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Thread Subject:
spectral derivation of aperiodic function

Subject: spectral derivation of aperiodic function

From: bouloumag@gmail.com

Date: 11 Feb, 2013 00:57:42

Message: 1 of 6

I would like to calculate the spatial derivative of a variable defined on the points of a uniform grid. The domain is NOT periodic, so the FFT method is useless here. I wonder if there exist other spectral methods to calculate the derivative on an aperiodic domain or if my only hope is to use the finite difference method?

Subject: spectral derivation of aperiodic function

From: Eileen Tudaleft

Date: 11 Feb, 2013 20:15:43

Message: 2 of 6

bouloumag disgorged this amusing substitute for thought:

> I would like to calculate the spatial derivative of a variable defined
> on the points of a uniform grid. The domain is NOT periodic, so the FFT
> method is useless here.

really?

Google: aperiodic FFT
About 179,000 results (0.22 seconds)

so all of that is entirely wrong?

> I wonder if there exist other spectral methods
> to calculate the derivative on an aperiodic domain or if my only hope is
> to use the finite difference method?

no, it's likely your 'other hope' is to spend some time thinking more carefully about your problem(s).

Subject: spectral derivation of aperiodic function

From: TideMan

Date: 11 Feb, 2013 21:51:35

Message: 3 of 6

On Tuesday, February 12, 2013 9:15:43 AM UTC+13, Eileen Tudaleft wrote:
> bouloumag disgorged this amusing substitute for thought:
>
>
>
> > I would like to calculate the spatial derivative of a variable defined
>
> > on the points of a uniform grid. The domain is NOT periodic, so the FFT
>
> > method is useless here.
>
>
>
> really?
>
>
>
> Google: aperiodic FFT
>
> About 179,000 results (0.22 seconds)
>
>
>
> so all of that is entirely wrong?
>
>
>
> > I wonder if there exist other spectral methods
>
> > to calculate the derivative on an aperiodic domain or if my only hope is
>
> > to use the finite difference method?
>
>
>
> no, it's likely your 'other hope' is to spend some time thinking more carefully about your problem(s).

Yes, I was bemused by this post also.
It implies that Kolmogorov's -5/3 law of turbulence and all other such work is rubbish.
Perhaps OP is confusing non-periodic with non-stationary?
FFT is not good for non-stationary data.

Subject: spectral derivation of aperiodic function

From: Nasser M. Abbasi

Date: 11 Feb, 2013 22:37:19

Message: 4 of 6

On 2/11/2013 3:51 PM, TideMan wrote:

>>
>>
>>> I wonder if there exist other spectral methods
>>
>>> to calculate the derivative on an aperiodic domain or if my only hope is
>>
>>> to use the finite difference method?
>>
>>
>>
>> no, it's likely your 'other hope' is to spend some time thinking more carefully about your problem(s).
>

> Yes, I was bemused by this post also.
> It implies that Kolmogorov's -5/3 law of turbulence and all other such work is rubbish.
> Perhaps OP is confusing non-periodic with non-stationary?
> FFT is not good for non-stationary data.
>

Actually, what I was confused about is not that saying that
FFT can't be used for aperiodic signals, but the need to use
FFT to find derivatives.

At school the teacher did not talk about this part of FFT.
He just told us FFT is used to find frequencies on signals.

I mean, if one wants to find derivative of a discrete
sequence in Matlab, why not use the command diff() ?

http://www.mathworks.com/help/matlab/ref/diff.html

or 3 points centered difference, or such schemes.

So I think there is still more to this issue than meets
the eyes.

--Nasser

Subject: spectral derivation of aperiodic function

From: Eileen Tudaleft

Date: 12 Feb, 2013 00:10:12

Message: 5 of 6

Nasser M. Abbasi disgorged this amusing bit:

> On 2/11/2013 3:51 PM, TideMan wrote:
>
>
>>>
>>>> I wonder if there exist other spectral methods
>>>
>>>> to calculate the derivative on an aperiodic domain or if my only hope
>>>> is
>>>
>>>> to use the finite difference method?
>>>
>>> no, it's likely your 'other hope' is to spend some time thinking more
>>> carefully about your problem(s).
>>
>>
>> Yes, I was bemused by this post also.
>> It implies that Kolmogorov's -5/3 law of turbulence and all other such
>> work is rubbish.
>> Perhaps OP is confusing non-periodic with non-stationary?
>> FFT is not good for non-stationary data.
>>
>>
> Actually, what I was confused about is not that saying that FFT can't be
> used for aperiodic signals, but the need to use FFT to find derivatives.
>
> At school the teacher did not talk about this part of FFT. He just told
> us FFT is used to find frequencies on signals.
>
> I mean, if one wants to find derivative of a discrete sequence in
> Matlab, why not use the command diff() ?
>
> http://www.mathworks.com/help/matlab/ref/diff.html
>
> or 3 points centered difference, or such schemes.
>
> So I think there is still more to this issue than meets the eyes.
>
> --Nasser

yes, I skipped that part. wasn't clear to me the OP understood the full implication of what actually got posted.

Subject: spectral derivation of aperiodic function

From: anyone

Date: 12 Feb, 2013 01:47:41

Message: 6 of 6

On Mon, 11 Feb 2013 13:51:35 -0800, TideMan wrote:

> On Tuesday, February 12, 2013 9:15:43 AM UTC+13, Eileen Tudaleft wrote:
>> bouloumag disgorged this amusing substitute for thought:
>>
>>
>>
>> > I would like to calculate the spatial derivative of a variable
>> > defined
>>
>> > on the points of a uniform grid. The domain is NOT periodic, so the
>> > FFT
>>
>> > method is useless here.
>>
>> really?
>>
>> Google: aperiodic FFT
>> About 179,000 results (0.22 seconds)
>>
>> so all of that is entirely wrong?
>>
>> > I wonder if there exist other spectral methods
>>
>> > to calculate the derivative on an aperiodic domain or if my only hope
>> > is >> > to use the finite difference method?
>>
>> no, it's likely your 'other hope' is to spend some time thinking more
>> carefully about your problem(s).
>
> Yes, I was bemused by this post also.
> It implies that Kolmogorov's -5/3 law of turbulence and all other such
> work is rubbish.
> Perhaps OP is confusing non-periodic with non-stationary?
> FFT is not good for non-stationary data.

Yup. Also, it's not clear (to me) what lead the OP to FDTD.

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