Re: Signal from noise

[Me, Dave Keenan TD 186.4]
>>If you listen to a noise signal along with a copy that is delayed by 20ms
>>you will hear a 50Hz tone, where none exists.

[Jeff Scott TD 188.16:]
>(White) noise consists of all frequencies in equal mixture:
>
> |
> |
>a|
>m|----------------------
>p|
> |
> |
> |______________________
> 0 freq
>
>Running a noise signal through 20ms delay will cause the signal present
>which peaks every 20ms (that is, 50Hz) to be reinforced and thus
>become twice as loud. The other frequencies are not so reinforced and
>stay about the same. Another way of looking at it is to consider the
>delay line as introducing a resonance at 50Hz.
>
>So - voila! A magical tone from "nowhere".

No. Nice try though.

First, a doubling of amplitude is not "twice as loud" but only 6dB louder,
and second, in white noise the amount of energy at precisely 50Hz is
infinitesimal. Also, my understanding is that you can use band-limited
noise which need not contain any 50Hz. Sorry I didn't make that clear. It
is presumably due to the same neural processing that gives rise to the
virtual fundamental effect. It's just somewhat more surprising in this
context. The processing looks an awful lot like auto-correlation.

I'm not sure if the effect occurs when the original and delayed are
presented to opposite ears, or when combined for any or both ears, or under
both these conditions. You there Paul E.? Bill S.?

I would guess it is only experienced when the signals are combined
pre-brain. In which case I think the spectrum (on a log scale, i.e.
loudness scale) looks like a comb, or a row of arches side-by-side, with
notches going to minus infinity at the odd multiples of 25Hz and broadly
rounded 6dB humps in between. Frequencies either side of multiples of 50Hz
will be reinforced nearly as much as the 50Hz multiple. So the spectrum
alone, gives no reason to expect a perceptual component the same as that
produced by a 50Hz tone. For example it would obviously be meaningless to
ask what the phase of this virtual 50Hz tone was at any point in time.

Instead, I expect that this common component in the perception of (a) real
50Hz, (b) chords with a virtual 50Hz fundamental, and (c) 20ms delayed
summed noise, are all better viewed in the time domain as the perception of
a signal that is most self-similar after a 20ms delay (hence
auto-correlation). I understand this is referred to as "periodicity".

Hey thanks Paul E. and Bill S. for teaching me this stuff, so I can now
happily regurgitate it. :-)

Regards,
-- Dave Keenan
http://dkeenan.com

> First, a doubling of amplitude is not "twice as loud" but only 6dB louder

Sorry, that was just a brain fart on my part. I meant twice the amplitude.
And I think it would actually be 3dB since it is a single pole filter.
2x amplitude = +6dB amplitude = +3dB power. (perceived "loudness" curves
are related to power intensity though not the same).

> and second, in white noise the amount of energy at precisely 50Hz is
> infinitesimal.

I disagree - if you really believe that the amount of energy present
for any given frequency is infintesimal, then the spectrum wold be flat
with a peak at -infinity dB. There is significant energy at 50Hz in
white noise. If you don't believe me look at any white noise signal you
like in any spectrum analyzer you like. The summation of an infinite number
of frequencies at finite amplitude does not result in a signal of infinite
amplitude.

> I'm not sure if the effect occurs when the original and delayed are
> presented to opposite ears, or when combined for any or both ears, or under
> both these conditions.

With headphones? You wouldn't hear it. With speakers - yes.

Hey everybody, a delay line combined with the original
is just a digital filter! That's why this works.

Dave, I believe you're right about the multiples of 50Hz
thing which I stupidly failed to mention - it's really a
comb filter. Whoosh! (makes airplane sound)

- Jeff

PS - I'm disconnecting my computer soon and moving
so I might not be an the list for a while.

Jeff Scott wrote,

>(White) noise consists of all frequencies in equal mixture:

> |
> |
>a|
>m|----------------------
>p|
> |
> |
> |______________________
> 0 freq

>Running a noise signal through 20ms delay will >cause the signal present
>which peaks every 20ms (that is, 50Hz) to be >reinforced and thus
>become twice as loud. The other frequencies are >not so reinforced and
>stay about the same. Another way of looking at >it is to consider the
>delay line as introducing a resonance at 50Hz.
>So - voila! A magical tone from "nowhere".

The result of applying the delay to the white noise has a graph of amplitude vs. frequency exactly like the one above. So speaking of some frequencies being reinforced and others not is not quite correct. And yet one hears a 50Hz tone (especially if some feedback is used in the delay). It is not because of any kind of resonance, though it sure sounds like one. The reason is that periodicity does play a role in pitch perception, and the repetition of similar features every 20 ms will "fool" the ear into hearing a 50Hz tone, even though there isn't an amplitude peak at that frequency.

> The result of applying the delay to the white noise has a graph of
amplitude vs. frequency exactly like the one > above. So speaking of some
frequencies being reinforced and others not is not quite correct.

I think what Jeff Scott meant was applying the delay and mixing it with the
original input
signal. This makes indeed a filter where the transfer function H(s) is not
a constant so
it changes white noise into coloured noise. The power spectral density is
not a straight line
anymore then.

Manuel Op de Coul coul@ezh.nl