| Re: Discrete sine transform [message #30545] |
Fri, 03 May 2002 00:41 |
Matthew Angling
Messages: 5
Registered: May 2002
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Junior Member |
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Mirko Vukovic <mvukovic@taz.telusa.com> wrote in message
news:d96c8f7c.0205020736.6eceab0d@posting.google.com...
> "Dominik Paul" <dpaul@ukl.uni-freiburg.de> wrote in message
news:<aar135$hqq$1@n.ruf.uni-freiburg.de>...
>> I am not 100% sure about it, but I think the sin transform is just
the
>> imaginary part of the Fourie Transformation.
>>
>> Dom
>>
>> "Matthew Angling" <mjangling@QinetiQ.com> schrieb im Newsbeitrag
>> news:aaqvkg$85k$1@hamble.qinetiq.com...
>>> Hello all,
>>>
>>> I'm another lurker drawn out to ask for help. I think this is
more of
>>> a maths question rather than IDL, but as I'm working with IDL
and this
>>> seems to be the most friendly newsgroup I know of, I thought I'd
try
>>> here!
>>>
>>> Does anybody have the algorithm for the discrete sine tranform
coded
>>> in IDL. If I understand correctly it can be done (with some
>>> redundency) by using the FFT - but I'm not sure how!
>>>
>>> Thanks in advance for your help,
>>>
>>> Matt
>>>
>>> --
>
> nope! Funny, I was just leafing Numerical Recipes on that topic
> yesterday. By way of explanation (and probably quoting the Book and
> other authorities), the sine transform is a ``complete'' transform
of
> the data, i.e., you can get the data back by doing an inverse
> transform. If you were just to take the imaginary part of your FFT,
> you would loose half the information, and could not recover it when
> doing the inverse.
>
> The Book does provide an algorithm to do it using the FFT. You have
> to make an anti-symmetric series out of your data by extending the
> data series. The first N samples stay the same. The other N
samples
> are anti-symmetric about N+1 where the N+1 sample must be zero.
I've
> never done it, and advise going to the Book itself to make sure you
> got everything right. The topic is covered in Ch. 12 of the second
> edition.
>
> Mirko
Hi!
Thanks for everybody's comments. If anybody is interested I have
attached my dst function below. Its a translation of the matlab dst
routine.
Matt
--
Dr. M. J. Angling
Centre for RF Propagation and Atmospheric Research
QinetiQ Malvern
Tel: +44 (0)1684 896460
Fax: +44 (0)1684 894657
email: mjangling@QinetiQ.com
------------------------------------------------------------ ----------
--------
Function mldst,a
;function to calculate the discrete sine transform
;translated from the matlab routine dst
;normalisation is split between the forward
;and inverse transforms
;i.e. mldst(mldst(test) is equal to test
;
;NB to take advantage of efficient FFTs the input vector
;should be length 2^m-1
n=n_elements(a)
i=complex(0,1)
;set up antisymmetric vector
y=[0,a,0,-1.*reverse(a)]
;do fft and normalise
yy=2.*sqrt(2*(n+1))*fft(y)
out=yy[1:n]/(-2.*i)
;check type
type=size(out,/type)
;return real part if input was real
if type ne 6 and type ne 9 then out=float(out)
return,out
end
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| Re: Discrete sine transform [message #30553 is a reply to message #30545] |
Thu, 02 May 2002 08:36  |
mvukovic
Messages: 63
Registered: July 1998
|
Member |
|
|
"Dominik Paul" <dpaul@ukl.uni-freiburg.de> wrote in message news:<aar135$hqq$1@n.ruf.uni-freiburg.de>...
> I am not 100% sure about it, but I think the sin transform is just the
> imaginary part of the Fourie Transformation.
>
> Dom
>
> "Matthew Angling" <mjangling@QinetiQ.com> schrieb im Newsbeitrag
> news:aaqvkg$85k$1@hamble.qinetiq.com...
>> Hello all,
>>
>> I'm another lurker drawn out to ask for help. I think this is more of
>> a maths question rather than IDL, but as I'm working with IDL and this
>> seems to be the most friendly newsgroup I know of, I thought I'd try
>> here!
>>
>> Does anybody have the algorithm for the discrete sine tranform coded
>> in IDL. If I understand correctly it can be done (with some
>> redundency) by using the FFT - but I'm not sure how!
>>
>> Thanks in advance for your help,
>>
>> Matt
>>
>> --
>> Dr. M. J. Angling
>> Centre for RF Propagation and Atmospheric Research
>> QinetiQ Malvern
>> mjangling@QinetiQ.com
>>
>>
>>
nope! Funny, I was just leafing Numerical Recipes on that topic
yesterday. By way of explanation (and probably quoting the Book and
other authorities), the sine transform is a ``complete'' transform of
the data, i.e., you can get the data back by doing an inverse
transform. If you were just to take the imaginary part of your FFT,
you would loose half the information, and could not recover it when
doing the inverse.
The Book does provide an algorithm to do it using the FFT. You have
to make an anti-symmetric series out of your data by extending the
data series. The first N samples stay the same. The other N samples
are anti-symmetric about N+1 where the N+1 sample must be zero. I've
never done it, and advise going to the Book itself to make sure you
got everything right. The topic is covered in Ch. 12 of the second
edition.
Mirko
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| Re: Discrete sine transform [message #30562 is a reply to message #30553] |
Thu, 02 May 2002 04:16 |
Kenneth P. Bowman
Messages: 585
Registered: May 2000
|
Senior Member |
|
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In article <aar135$hqq$1@n.ruf.uni-freiburg.de>,
"Dominik Paul" <dpaul@ukl.uni-freiburg.de> wrote:
> I am not 100% sure about it, but I think the sin transform is just the
> imaginary part of the Fourie Transformation.
>
>> Does anybody have the algorithm for the discrete sine tranform coded
>> in IDL. If I understand correctly it can be done (with some
>> redundency) by using the FFT - but I'm not sure how!
Dominik Paul is correct, but the discrete sine transform is usually
defined from (0, pi) rather than (0, 2 pi). So if your series is of
length N, I think that you need to double the length of the series by
adding N zeros. The coefficients will also need to be adjusted by a
factor of 2 (because your are integrating over a domain that is twice as
large).
Hope that helps,
Ken Bowman
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| Re: Discrete sine transform [message #30564 is a reply to message #30562] |
Thu, 02 May 2002 02:38 |
Dominik[1]
Messages: 46
Registered: April 2001
|
Member |
|
|
I am not 100% sure about it, but I think the sin transform is just the
imaginary part of the Fourie Transformation.
Dom
"Matthew Angling" <mjangling@QinetiQ.com> schrieb im Newsbeitrag
news:aaqvkg$85k$1@hamble.qinetiq.com...
> Hello all,
>
> I'm another lurker drawn out to ask for help. I think this is more of
> a maths question rather than IDL, but as I'm working with IDL and this
> seems to be the most friendly newsgroup I know of, I thought I'd try
> here!
>
> Does anybody have the algorithm for the discrete sine tranform coded
> in IDL. If I understand correctly it can be done (with some
> redundency) by using the FFT - but I'm not sure how!
>
> Thanks in advance for your help,
>
> Matt
>
> --
> Dr. M. J. Angling
> Centre for RF Propagation and Atmospheric Research
> QinetiQ Malvern
> mjangling@QinetiQ.com
>
>
>
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