(Mike Rivers) writes:

In article writes:

In one context (the one we're primarily discussing here), "phase" is
the phase response of a system as a function of frequency f, which
I'll denote as phi(f). In this context, the derivative of phi(f) with
respect to f is related to the group delay G(f),

What's the phase response? The phase of the output relative to the
input?

Hi Mike,

Yes, that is correct.

"Phase response" is a property of a system, not a signal.
Using the notation I introduced above, the phase response
of a system, phi(f), is related to the time delay T(f) of the
signal through the system at frequency f by the following:

T(f) = phi(f)/(2*pi*f),

where T(f) is in seconds. In other words, the phase response of a
system provides, indirectly, the frequency-dependent delay through the
system.

Oh, I give up. What you write is probably correct, and I understand
your tutorials about the meaning of words, but I see no connection
with practical audio systems whatsoever.

No problem. Sorry if I'm failing to connect with you.

Can you answer these three questions:

Good questions! Let me try to answer:

1. What physical device can be used to apply a 90 degree phase shift
to a complex audio signal? You can ignore anything below 20 Hz and
above 20 kHz.

A PC with a soundcard and some software. I don't know of a Hilbert
transformer that you can buy as a single component, but that doesn't
mean one couldn't be built.

Let me emphasize that the phase response is a property of a *system*,
NOT a signal. So if the system has a 90 degree response at all
frequencies, then that characteristic is going to be imparted to ALL
signals that are passed through it, complex or otherwise.

In other words, you needn't consider a "complex" audio signal to
validate the system - a simple sine wave sweep will do.

2. How you know you've accomplished it? (how would you measure it?)

One easy way would be to connect a sine wave signal generator as an
input into the system. Connect the output of the system into a scope
and Y the output of the signal generator into the X input of the
scope. Place the scope into X-Y mode (ala Lissajous patterns). Then
at any one frequency, you should see a circle displayed on the scope
because the output and input are 90 degrees apart. The geometry should
remain a circle as you sweep the sine wave generator across the
frequency band.

3. What change would you expect to hear as a result of this phase
shift if the content was, say, human
speech?

Listen for yourself:

http://www.uspsdata.org/OurHouse90.wav
--
% Randy Yates % "I met someone who looks alot like you,
%% Fuquay-Varina, NC % she does the things you do,
%%% 919-577-9882 % but she is an IBM."
%%%% % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr