[comp.dsp] Hilbert Transformer

cdc@uafhcx.uucp (C. D. Covington) (06/27/90)

In article <267ADD3E.18081@maccs.dcss.mcmaster.ca>, darel@maccs.dcss.mcmaster.ca (Darel Mesher) writes:
> 
>   I was wondering if anyone has a reference to an analog implementation
> of a Hilbert transformer (ie. 90 degree phase shift). I also need
> a digital implementation but that should be fairly easy to find 
> (Oppenheimer/Schafer).

     I would say the analog version would be difficult to come by.  The digital
version benefits from the fact that the signal is lowpass by definition (Nyquist
and all that).  If memory serves me, the digital version is simply:

                1/n    n odd
      h(n) =
                 0     n even

     Or even simpler in the frequency domain.

C. David Covington (WA5TGF)  cdc@uafhcx.uark.edu     (501) 575-6583
Asst Prof, Elec Eng          Univ of Arkansas        Fayetteville, AR 72701

kchen@Apple.COM (Kok Chen) (06/27/90)

cdc@uafhcx.uucp (C. D. Covington) writes:

>In article <267ADD3E.18081@maccs.dcss.mcmaster.ca>, darel@maccs.dcss.mcmaster.ca (Darel Mesher) writes:
>> 
>>   I was wondering if anyone has a reference to an analog implementation
>> of a Hilbert transformer (ie. 90 degree phase shift). I also need
>> a digital implementation but that should be fairly easy to find 
>> (Oppenheimer/Schafer).

>     I would say the analog version would be difficult to come by.  
                                              ^^^^^^^^^

Not quite. There is a simple (and, very insensitive to component 
tolerances) iterative method in the analog world for successively 
approximating quadrature shifts known as a Phase Sequence Filter.  
Unfortunately, the only references I have found on it are in 
Horowitz and Hill's "The Art of Electronics" and the ARRL (yeah, 
no kidding) "1990 Radio Amateur Handbook."  Both of which are a
little embarassing to use as citations (sorry, Paul)  :-) :-).

I, myself, would appreciate Email from anyone who knows a source 
with a better mathematical description of the Phase Sequence filter.  
My interest in that is whether an equally simple analogous (no pun 
intended) animal exists in the digital world.


Kok Chen, AA6TY				kchen@apple.com
Apple Computer, Inc.

cdc@uafhcx.uucp (C. D. Covington) (06/28/90)

> >     I would say the analog version would be difficult to come by.  
> 
> Not quite. There is a simple (and, very insensitive to component 
> tolerances) iterative method in the analog world for successively 
> approximating quadrature shifts known as a Phase Sequence Filter.  

     I really haven't done much with phase shifting in the analog world.  The
point I was making was that you would have to constrain the bandwidth in some
way.  I guess that's what you mean by 'iterative', perhaps a ladder of some
kind.
                                                d. covington

schw@maxwell.tmc.edu (David Schwartz) (06/29/90)

Here are some analog Hilbert Transformer references to get you started.  They
work by using two all-pass filter sections where the phase difference betweeen
the sections is 90 degrees of the frequency band of interest
-----------------------------------------------------------------------------

[1] Frederrick Shirley, "Shift Phase Independent of Frequency," Electronic
Design 18, Sept, 1970, pp. 62-66.

[2] Gerald Roberts, "The Design of Broad-Band Active Delay Line/90 Degree Phase
Difference Networks," IEEE Trans. on Circuits and Systems, Vol. CAS-21, No. 5,
Sept. 1974, pp. 614-617.

[3] S.D. Bedrosian, "Normalized Design of 90 Degree Phase Difference Networks,"
IRE Trans. on Circuit Theory, vol CT-7, June 1963, pp. 128-136.

------------------------------------------------------------------------------
David Schwartz, Ph.D.                    schw@maxwell.hrl.hac.com
Hughes Research Laboratories
RL69                                     
3011 Malibu Canyon rd
Malibu, CA 90265

fogelberg@lne.kth.se (Ingemar Fogelberg SM0AJV) (07/06/90)

In article <267ADD3E.18081@maccs.dcss.mcmaster.ca>, darel@maccs.dcss.mcmaster.ca (Darel Mesher) writes:
>
>  Hello;
>
>  I was wondering if anyone has a reference to an analog implementation
>of a Hilbert transformer (ie. 90 degree phase shift). I also need
>a digital implementation but that should be fairly easy to find 
>(Oppenheimer/Schafer).
>
>Thanks in advance for any leads;
>
>  Darel
>
>
>-- 
>=============================================================================
>Darel Mesher			
>Electrical and Computer Engineering
>McMaster University			    darel@maccs.dcss.mcmaster.ca

In "Introduction to Digital Signal Processing" by Manolakis & Proakis 
chapter 8.1.5 you will find a very good description on how to make 
DIGITAL Hilbert Transformers. I have used it as reference my self.

MATLAB (from Mathworks) have a routine called REMEZ were you easily can 
design a FIR-filter wich approximate the Hilbert-transformer. In my 
application I used the filter in a Quadratur-modulator used to perform
a exp(-jw) multiplication.

Good Luck
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