| Re: IDL hilbert() function [message #63175] |
Mon, 03 November 2008 01:16  |
Wout De Nolf
Messages: 194
Registered: October 2008
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Senior Member |
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On Sat, 1 Nov 2008 02:14:54 -0700 (PDT), lecacheux.alain@wanadoo.fr
wrote:
> Is this function actually computing the Hilbert transform ?
> The Hilbert transform is known to be idempotent, i.e. H(H(x)) = -x.
> However, by applying the IDL function, one get for instance :
> IDL> print, hilbert (hilbert (indgen(8)))
> ( 6.00000, 0.000000)( 7.00000, 0.000000)
> ( 4.00000, 0.000000)( 5.00000, 0.000000)
> ( 2.00000, 0.000000)( 3.00000, 0.000000)
> ( 0.000000, 0.000000)( 1.00000, 0.000000)
It works for this:
x=findgen(180)/90.*!pi
plot,x,hilbert(hilbert(sin(x))),/xs
oplot,x,-sin(x),psym=1
Not for this (flips):
plot,hilbert(hilbert((indgen(1000))))
oplot,indgen(1000),psym=1
I'm not sure why, but check the hilbert.pro in the IDL-lib directory
to see how it's implemented.
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| Re: IDL hilbert() function [message #63313 is a reply to message #63175] |
Mon, 03 November 2008 10:26  |
ed.schmahl
Messages: 11
Registered: October 2008
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Junior Member |
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On Nov 3, 2:16 am, Wox <s...@nomail.com> wrote:
> On Sat, 1 Nov 2008 02:14:54 -0700 (PDT), lecacheux.al...@wanadoo.fr
> wrote:
>
>> Is this function actually computing the Hilbert transform ?
>> The Hilbert transform is known to be idempotent, i.e. H(H(x)) = -x.
>> However, by applying the IDL function, one get for instance :
>> IDL> print, hilbert (hilbert (indgen(8)))
>> ( 6.00000, 0.000000)( 7.00000, 0.000000)
>> ( 4.00000, 0.000000)( 5.00000, 0.000000)
>> ( 2.00000, 0.000000)( 3.00000, 0.000000)
>> ( 0.000000, 0.000000)( 1.00000, 0.000000)
>
> It works for this:
> x=findgen(180)/90.*!pi
> plot,x,hilbert(hilbert(sin(x))),/xs
> oplot,x,-sin(x),psym=1
>
> Not for this (flips):
> plot,hilbert(hilbert((indgen(1000))))
> oplot,indgen(1000),psym=1
>
> I'm not sure why, but check the hilbert.pro in the IDL-lib directory
> to see how it's implemented.
Hello Hilbert fans,
Hilbert.pro is not a perfect implementation of the Hilbert function.
One of its failures is an inability to treat odd numbered arrays
properly. Try this:
x1=findgen(9)-4 ; Evenly distributed around the origin
y1=abs(x1) ; An even function of x1
h1=hilbert(y1) ; This should be an ODD function of x1, i.e. H(-
x)=-H(x)
plot,x1,y1
oplot,x1,h1,psym=-6 ; But it's clearly not exactly anti-symmetric
about the origin!
The problem goes away if you use 10 values instead of 9:
x2=findgen(10)-4.5 ; Again evenly distributed around the origin
y2=abs(x2) ; An even function of x2
h2=hilbert(y2) ; This should be an ODD function, i.e., H(-x)=-
H(x)
plot,x2,y2
oplot,x2,h2,psym=-6 ; ... and it is: h2(x2)=-h2(-x2) plus a constant
Looking at the source code suggests that an easy fix is possible.
Ed Schmahl
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