Jason Grout]

On 05/19/2010 09:58 AM, Tobias Katz wrote:
> Hi,
> Indeed I am looking for s.th. like
>
> g(t) = convolve(f,sin)
>
> I am not familiar with Maxima - I had a short look at it but I didn't
> find a function like this.
>
> Is the best way to convolve numerically?

You might look at scipy or numpy (both of which are included in Sage).
They have functions which do convolutions.

Jason

[William Stein]

On Wednesday, May 19, 2010, Jason Grout <jason...@creativetrax.com> wrote:
> On 05/19/2010 09:58 AM, Tobias Katz wrote:
>
> Hi,
> Indeed I am looking for s.th. like
>
> g(t) = convolve(f,sin)
>
> I am not familiar with Maxima - I had a short look at it but I didn't
> find a function like this.
>
> Is the best way to convolve numerically?
>
>
>
> You might look at scipy or numpy (both of which are included in Sage). They have functions which do convolutions.

I think the OP asked for *symbolic* convolution. I don't think
scipy/jumpy do anything symbolically.

>
> Jason
>
>
> --
> To post to this group, send email to sage-s...@googlegroups.com
> To unsubscribe from this group, send email to sage-support...@googlegroups.com
> For more options, visit this group at http://groups.google.com/group/sage-support
> URL: http://www.sagemath.org
>

--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

[Jason Grout]

On 05/19/2010 10:22 AM, William Stein wrote:
> On Wednesday, May 19, 2010, Jason Grout<jason...@creativetrax.com> wrote:
>> On 05/19/2010 09:58 AM, Tobias Katz wrote:

>> Is the best way to convolve numerically?
>>
>>
>>
>> You might look at scipy or numpy (both of which are included in Sage). They have functions which do convolutions.
>
> I think the OP asked for *symbolic* convolution. I don't think
> scipy/jumpy do anything symbolically.
>

I agree. I was responding to his last question about convolving things
numerically.

Thanks,

[kcrisman]

On May 19, 11:36 am, Jason Grout <jason-s...@creativetrax.com> wrote:
> On 05/19/2010 10:22 AM, William Stein wrote:
>

> > On Wednesday, May 19, 2010, Jason Grout<jason-s...@creativetrax.com>  wrote:
> >> On 05/19/2010 09:58 AM, Tobias Katz wrote:
> >> Is the best way to convolve numerically?
>
> >> You might look at scipy or numpy (both of which are included in Sage). They have functions which do convolutions.
>
> > I think the OP asked for *symbolic* convolution.   I don't think
> > scipy/jumpy do anything symbolically.
>
> I agree.  I was responding to his last question about convolving things
> numerically.
>

Symbolic is implemented in Mma (see http://mathworld.wolfram.com/Convolution.html)
but Maple seems to only have it for audio applications (? based on
brief search on maplesoft.com). Should we open a ticket for this?

- kcrisman

[William Stein]

On Wed, May 19, 2010 at 8:54 AM, kcrisman <kcri...@gmail.com> wrote:
>
>
> On May 19, 11:36 am, Jason Grout <jason-s...@creativetrax.com> wrote:
>> On 05/19/2010 10:22 AM, William Stein wrote:
>>
>> > On Wednesday, May 19, 2010, Jason Grout<jason-s...@creativetrax.com>  wrote:
>> >> On 05/19/2010 09:58 AM, Tobias Katz wrote:
>> >> Is the best way to convolve numerically?
>>
>> >> You might look at scipy or numpy (both of which are included in Sage). They have functions which do convolutions.
>>
>> > I think the OP asked for *symbolic* convolution.   I don't think
>> > scipy/jumpy do anything symbolically.
>>
>> I agree.  I was responding to his last question about convolving things
>> numerically.
>>
>
> Symbolic is implemented in Mma (see http://mathworld.wolfram.com/Convolution.html)
> but Maple seems to only have it for audio applications (? based on
> brief search on maplesoft.com).  Should we open a ticket for this?

Yes, based on the mission statement of Sage: "... viable alternative
to ... Mathematica"

--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

[kcrisman]

On May 19, 12:08 pm, William Stein <wst...@gmail.com> wrote:

> On Wed, May 19, 2010 at 8:54 AM, kcrisman <kcris...@gmail.com> wrote:
>
> > On May 19, 11:36 am, Jason Grout <jason-s...@creativetrax.com> wrote:
> >> On 05/19/2010 10:22 AM, William Stein wrote:
>
> >> > On Wednesday, May 19, 2010, Jason Grout<jason-s...@creativetrax.com>  wrote:
> >> >> On 05/19/2010 09:58 AM, Tobias Katz wrote:
> >> >> Is the best way to convolve numerically?
>
> >> >> You might look at scipy or numpy (both of which are included in Sage). They have functions which do convolutions.
>
> >> > I think the OP asked for *symbolic* convolution.   I don't think
> >> > scipy/jumpy do anything symbolically.
>
> >> I agree.  I was responding to his last question about convolving things
> >> numerically.
>

> > Symbolic is implemented in Mma (seehttp://mathworld.wolfram.com/Convolution.html)

> > but Maple seems to only have it for audio applications (? based on
> > brief search on maplesoft.com).  Should we open a ticket for this?
>
> Yes, based on the mission statement of Sage: "... viable alternative
> to ... Mathematica"

Sorry, I meant "is there already something related open, or is this
already implemented"...

And it turns out that there is a whole file (by David Harvey)
sage.rings.polynomial.convolution, as well as the method
sage.functions.piecewise.PiecewisePolynomial.convolution, not to
mention sage.gsl.dft.IndexedSequence.convolution (both of which are
due to David Joyner, who has already replied on this thread!).

So what do we *not* have implemented? Looks like polynomial
convolution is good, if hard to find, and also discrete/Dirichlet
convolution for IndexedSequences. How hard would it be to extend
these things - or would we want a totally new implementation for SR,
and for arithmetic functions?

This is now http://trac.sagemath.org/sage_trac/ticket/8994 . I also
hope that Tobias will find at least one of the already existing
functions useful, perhaps the piecewise implementation if he has
compact support?

- kcrisman

[Robert Dodier]

On May 19, 8:58 am, Tobias Katz <tobi...@web.de> wrote:

> Indeed I am looking for s.th. like
>
> g(t) = convolve(f,sin)
>
> I am not familiar with Maxima - I had a short look at it but I didn't
> find a function like this.

Maxima doesn't have a built-in symbolic convolution
function although you could formulate one easily enough
to just compute integrate(f(u)*g(x - u), u, minf, inf) or
whatever definition. I don't know whether a direct
approach like that is preferable, or if it's better to compute
the convolution via Fourier or Laplace transforms or some
other way.

FWIW

Robert Dodier