Phasors on stun

If you take a wav file and run it through a Hilbert transform, what happens to the sound?

On Mon, May 3, 2010 at 5:55 PM, genewardsmith
<genewardsmith@...> wrote:
>
> If you take a wav file and run it through a Hilbert transform, what happens to the sound?
>

Audibly? Nothing.

-Mike

Gene wrote:

> If you take a wav file and run it through a Hilbert transform, what > happens to the sound?

For me the easiest way to explain the HT is convolution with a particular kind of impulse which is symmetrical and therefore can't be used as an IIR filter (i.e. it requires non-zero coefficients even before the original sound). Similarly as you can use convolution to make a reverberated recording from a dry one, you can use convolution to phase-shift all the frequency bands by 90 degrees -- or, as shown in this example, by -90 degrees: http://en.wikipedia.org/wiki/Hilbert_transform#Discrete_Hilbert_transforms
The phase-shifted result by itself sounds the same as the original sound to an ordinary ear. However, if you do the same process for a second time, and then add the original sound at the same intensity, obviously, you'll get silence.
Hilbert transforms are very useful, for example, for linear frequency shifting, which allows you to decide whether you want to shift all the frequencies, let's say, 100Hz up or 100Hz down.

Petr

On Mon, May 3, 2010 at 6:20 PM, Petr Parízek <p.parizek@...> wrote:
> For me the easiest way to explain the HT is convolution with a particular
> kind of impulse which is symmetrical and therefore can't be used as an IIR
> filter (i.e. it requires non-zero coefficients even before the original
> sound).

Are you sure that a Hilbert-transformed impulse is symmetrical about
the x-axis? It is definitely anti causal but I thought there was a
jump discontinuity at x=0.

-Mike

Also, to add to this, it will sound the same as if you played the
original waveform "upside down". The "upside down" waveform is 180
degrees out of phase, the original waveform is 0 degrees out of phase,
this hilbert transform is 90 degrees leading the original... it all
sounds the same.

The only time that changing the phase of a waveform changes it audibly
is if the phase isn't changed linearly across the whole spectrum (i.e.
the phase response of the filter isn't a line).

-Mike

On Mon, May 3, 2010 at 6:02 PM, Mike Battaglia <battaglia01@...> wrote:
> On Mon, May 3, 2010 at 5:55 PM, genewardsmith
> <genewardsmith@...> wrote:
>>
>> If you take a wav file and run it through a Hilbert transform, what happens to the sound?
>>
>
> Audibly? Nothing.
>
> -Mike
>

Mike wrote:

> Are you sure that a Hilbert-transformed impulse is symmetrical about
> the x-axis? It is definitely anti causal but I thought there was a
> jump discontinuity at x=0.

That doesn't, by any means, make the filter impossible to be the same played both forwards and backwards. It can't, of course, be symmetrical "vertically", since inverting the polarity of a 90-degree phase shifter makes a -90-degree phase shifter.

Petr

Yes, but if you play it backwards you get a 90-degree phase shift in
the other direction, which was my point. It isn't symmetrical about
the x-axis. It's just not causal.

-Mike

On Mon, May 3, 2010 at 6:53 PM, Petr Parízek <p.parizek@...> wrote:
>
>
>
> Mike wrote:
>
> > Are you sure that a Hilbert-transformed impulse is symmetrical about
> > the x-axis? It is definitely anti causal but I thought there was a
> > jump discontinuity at x=0.
>
> That doesn't, by any means, make the filter impossible to be the same played
> both forwards and backwards. It can't, of course, be symmetrical
> "vertically", since inverting the polarity of a 90-degree phase shifter
> makes a -90-degree phase shifter.
>
> Petr
>
>

Mike wrote:

> Yes, but if you play it backwards you get a 90-degree phase shift in
> the other direction, which was my point. It isn't symmetrical about
> the x-axis. It's just not causal.

Phew, ... You're right in the end. :-D

Okay, so let's recap for myself ... If I take a 120-degree phase shifter and invert the polarity, I get a -60-degree phase shifter.
In contrast, if I take the same 120-degree phase shifter and play it backwards, I get a -120 degree phase shifter.
So, in conclusion, inverting the polarity changes the shift by 180 degrees, while reversing the filter changes the "sign" of the shift.
Yeah, now I'm recalling what I had already known years ago ... What a strange feeling. :-)

Petr

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, May 3, 2010 at 5:55 PM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > If you take a wav file and run it through a Hilbert transform, what happens to the sound?

I'd find that easier to believe if someone could produce examples using both musical and speech originals.