30 Aug
2021
30 Aug
'21
12:03 a.m.
Hi all,
During the last days, I looked into phase-ration: components of a signal
are delayed differently depending on their frequency.
A good write up on the subject can be found at [1], and a commercial
tool is available from [2].
The interesting aspect is that phase rotation does not alter the sound
of the signal nor the loudness. However changing the phase vs. frequency
relationship between lower and upper harmonics changes the waveform and
can affect where the digital peak occurs.
For this reason phase rotation is commonly used by radio stations to
reduce the signal peak, and make the signal more symmetrical. Phase
rotation circuits are also used during mastering to increase headroom.
To implementing this, the following operations are performed:
* FFT
* rotate phase, retain magnitude
* inverse FFT
This works well, except for the first FFT bin: 0 Hz, DC offset. If the
phase-shift changes the average DC level of the signal there is a
discontinuity.
I could use some of the collective expertise of this list.
Has anyone looked into this before?
Is it even possible with piecewise block processing?
Is there a way to calculate the DC offset?
Since the overall magnitude does not change simply summing up the bins
results in the same 0th bin. I considered to low-pass filter the DC
offset, or simply remove the DC offset using a high-pass before the FFT
to mitigate the issue. But either introduces different artifacts. If I
understand correctly, a Hilbert transform as mentioned at [1] has the
same issue.
I've condensed the DSP into a simple test tool to toy around with the
issue: https://gist.github.com/17fd61b04d4c4939727dfdccd79f53a5
with low frequencies, the differences are obvious:
* https://i2.paste.pics/cc32f6c5d622e31ab0e830ab1ce205e9.png (2.5 *
FFT's base-freq)
* https://i2.paste.pics/3e6eb827148b90800569843c11da2e48.png (0.37 *
FFT's base-freq)
I'd appreciate any insights.
--
robin
[1]
https://forum.juce.com/t/how-to-rotate-the-phase-of-an-audio-signal/39072/10
[2] https://www.izotope.com/en/products/rx/features/phase.html
30 Aug
30 Aug
9:06 p.m.
On Sun, Aug 29, 2021 at 10:03:20PM +0200, Robin Gareus wrote:
During the last days, I looked into phase-ration:
components of a signal
are delayed differently depending on their frequency.
This works well, except for the first FFT bin: 0 Hz,
DC offset. If the
phase-shift changes the average DC level of the signal there is a
discontinuity.
If you are working with real-valued signals, you can't change the phase
of DC or the Nyquist frequency (FS/2).
You can if you are using complex-valued signals, as often used in SDR.
To understand this, look at the real FFT. Assume the input is 256 samples.
The result is also 256 real values, which are in fact 129 complex ones.
Two of those, for DC and FS/2 will be purely real, with the imaginary
part zero. They have to be, as both sin (i * 0) and sin (i * pi) is zero
for all integer values of i. So we get in fact 256 and not 258
independent real values. This must be so as the FFT has an exact
inverse, so no information can be lost nor added.
To implement this you need more than just FFT and IFFT. Using only
those on each block would amount to circular convolution, while
what you need is linear convolution. Changing only the phase of
a signal is just a special case of filtering, which means the output
will be longer than the input.
You could use jconvolver to do this. Define the phase shift in the
frequency domain (i.e. as if it were the result of an FFT), do the
inverse FFT and use the result as the IR for the convolver.
In fact jconvolver can generate 90 degree phase shifters for you,
see the 'hilbert' command in the README. Combined with an equivalent
delay this can be used to obtain any phase shift you want.
Now don't believe that phase shifting a signal will always result
in a waveform with a lower peak/RMS ratio. It could very well
have the opposite effect. Any phase shift can be undone by
just another one. If one of those decreases the peak/RMS
ratio the the other will increase it... There is a bit more
to it that they won't tell you in ads.
Greetings to all from sunny Crete.
--
FA
31 Aug
31 Aug
6:24 a.m.
Hi Fons,
Thanks for the reply, and from vacation no less.
On 8/30/21 7:06 PM, Fons Adriaensen wrote:
To implement this you need more than just FFT and
IFFT. Using only
those on each block would amount to circular convolution, while
what you need is linear convolution. Changing only the phase of
a signal is just a special case of filtering, which means the output
will be longer than the input.
Aha! That is what I was missing and didn't understand. Thank you.
Define the phase shift in the
frequency domain (i.e. as if it were the result of an FFT), do the
inverse FFT and use the result as the IR for the convolver.
So just compute a FIR and apply it. I now have a working prototype.
I hoped to sidestep that because the phase-angle should be a sweepable
parameter. I can probably make this work by cross-fading the computed
FIR when the parameter changes.
Now don't believe that phase shifting a signal
will always result
in a waveform with a lower peak/RMS ratio. It could very well
have the opposite effect.
Well, there is a minimum. So far I just brute force detect it, trying
all angles in 1 deg steps on a file.
Finding out if it can be computed is up next. Perhaps using linear
regression on the spectrum of the file. I may pick your brain again when
I progress to that stage.
Greetings to all from sunny Crete.
The next retsina is on me, unless you prefer a cold ΑΛΦΑ beer :)
Stay safe!
robin
4:49 p.m.
On Tue, Aug 31, 2021 at 04:24:43AM +0200, Robin Gareus wrote:
I hoped to sidestep that because the phase-angle
should be a sweepable
parameter. I can probably make this work by cross-fading the computed
FIR when the parameter changes.
Provided that what you want is the same phase angle on all frequencies,
you can easily make it 'sweepable' without recomputing the IR.
The N-point hilbert IR will give you 90 degrees plus a delay of N/2
samples [1]. So in a second channel make a delay of N/2 samples.
Then by combining both in the right proportions you can make any
phase angle you want. For A degrees, just do
out = cos (A) * D + sin (A) * H, where D and H are the delay and
hilbert convolution outputs respectively.
[1] It's not possible to do the phase shift without additional
delay. It's more or less the opposite of a linear phase filter:
for 90 degrees the IR must be anti-symmetric. The lenght of the
hilbert IR determines its bandwidth, the 3 dB points will be
near FS / N and FS / 2 - FS / N. So ideally instead of a delay
for the second channel you should use a FIR with the same
magnitude response as the Hilbert IR.
Ciao,
--
FA
5:09 p.m.
On Tue, Aug 31, 2021 at 04:24:43AM +0200, Robin Gareus wrote:
Brute force indeed...
Now there is something else to consider. Using this method of course
makes complete fools of those listeners who have spent k$ on e.g.
speakers with a good transient resonse, or the recording engineers
who are using expensive mics for the same reason. In other words,
this really kills whatever snappy transient response you may have
had. And in some cases you *can* hear it quite clearly. Like
everything else in the loudness wars, it kills quality,
Ciao,
--
FA
Now don't
believe that phase shifting a signal will always result
in a waveform with a lower peak/RMS ratio. It could very well
have the opposite effect.
Well, there is a minimum. So far I just brute force detect it, trying
all angles in 1 deg steps on a file.
7 Sep
7 Sep
6:02 a.m.
To follow up, there is
https://github.com/x42/phaserotate.lv2#readme
Binaries of the plugins are available from
https://x42-plugins.com/x42/x42-phaserotate
The commandline tool is currently only available when building from source.
On 8/31/21 3:09 PM, Fons Adriaensen wrote:
On Tue, Aug 31, 2021 at 04:24:43AM +0200, Robin Gareus
wrote:
Brute force indeed...
Works sufficiently well and fast, I have a few ideas how to integrate it
into the plugins, but it is tricky since it requires context.
Now
don't believe that phase shifting a signal will always result
in a waveform with a lower peak/RMS ratio. It could very well
have the opposite effect.
Well, there is a minimum. So far I just brute force detect it, trying
all angles in 1 deg steps on a file. In other words, this really kills whatever snappy
transient response
you may have had.
I did some listening tests, both on individual samples as well as
using
the plugin on the master-bus with various performances. In many cases it
is audibly transparent.
But yes, it can kill quality, just like [multiband] compressors,
limiters, or any tool, really.
On the upside I now have better understanding of segmented convolution,
hilbert filter and related FFT topics, which is what this exercise was
about.
Cheers!
robin
10:07 p.m.
On Tue, Sep 07, 2021 at 04:02:19AM +0200, Robin Gareus wrote:
I did some listening tests, both on individual samples
as well as using
the plugin on the master-bus with various performances. In many cases it
is audibly transparent.
Then the next question is of course: in those cases where it is audibly
transparent, what reduction in peak level does it provide ?
And second question: why should peaks be a problem ? Just reduce the
level. The listener can compensate by increasing his/her volume :-)
Ciao,
--
FA
30 Aug
30 Aug
10:51 p.m.
On Sun, Aug 29, 2021 at 10:03:20PM +0200, Robin Gareus wrote:
This works well, except for the first FFT bin: 0 Hz,
DC offset. If the
phase-shift changes the average DC level of the signal there is a
discontinuity.
To understand why you can't chage the phase of DC at an even more
fundamental level, imagine the complex plane, and a vector starting
at the origin and rotating anti-clockwise with frequency F.
So its angle will be
A(t) = 2 * pi * F + P for some F and P, where P (or sometime A(t),
depending on context) is called the phase.
Your 'signal' is the endpoint of the vector, clearly a complex value,
To get a real-valued signal you need a second vector, the mirror image
of the first one w,r.t. the real axis, and so rotating clockwise, i.e.
with a negative frequency,
The sum of the two vectors is then always purely real.
That's why it is said that real-valued signals always contain both
positive and negative frequencies with equal magnitude.
The angle of the second vector is -A(t). So its phase is -P
So the condition for having a real-valued signal is that the phase
for the negative frequency is minus the phase of the positive one,
and both have the same amplitude. The only way to satisfy this
condition for 0 Hz is that the phase must be zero,
--
FA
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