"Mark" <makolber@yahoo.com> wrote in message
news:1110915462.157767.20360@z14g2000cwz.googlegroups.com...
> OK
> By convention the phase shift is measured relative to the central tap.
> thank you
>
> And yes, my second question should have been.... can you create an
> ALLPASS   90 deg phase shift OVER A RANGE OF FREQUENCIES.
>
> I understand an integrator works but changes the amplitude so is not
> allpass.
> I understand a 1/4 wave line or digital delay works but it is
> narrowbad.
> I understand a HT works but not relative to the input signal itself.

BTW, if you are doing off-line processing (as opposed to real-time), non-causal
filters are no problem.  So you can create a true Hilbert filter where the
output is 90 degrees phase shifted from the input, at least over some finite
bandwidth.  But for real-time, you have to delay your original signal to get the
90 degree offset.

OK
By convention the phase shift is measured relative to the central tap.
thank you

And yes, my second question should have been.... can you create an
ALLPASS   90 deg phase shift OVER A RANGE OF FREQUENCIES.

I understand an integrator works but changes the amplitude so is not
allpass.
I understand a 1/4 wave line or digital delay works but it is
narrowbad.
I understand a HT works but not relative to the input signal itself.

thanks

Mark

Mark wrote:
> The short definition of a HT is that it provides a +90 deg phase
shift
> for negative frequencies and a  -90 deg phase shift for positive
> frequencies.   But phase shift relative to what?, relative to the HT
> input?  Apparently not.  I used QED to design a HT and looked at the
> phase response (for positive frequencies) expecting to see about a
-90
> deg phase shift over the range of frequencies, but instead I saw the
> usual sawtooth  (linear response with wrapping at +/-pi) shaped phase
> response.    The phase response looks similar to that of any other
> filter that has delay.  So my conclusion is that QED is graphing the
> phase response of the output of the HT relative to the input to the
HT
> and most of that phase shift is due to the delay through the HT.   In
> order to see a constant 90 deg relationship, you must compare the
> output of the HT to a DELAYED version of the HT input.   Is this
> correct?
>
> I also conclude that it is difficult (impossible?) to create a 90 deg
> phase shifted version of a given signal.   The HT and delay create a
90
> deg phase shifted version between two signals (the HT output and the
> delay output), but is there any device that can create a 90 deg phase
> shift between its output and it's input?
>
> thanks
> Mark

I believe that a true "wideband" HT (90 degree phase shifter) is
non-causal.  To make it realizable you then convolve it with an FIR
filter.  So now you have built a Hilbert Transform + a filter.  That is
what QED gave you.  To find the 90 degree phase shift, run the same
input signal through the FIR filter (without the Hilbert Transform
convolved in it).  The output of these two filters will be 90 degrees
out of phase (until you get close to the edges, where the HT doesn't
match the FIR prototype).

Building a narrowband 90 degree phase shifter is easy.  If you want to
do it in analog, search on quarter wave sections.
In the digital domain, just delay the signal the appropriate amount of
time (samples).

in article 1110912454.975225.185480@f14g2000cwb.googlegroups.com, Mark at
makolber@yahoo.com wrote on 03/15/2005 13:47:

> The short definition of a HT is that it provides a +90 deg phase shift
> for negative frequencies and a  -90 deg phase shift for positive
> frequencies.   But phase shift relative to what?, relative to the HT
> input?  Apparently not.  I used QED to design a HT and looked at the
> phase response (for positive frequencies) expecting to see about a  -90
> deg phase shift over the range of frequencies, but instead I saw the
> usual sawtooth  (linear response with wrapping at +/-pi) shaped phase
> response.    The phase response looks similar to that of any other
> filter that has delay.  So my conclusion is that QED is graphing the
> phase response of the output of the HT relative to the input to the HT
> and most of that phase shift is due to the delay through the HT.   In
> order to see a constant 90 deg relationship, you must compare the
> output of the HT to a DELAYED version of the HT input.   Is this
> correct?

yes.  the delay of the HT is like any other N tap causal, linear phase, FIR
filter.  the delay is (N-1)/2 samples.  (now of your N taps, the HT will
have, for odd N, (N-1)/2 zeros in the tap coefs, if you have half-band
symmetry in your HT.)  so to use this to mix with the non-HTed signal, you
should delay the non-HT signal by the same amount.  *then* the two signals
will be 90 degrees out of phase.

> I also conclude that it is difficult (impossible?) to create a 90 deg
> phase shifted version of a given signal.   The HT and delay create a 90
> deg phase shifted version between two signals (the HT output and the
> delay output), but is there any device that can create a 90 deg phase
> shift between its output and it's input?

a true Hilbert Transformer is a conceptual device since it requires both an
infinite number of taps and it is non-causal.  it has an impulse response
that happens before the input impulse, thus is predicting the future.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

Mark wrote:

> The short definition of a HT is that it provides a +90 deg phase shift
> for negative frequencies and a  -90 deg phase shift for positive
> frequencies.   But phase shift relative to what?, relative to the HT
> input?  Apparently not.  I used QED to design a HT and looked at the
> phase response (for positive frequencies) expecting to see about a  -90
> deg phase shift over the range of frequencies, but instead I saw the
> usual sawtooth  (linear response with wrapping at +/-pi) shaped phase
> response.    The phase response looks similar to that of any other
> filter that has delay.  So my conclusion is that QED is graphing the
> phase response of the output of the HT relative to the input to the HT
> and most of that phase shift is due to the delay through the HT.   In
> order to see a constant 90 deg relationship, you must compare the
> output of the HT to a DELAYED version of the HT input.   Is this
> correct?

Yes.  The phase convention in symmetric FIR filters is to take the phase 
relative to the signal that's delayed to the center of the filter -- so 
if your filter is symmetrical around tap # 100 then you compare the 
phase shift to a signal that's delayed 100 samples.
> 
> I also conclude that it is difficult (impossible?) to create a 90 deg
> phase shifted version of a given signal.   The HT and delay create a 90
> deg phase shifted version between two signals (the HT output and the
> delay output), but is there any device that can create a 90 deg phase
> shift between its output and it's input?
> 
It's easy to create a 90 degree phase shifted signal -- just integrate. 
  What's hard is to create a 90 degree phase shifted signal with 
constant amplitude.  Even a "pure" hilbert transform with delay is 
impossible to implement in practice -- not only does the hilbert 
transform extend to infinite time in both directions requiring an 
infinitely long filter, but it also goes to infinity at DC, requiring 
infinite precision.  In practice you can implement a band-limited 
hilbert transform with a lower frequency bound that restrains the 
amplitude and an upper frequency bound and frequency shaping that 
restrains the delay.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

The short definition of a HT is that it provides a +90 deg phase shift
for negative frequencies and a  -90 deg phase shift for positive
frequencies.   But phase shift relative to what?, relative to the HT
input?  Apparently not.  I used QED to design a HT and looked at the
phase response (for positive frequencies) expecting to see about a  -90
deg phase shift over the range of frequencies, but instead I saw the
usual sawtooth  (linear response with wrapping at +/-pi) shaped phase
response.    The phase response looks similar to that of any other
filter that has delay.  So my conclusion is that QED is graphing the
phase response of the output of the HT relative to the input to the HT
and most of that phase shift is due to the delay through the HT.   In
order to see a constant 90 deg relationship, you must compare the
output of the HT to a DELAYED version of the HT input.   Is this
correct?

I also conclude that it is difficult (impossible?) to create a 90 deg
phase shifted version of a given signal.   The HT and delay create a 90
deg phase shifted version between two signals (the HT output and the
delay output), but is there any device that can create a 90 deg phase
shift between its output and it's input?

thanks
Mark