🚀 go-pugleaf

In article <LcVHqB1w165w@precipice.chi.il.us> jjw@precipice.chi.il.us (John Welch) writes:
>    I would like to make a DSP project that would digitize
>voice grade audio (300-3000 Hz) and provide the original signal
>and that signal phase-shifted by 90 degrees.  I believe this 90
>degree phase shift is done with a Hilbert Transform.  I have found
>the name, but no info on *how* to do a Hilbert Transform.  Any
>assistance would be greatly appreciated.  -->jjw

A Hilbert transform is simply a filter whose frequency response is j
(magnitude 1, phase 90 degrees) for positive frequencies and -j (magnitude
1, phase -90 degrees) for negative frequencies.  The exact Hilbert
transform is unrealizable, just as the perfect low-pass filter is
unrealizable; however, you only need this response in the 300-3000 Hz
bandwidth.  One good way to do this is to use the Parks-McClellan
algorithm to design an FIR filter that approximates the Hilbert transform
in this band (with arbitrary response elsewhere).  I have an ancient
Fortrash program that can do this; it is included as part of the Ptolemy
distribution for those that have that.  Another way that's not as good is
to simply truncate the ideal Hilbert transform impulse response to finite
length and add a delay.  The ideal impulse response is

h(n) = 2/(n*pi) for n odd
0               for n even

and that's for both positive and negative n.







--
Joe Buck	jbuck@ohm.berkeley.edu

You are in luck, an audio grade Hilbert transform is one of the most
trivial transforms known to man.
Construct a FIR filter with samples from a windowed version of
1.0/(PI*t) and you're in business.

I too am interested in info on the theory and practice of Hilbert
transforms.  I have seen contexts where the HT is used but would like
to understand what it does, and why, better.

--Marv Frandsen   frandsen@beno.css.gov

-- 
-------------------------------------------------------------------
	  Marvin Vaun Frandsen       frandsen@beno.css.gov
	    

frandsen@seismo.CSS.GOV (Marvin Vaun Frandsen) writes:

>I too am interested in info on the theory and practice of Hilbert
>transforms.  I have seen contexts where the HT is used but would like
>to understand what it does, and why, better.

>--Marv Frandsen   frandsen@beno.css.gov

>-- 
>-------------------------------------------------------------------
>	  Marvin Vaun Frandsen       frandsen@beno.css.gov
>	    
It shifts any frequency components by 90 degree of phase.
So if you have a clean sine signal of arbitrary phase, and add the
square of it to the square of the Hilbert transform, you get a
constant term with the mean energy of your original wave.

In article <dak.716052742@kaa> dak@kaa.informatik.rwth-aachen.de (David Kastrup) writes:
>frandsen@seismo.CSS.GOV (Marvin Vaun Frandsen) writes:
>
>>I too am interested in info on the theory and practice of Hilbert
>>transforms.  I have seen contexts where the HT is used but would like
>>to understand what it does, and why, better.
>
>>--Marv Frandsen   frandsen@beno.css.gov
>
>>-- 
>>-------------------------------------------------------------------
>>	  Marvin Vaun Frandsen       frandsen@beno.css.gov
>>	    
>It shifts any frequency components by 90 degree of phase.
>So if you have a clean sine signal of arbitrary phase, and add the
>square of it to the square of the Hilbert transform, you get a
>constant term with the mean energy of your original wave.

They are useful for generating SSB (single side band) signals and
also as a conceptual link between passband signals and their equiv-
alent complex baseband representation.  See "Communication Systems"
by Simon Haykin, readable and aimed at undergrads.