```mailprassi@gmail.com wrote:

>     i am designing a low pass filter and high pass filter to pass my
> audio samples. in matlab i checked out both butterworth and
> chebyshev(cheby2) 3rd order filter.
>    I have observed there is a lot of differance in the phase plot of
> both the filters.
>    Now my query went to what actuall effect of phase in audio? please
> anybody help me in solving this.

As I understand it, phase shifts are audible, but much less than many
other effects that can happen to a signal.

It was explained to me that at low frequencies the nerve impulses
are generated once per cycle at a fairly fixed point on the cycle.
At higher frequencies nerve impulses are not generated on each cycle,
but once every few cycles, and again at an approximately fixed position
in the cycle.

If phase wasn't important to evolution, there wouldn't be any reason
for us to be sensitive to it.

Sensing the direction of a sound source is important, and in one
dimension can be done by the time difference in arrival between the
two ears.  Phase shifts that are the same between left and right won't
affect that much.

Sensing direction on a different axis is a complicated function of the
frequency spectra due to the shape of the outer ear.  There might be
some effects of phase on that, though in a stereo signal there won't
be any such signal left.

Some audiophiles like to make a big thing about phase, sometimes
even absolute phase.  (A 180 degree phase shift in both channels.)
I mostly don't believe phase is important.

-- glen

```
```Andor wrote:

>
> With max_harmonic = 10, the "flanging" effect is still audible, albeit

make sure you changed it on the MATLAB command line:

>>max_harmonic = 10;
>>square_phase

because, if you ran it with:

if ~exist('max_harmonic')
max_harmonic = floor((Fs/2)/f0) - 1
end

then changed it to

if ~exist('max_harmonic')
max_harmonic = 10
end

and ran it again without

>>clear

then the old number would still be used.

> I can't hear it when I compare the two sound
> files over speakers. Then again, the construction work outside my
> window isn't making audibility tests very reliable ...

another thing to do is to slow down the change rate.  if there is a
change rate that is slow enough that you can't hear the difference,
that still means that you can't hear the absolute phase difference.

> Nice test, thanks.

just to reiterate, my side of this little dispute was that phase *was*
or *is* or *can be* perceptually salient.  i just thought that this was
a useful example of where this perception is difficult (granting that
to the other side).  but, even in this case, since the waveforms are
clearly different, you toss in sufficient non-linearity, and you'll
hear a difference.  that, plus the other cases (detuning) is where i
based my claim that Andrew Horner did not sufficiently justify setting
the phase angles of all of his harmonics to zero at the outset of all
of his wavetable synthesis work.  i believe he has not addressed this,
even in his response to my letter to the AES editor 3 years ago.

r b-j

```
```robert bristow-johnson wrote:
> Andor wrote:
> > robert bristow-johnson wrote:
> > ...
> > > i'm wondering - did anyone run my MATLAB program?  you can use the
> > > axis() command to zoom in and look at the waveform.
> >
> > Yes. A normal square wave I get with this code:
> >
> > %        x = x - (1/n)*cos(2*pi*(n*f0+detune)*t);
> >         x = x - (1/n)*cos(2*pi*(n*f0)*t);
> >
> > The wave that your original code
> >
> >         x = x - (1/n)*cos(2*pi*(n*f0+detune)*t);
> > %        x = x - (1/n)*cos(2*pi*(n*f0)*t);
> >
> > generates sounds like a flanged version of the first. Very audible
> > difference.
>
> try it with a reduced number of harmonics.  maybe with max_harmonic =
> 10.

With max_harmonic = 10, the "flanging" effect is still audible, albeit
only over headphones. I can't hear it when I compare the two sound
files over speakers. Then again, the construction work outside my
window isn't making audibility tests very reliable ...

Nice test, thanks.

Regards,
Andor

>
> r b-j

```
```Andor wrote:
> robert bristow-johnson wrote:
> ...
> > i'm wondering - did anyone run my MATLAB program?  you can use the
> > axis() command to zoom in and look at the waveform.
>
> Yes. A normal square wave I get with this code:
>
> %        x = x - (1/n)*cos(2*pi*(n*f0+detune)*t);
>         x = x - (1/n)*cos(2*pi*(n*f0)*t);
>
> The wave that your original code
>
>         x = x - (1/n)*cos(2*pi*(n*f0+detune)*t);
> %        x = x - (1/n)*cos(2*pi*(n*f0)*t);
>
> generates sounds like a flanged version of the first. Very audible
> difference.

try it with a reduced number of harmonics.  maybe with max_harmonic =
10.

r b-j

```
```robert bristow-johnson wrote:
...
> i'm wondering - did anyone run my MATLAB program?  you can use the
> axis() command to zoom in and look at the waveform.

Yes. A normal square wave I get with this code:

%        x = x - (1/n)*cos(2*pi*(n*f0+detune)*t);
x = x - (1/n)*cos(2*pi*(n*f0)*t);

The wave that your original code

x = x - (1/n)*cos(2*pi*(n*f0+detune)*t);
%        x = x - (1/n)*cos(2*pi*(n*f0)*t);

generates sounds like a flanged version of the first. Very audible
difference.

Regards,
Andor

```
```Andor wrote:
> robert bristow-johnson wrote:
> > Andor wrote:
> >
> > >
> > > I got some interesting articles by googling for "is phase audible".
> >
> > "article_s_" (plural)?  i got one hit.  some guy's powerpoint in pdf
> > about watermarking and hiding bits:
>
> Don't know which Google you used,

i used quotes (which i mistakenly thought you did).

> mine revealed this:
>
>
> The second hit seemed quite relevant.

ya.

> There's more further down.

i'm wondering - did anyone run my MATLAB program?  you can use the
axis() command to zoom in and look at the waveform.

r b-j

```
```robert bristow-johnson wrote:
> Andor wrote:
>
> >
> > I got some interesting articles by googling for "is phase audible".
>
> "article_s_" (plural)?  i got one hit.  some guy's powerpoint in pdf
> about watermarking and hiding bits:

Don't know which Google you used, mine revealed this:

The second hit seemed quite relevant. There's more further down.

Regards,
Andor

```
```ooops.

robert bristow-johnson wrote:

...
> if you run this under ideal linear playback conditions, it's unlikely
> you'll be able to hear the change in waveshape.  if there is a slight
> non-linearity in between, you may very well.  i have an ongoing
> disagreement with Andrew Horner who has just published, in the JAES,
> his umpteenth paper about Wavetable Synthesis

this was copied from an earlier post of mine and i didn't read it
enough to see it contained dated information.  Andrew published that
paper a couple of years ago.  he may have published continuations to it
since, but i can't remember.

> where he just assumes, at
> the very beginning, that phase is inaudible and he can set phase to whatever he wants.
>
> r b-j

```
```Andor wrote:

>
> I got some interesting articles by googling for "is phase audible".

"article_s_" (plural)?  i got one hit.  some guy's powerpoint in pdf

When is phase audible?
=B7 Sometimes ... in certain compound tones with frequency
components lying within a critical band

s(t) =3D A*[ (1/2)*cos((w1-w2 )*t)
+ cos(w1*t + phi)
+ (1/2)*cos((w1+w2 )*t) ]

that's not the only case.  but it's another good special "pathological"
case.

i invite anyone with MATLAB to run this program (or translate it to
Mathcad or Octave or Python or Mathematica or whatever).  the waveform
transistions in such a way that it looks pathologically different, but
sounds the same.  especially if max_harmonic is about 10 or 15.

___________________

%
%   square_phase.m
%
%   a test to see if we can really hear phase changes
%   in the harmonics of a Nyquist limited square wave.
%
%   (c) 2004 rbj@audioimagination.com
%

if ~exist('Fs')
Fs =3D 44100                      % sample rate, Hz
end

if ~exist('f0')
f0 =3D 110.25                     % fundamental freq, Hz
end

if ~exist('tone_duration')
tone_duration =3D 2.0             % seconds
end

if ~exist('change_rate')
change_rate =3D 1.0               % Hz
end

if ~exist('max_harmonic')
max_harmonic =3D floor((Fs/2)/f0) - 1
end

if ~exist('amplitude_factor')
amplitude_factor =3D 0.25   % this just keeps things from clipping
end

if ~exist('outFile')
outFile =3D 'square_phase.wav'
end

% make sure we don't uber-Nyquist anything
max_harmonic =3D min(max_harmonic, floor((Fs/2)/f0)-1);

t =3D linspace((-1/4)/f0, tone_duration-(1/4)/f0, Fs*tone_duration+1);

detune =3D change_rate;

n =3D 3;                               % continue with 3rd harmonic
while (n <=3D max_harmonic)
% lessee if it's an "even" or "odd" term
if ((n-1) =3D=3D 4*floor((n-1)/4))
x =3D x + (1/n)*cos(2*pi*n*f0*t);
else
x =3D x - (1/n)*cos(2*pi*(n*f0+detune)*t);
detune =3D -detune;     % comment this line in an see some
end                        % funky intermediate waveforms
n =3D n + 2;                   % continue with next odd harmonic
end

x =3D amplitude_factor*x;

% x =3D sin(pi/2*x);               % toss in a little soft clipping

plot(t, x);                      % see
sound(x, Fs);                    % hear
wavwrite(x, Fs, outFile);        % remember

___________________

if you run this under ideal linear playback conditions, it's unlikely
you'll be able to hear the change in waveshape.  if there is a slight
non-linearity in between, you may very well.  i have an ongoing
disagreement with Andrew Horner who has just published, in the JAES,
his umpteenth paper about Wavetable Synthesis where he just assumes, at
the very beginning, that phase
is inaudible and he can set phase to whatever he wants.=20

r b-j

```
```Prasad wrote:

> Hello all,
>
>     i am designing a low pass filter and high pass filter to pass my
> audio samples. in matlab i checked out both butterworth and
> chebyshev(cheby2) 3rd order filter.
>    I have observed there is a lot of differance in the phase plot of
> both the filters.
>    Now my query went to what actuall effect of phase in audio? please
> anybody help me in solving this.

I got some interesting articles by googling for "is phase audible".

```