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From: "David Egger" <eggerd@sbox.tugraz.at>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Hilbert Transform
Date: Thu, 8 May 2008 10:33:03 +0000 (UTC)
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"Andy Robb" <ajrobb@hotmail.com> wrote in message
<fvt3gt$dse$1@fred.mathworks.com>...
> "David Egger" <eggerd@sbox.tugraz.at> wrote in message
> <fvs88h$j98$1@fred.mathworks.com>...
> > "Andy Robb" <ajrobb@hotmail.com> wrote in message
> > <fvrv3v$8ja$1@fred.mathworks.com>...
> > > "David Egger" <eggerd@sbox.tugraz.at> wrote in message
> > > <fvriev$b1i$1@fred.mathworks.com>...
> > > 
> > > 
> > > 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.
> > ---------------------------------------------------------
> > Hey,
> > 
> > thank you for answering!
> > Okay, I want to keep the algorithm based on the manipulation
> > in the frequency domain you explained.
> > Do you know who invented this algorithm?
> > 
> > You said, it is an approach.So this is not an ideal filter?
> > Is an ideal Hilbert filter possible?
> > 
> > You also said,the problem with this approach are the same as
> > in any fft approach.Could you name some of them?
> > 
> > 
> > Regards!
> 
> FFT is just a fast (efficient) form of DFT calculation.
> 
> The basic requirement for a DFT to be accurate are:
> 1. The original signal contains no component at frequencies
> above half the sample frequency (Nyquist-Shannon*)
> 2. The signal is either an event completely sampled over the
> sample period or is periodic in the sample period (the start
> and 'end' conditions must be the same)
> 
> NOTE: the 'end' condition is the next sample AFTER the last
> sample.
> 
> If these conditions are not met then expect some 'ringing'
> in the synthesised imaginary component at the ends of the
> sample period. However, if they are met, then the Hilbert
> transform will also be accurate.
> 
> *By convention, Nyquist is often associated with the Nyquist
> frequency limit. Shannon is associated with reconstruction
> (interpolation with sinc waveform FIR filters). However,
> they worked closely together at AT&T Bell Labs.


Okay, thank you!

So if the two conditions are satisfied, fft is equal dft?

Is the hilbert transform using the fft an approach or not?

And who invented the fft algorithm for Hilbert?Shannon and
Nyquist?


Greetings!!