Path: news.mathworks.com!newsfeed-00.mathworks.com!newscon02.news.prodigy.net!prodigy.net!news-feed01.roc.ny.frontiernet.net!nntp.frontiernet.net!news02.roc.ny.POSTED!33b9410e!not-for-mail
From: Doug Schwarz <see@sig.for.address.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Hilbert Transform
References: <fvriev$b1i$1@fred.mathworks.com> <fvrv3v$8ja$1@fred.mathworks.com>
MIME-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
User-Agent: MT-NewsWatcher/3.5.2 (Intel Mac OS X)
Message-ID: <see-54395D.08141107052008@71-129-133-66.dollamir.com>
Lines: 49
X-Complaints-To: abuse-news@frontiernet.net
X-Trace: 52616e646f6d495657ef544f6079382079a311aa8c061f8fb317e7b4ffeec29d4731ea3515d974beb1afa83b2a07d2c6ab3a0eaad4c66b1808242d0addc03ac8880a343693989701a0ee1e1db25f26ecdcd6f6a5914690aa0147a8ac244b40c2252789a717bc0c14c7e34502161e23cf74063b3c3babb708634292392002be5b
X-Abuse-Info: Please be sure to forward ALL headers so that we may process your complaint properly.
NNTP-Posting-Date: Wed, 07 May 2008 08:13:46 EDT
Date: Wed, 07 May 2008 12:13:46 GMT
Xref: news.mathworks.com comp.soft-sys.matlab:467151


In article <fvrv3v$8ja$1@fred.mathworks.com>,
 "Andy Robb" <ajrobb@hotmail.com> wrote:

> "David Egger" <eggerd@sbox.tugraz.at> wrote in message
> <fvriev$b1i$1@fred.mathworks.com>...
> > Hey,
> > 
> > 
> > I unterstand the algorithm hilbert.m in Matlab.
> > But can anyone tell me:
> > 
> > 1)Is this the ideal Hilbert or an approximation?
> > 2)Who invented the algorithm?
> > 3)do anyone know a book where I can find the alg.?
> > 
> > Regards!
> 
> I spent many years applying Hilbert transforms, often
> combining them with re-sampling techniques (Shannon et al).
> 
> There are two approaches to the Hilbert transform. Both
> synthesise an imaginary component of a complex analytic
> waveform from the 'real' signal. The real component should
> be unchanged.
> 
> From memory, hilbert.m uses an FFT approach, it zeros
> frequency components below 0 and double frequency components
> between zero and Nyquist. The IFFT then produces a complex
> analytic waveform. The problems with this approach are the
> same as any FFT technique and can suffer the effects of
> truncation.
> 
> An alternative approach is to synthesise the imaginary
> component directly from the real component using a
> time-domain filter. From my dim and distant pass, I think
> you can see the shape of an FIR by synthesising a spectrum
> with 1i in positive frequencies and -1i in negative
> frequencies and zero in all real components (including 0 and
> Nyquist). Then take the IFFT.


The functions firls and firpm from the Signal Processing Toolbox can be 
used to synthesize the imaginary component.  See the help for those 
functions.

-- 
Doug Schwarz
dmschwarz&ieee,org
Make obvious changes to get real email address.