10 Aug
2004
10 Aug
'04
6:29 a.m.
HI all,
There was a discussion on the LAU list about jamin using FFT
based filtering. I I missed much of the discussion but that
particular point just jumped out at me.
Has anyone thought of trying linear phase FIR filters instead of
FFT methods? Any filter that can be specified in the frequency
domain can be implemented in the time domain and vice-versa.
Often (but not always), the time domain version is significantly
cheaper in CPU cycles.
Erik
--
+-----------------------------------------------------------+
Erik de Castro Lopo nospam(a)mega-nerd.com (Yes it's valid)
+-----------------------------------------------------------+
"Neither noise nor information is predictable."
-- Ray Kurzweil
10 Aug
10 Aug
7:41 a.m.
On Tue, Aug 10, 2004 at 06:13:33PM +1000, Erik de Castro Lopo wrote:
There was a discussion on the LAU list about jamin
using FFT
based filtering. I I missed much of the discussion but that
particular point just jumped out at me.
Has anyone thought of trying linear phase FIR filters instead of
FFT methods? Any filter that can be specified in the frequency
domain can be implemented in the time domain and vice-versa.
Often (but not always), the time domain version is significantly
cheaper in CPU cycles.
ISTR (from Karlsruhe) the FFT method was chosen because it was
convenient for two reasons:
- the bandsplitting and EQ can be combined,
- the filter response curves can be 'interpolated' easily
during scene changes.
But I'd like to raise another point. Why should these filters
be 'linear phase' ? The widespread belief that LP filters
always sound 'better' has been questioned long ago (by Michael
Gerzon and others).
The reason seems to be their symmetry in the time domain,
giving a long 'pre-ringing zone' before the central main peak,
It seems human hearing is very sensitive to this 'pre-ringing',
in particular on transient and percussive sounds.
The impulse response of a typical non-LP analog filter only has
a tail at the end, which seems more 'natural'.
--
FA
8:09 a.m.
On Tue, Aug 10, 2004 at 11:25:15AM +0200, Alfons Adriaensen wrote:
ISTR (from Karlsruhe) the FFT method was chosen
because it was
convenient for two reasons:
- the bandsplitting and EQ can be combined,
- the filter response curves can be 'interpolated' easily
during scene changes.
Yup, thats pretty much it.
But I'd like to raise another point. Why should
these filters
be 'linear phase' ? The widespread belief that LP filters
always sound 'better' has been questioned long ago (by Michael
Gerzon and others).
At the time I started working on jamin, LP filters were the fashionable
thing in mastering software. It didn't seem like a totally bad idea, and I
allready had the code, so I went that way. I had a plan to also offer
parametric IIR's as an alternative, but the EQ UI has grown to the point
were users would loose a lot of functionality if they chose IIRs.
The reason seems to be their symmetry in the time
domain,
giving a long 'pre-ringing zone' before the central main peak,
It seems human hearing is very sensitive to this 'pre-ringing',
in particular on transient and percussive sounds.
Yep, we have heard this on some material where you have sharp diconnects
in the gain of adjacent bins, particularly in the low frequencies, it can
be moderated by increasing the overlap, but I dont really understand why.
The effect is not often very noticable though.
- Steve
8:44 a.m.
On Tue, Aug 10, 2004 at 10:53:39AM +0100, Steve Harris wrote:
Yep, we have heard this on some material where you
have sharp diconnects
in the gain of adjacent bins, particularly in the low frequencies, it can
be moderated by increasing the overlap, but I dont really understand why.
The effect is not often very noticable though.
You don't need sharp discontinuities in the frequency curve in order to
have these pre-ringing or pre-echo effects. Consider the following freq
response:
G = 1 + 0.0116 * cos (2 * PI * f / 100 Hz)
This is a flat response plus a 'ripple' with an amplitude of 0.1 dB and
a period of 100 Hz. For all practical purposes, this a a flat response
that should have no audible effect at all.
Now the inverse FFT of this is an impulse response consisting of a
single impulse at the centre, and two smaller impulses 10 ms before
and after it.
On other words, there will be a pre-echo 10 ms before the signal, at
a level of approx. -42 dB. This is *very* audible.
--
FA
11 Aug
11 Aug
6:47 a.m.
On Tue, Aug 10, 2004 at 12:28:40 +0200, Alfons Adriaensen wrote:
You don't need sharp discontinuities in the
frequency curve in order to
have these pre-ringing or pre-echo effects. Consider the following freq
response:
G = 1 + 0.0116 * cos (2 * PI * f / 100 Hz)
This is a flat response plus a 'ripple' with an amplitude of 0.1 dB and
a period of 100 Hz. For all practical purposes, this a a flat response
that should have no audible effect at all.
Now the inverse FFT of this is an impulse response consisting of a
single impulse at the centre, and two smaller impulses 10 ms before
and after it.
On other words, there will be a pre-echo 10 ms before the signal, at
a level of approx. -42 dB. This is *very* audible.
I just checked jamin, and there is some ripple around the impulse (as you
would expect), but it peaks at around -56dB, and I couldn't find traces of
a pre echo visibly, or audibly when amplified. There is what looks like
post echo though (at around -66dB, 4.5ms after), which is odd, I would
have expected the response to be symmetrical?
Theres a screenshot from audacity with 50-odd dB's of gain applied:
http://www.ecs.soton.ac.uk/~swh/jamin-impulse.png
and a gzipped float WAV file of the output, when given an impulse:
http://www.ecs.soton.ac.uk/~swh/jamin-impulse.wav.gz
The wave which makes up the ripple looks like a fs/2 sinewave.
- Steve
8:40 a.m.
On Wed, Aug 11, 2004 at 09:32:11AM +0100, Steve Harris wrote:
I just checked jamin, and there is some ripple around
the impulse (as you
would expect), but it peaks at around -56dB, and I couldn't find traces of
a pre echo visibly, or audibly when amplified. There is what looks like
post echo though (at around -66dB, 4.5ms after), which is odd, I would
have expected the response to be symmetrical?
Yes, that's odd.
The wave which makes up the ripple looks like a fs/2
sinewave.
It's not clear to me what exactly you did to obtain these results.
I assume it's of the form
1. input --> FFT --> complex x(f)
2. y(f) = x(f) * r(f), with r(f) a real symmterical function
3. y(f) --> IFFT ---> real output
Note that for symmetry, r(f) must be of the form
1 + a * cos (b * f), not 1 + a * sin (b * f)
Using a sine 'ripple' would only show up in the imaginary component
the output, which is probably not even computed.
If the ripple is at "fs/2", it would be removed anyway by any windowing
that is apllied before overlapping parts are added together.
Could you try a cosine ripple at "fs/4" or "fs/8" ?
BTW, when do you apply windowing : before step 1, after step 3,
or both ? What is the FFT size ?
--
FA
9:19 a.m.
On Wed, Aug 11, 2004 at 12:24:36 +0200, Alfons Adriaensen wrote:
On Wed, Aug 11, 2004 at 09:32:11AM +0100, Steve Harris
wrote:
Its a full JAMin running with a flat freq response. I was testing it to see
how bad the pre-echo was.
I just checked jamin, and there is some ripple
around the impulse (as you
would expect), but it peaks at around -56dB, and I couldn't find traces of
a pre echo visibly, or audibly when amplified. There is what looks like
post echo though (at around -66dB, 4.5ms after), which is odd, I would
have expected the response to be symmetrical?
Yes, that's odd.
The wave which makes up the ripple looks like a
fs/2 sinewave.
It's not clear to me what exactly you did to obtain these results. I assume it's of the form
1. input --> FFT --> complex x(f)
2. y(f) = x(f) * r(f), with r(f) a real symmterical function
3. y(f) --> IFFT ---> real output
Note that for symmetry, r(f) must be of the form
1 + a * cos (b * f), not 1 + a * sin (b * f)
In this example r(f) = 1, its just a flat response.
Using a sine 'ripple' would only show up in
the imaginary component
the output, which is probably not even computed.
Yes, its a half-complex FFT.
If the ripple is at "fs/2", it would be
removed anyway by any windowing
that is apllied before overlapping parts are added together.
Could you try a cosine ripple at "fs/4" or "fs/8" ?
Applied where?
BTW, when do you apply windowing : before step 1,
after step 3,
or both ? What is the FFT size ?
Before 1, the FFT is 2048 bins, 8x overlap.
- Steve
10:12 a.m.
On Wed, Aug 11, 2004 at 12:04:16PM +0100, Steve Harris wrote:
Step 2. above. With "fs/n" a mean of course a ripple with a period
of n bins. But don't waste your time with this, unless you are
curious :-)
With 8x overlap probably even the effect of "fs/4" and "fs/8" would
be attenuated if there is windowing after step 3. IMHO, this windowing
is necessary: there is no reason why, in the general case, the result
of the IFFT would start of and go back to zero amplitude. I'd use
a square root raised cosine before the FFT and after the IFFT.
The 8x overlap seems extreme. IF your bandpass responses are not
'brick wall', and the EQ curves are also smooth, 8x overlap should
not be necessary.
--
FA
> 1. input --> FFT --> complex x(f)
>
> 2. y(f) = x(f) * r(f), with r(f) a real symmterical function
>
> 3. y(f) --> IFFT ---> real output
In this example r(f) = 1, its just a flat response.
Ok, in that case there should be no pre-echo at all, as you
verified. But what then is that blob around the main impulse,
and the echo at 4.5 ms ? (not that it matters much, I don't
think any of them can be detected by ear).
The point of my example was to show that even a nearly flat,
'inaudable' frequency response can give audible artefacts in
the time domain when the filter is forced to be linear phase.
If the ripple
is at "fs/2", it would be removed anyway by any windowing
that is apllied before overlapping parts are added together.
Could you try a cosine ripple at "fs/4" or "fs/8" ?
Applied where? BTW, when do
you apply windowing : before step 1, after step 3,
or both ? What is the FFT size ?
Before 1, the FFT is 2048 bins, 8x overlap.
11:22 a.m.
On Wed, Aug 11, 2004 at 01:56:52 +0200, Alfons Adriaensen wrote:
Step 2. above. With "fs/n" a mean of course a ripple with a period
of n bins. But don't waste your time with this, unless you are
curious :-)
I am curious, but more busy than curious sadly.
With 8x overlap probably even the effect of "fs/4" and "fs/8" would
be attenuated if there is windowing after step 3. IMHO, this windowing
is necessary: there is no reason why, in the general case, the result
of the IFFT would start of and go back to zero amplitude. I'd use
a square root raised cosine before the FFT and after the IFFT.
OK, thanks I'l try that. I would have thought that the IFFT would go
to zero at both ends though, as it was windowed at input.
Ok, in that case there should be no pre-echo at all,
as you
verified. But what then is that blob around the main impulse,
and the echo at 4.5 ms ? (not that it matters much, I don't
think any of them can be detected by ear).
The point of my example was to show that even a nearly flat,
'inaudable' frequency response can give audible artefacts in
the time domain when the filter is forced to be linear phase.
Oh, I see, yes, so dont :) I supect that the small ammount of noise
arround the impulse is a result of rounding errors in the FFT, but I dont
really have time to test it, and FFTs with greater recision are just too
expensive in CPU.
If the ripple is at "fs/2", it would be
removed anyway by any windowing
that is apllied before overlapping parts are added together.
Could you try a cosine ripple at "fs/4" or "fs/8" ?
Applied where? BTW, when do you apply windowing : before step 1,
after step 3,
or both ? What is the FFT size ?
Before 1, the FFT is 2048 bins, 8x overlap. The 8x overlap seems extreme. IF your bandpass
responses are not
'brick wall', and the EQ curves are also smooth, 8x overlap should
not be necessary.
The EQ curves are often not smoth, expecailly in the low frequency range,
as users make aparently smooth adjustments in the low octaves that only
span a couple of bins. It brings the lantecy down a bit too, which isn't a
huge issue, but doesn't hurt.
The crossover band joins are curretly quite sharp (2 bins I think), maybe
I should try smoothing them out more, but I didn't hear any sonic artifacs
when sliding them up and down with the compressors bypassed.
- Steve
12:09 p.m.
On Wed, Aug 11, 2004 at 02:06:28PM +0100, Steve Harris wrote:
I am curious, but more busy than curious sadly.
Same problem here :-)
OK, thanks I'l try that. I would have thought that
the IFFT would go
to zero at both ends though, as it was windowed at input.
In general it will not. Consider a simple case: your signal is a cosine
wave with n periods in the FFT length and amplitude 1. When you apply
the raised cosine window, what happens is that two new cosines with
resp. n-1 and n+1 periods per FFT length and amplitude -0.5 are added,
giving of course zero at both ends.
The same happens with a more complex signal: the amplitudes of all cosine
components are modified so as to make them cancel at the ends. When you
disturb that delicate balance, they will no longer cancel out.
Now for each group of three adjacent bins, a linear g(f) slope will not
modify the sum of the ampitudes, e.g. it could transform the -0.5, 1,
-0.5 of above into -0.6 1 -0.4, but the sum is still zero. So the
inbalance and the expected signal amplitude at the ends after the IFFT
will be proportional to the second derivative of the frequency response.
When you simulate a resonance with only a few bins (as is likely to
happen at the LF end), this second dervative can take on quite high
values.
--
FA
1:14 p.m.
On Wed, Aug 11, 2004 at 03:53:09 +0200, Alfons Adriaensen wrote:
In general it will not. Consider a simple case: your
signal is a cosine
wave with n periods in the FFT length and amplitude 1. When you apply
the raised cosine window, what happens is that two new cosines with
resp. n-1 and n+1 periods per FFT length and amplitude -0.5 are added,
giving of course zero at both ends.
The same happens with a more complex signal: the amplitudes of all cosine
components are modified so as to make them cancel at the ends. When you
disturb that delicate balance, they will no longer cancel out.
Now for each group of three adjacent bins, a linear g(f) slope will not
modify the sum of the ampitudes, e.g. it could transform the -0.5, 1,
-0.5 of above into -0.6 1 -0.4, but the sum is still zero. So the
inbalance and the expected signal amplitude at the ends after the IFFT
will be proportional to the second derivative of the frequency response.
OK, thanks, I think I followed that, but I need to think on it harder.
BTW, before you mentioned root raised consine windows before and after, I
did a bit of googling, and couldn't find much reference to root raised cos
in windowing (just pentions in-passing), do you have a reference or
the windowing function/attentuaion factor or anything?
In the meantime I'l try it with vanilla raised cosines.
- Steve
1:43 p.m.
On Wed, Aug 11, 2004 at 03:58:40PM +0100, Steve Harris wrote:
BTW, before you mentioned root raised consine windows
before and after, I
did a bit of googling, and couldn't find much reference to root raised cos
in windowing (just pentions in-passing), do you have a reference or
the windowing function/attentuaion factor or anything?
SRRC is used very often in telecomm DSP, but I have not seen it in the
context of analysis or audio. The idea behind my suggestion was just this:
since you do the SRRC twice, the net result after the IFFT is a raised
cosine, and this is perfect to do 2x overlap (or any multiple thereof).
The window function of course is just the square root of a raised cosine.
For an N-point FFT:
W(i) = sqrt (0.5 * (1 - cos (2 * pi * i / N))), i = 0 ... N-1
--
FA
1:52 p.m.
On Wed, Aug 11, 2004 at 03:58:40PM +0100, Steve Harris wrote:
In the meantime I'l try it with vanilla raised
cosines.
I don't think this will work. There's a condition on the window
shape: if you add up all the time-shifted overlapping windows
the result must be a constant, otherwise you introduce AM.
If you do the raised cosine twice, this condition is not
satisfied. The 8x overlap will mitigate the effect, but
I don't think is usable.
The nice thing about SRRC is that if you do it twice, the
result is a raised cosine, and that will combine perfectly
with the next an previous ones if they are half an FFT length
apart. So any 2n overlap will work.
--
FA
10:59 a.m.
On Wed, 11 Aug 2004 12:04:16 +0100
Steve Harris <S.W.Harris(a)ecs.soton.ac.uk> wrote:
What kind of window do you use?
Erik
--
+-----------------------------------------------------------+
Erik de Castro Lopo nospam(a)mega-nerd.com (Yes it's valid)
+-----------------------------------------------------------+
"TLC declared bankruptcy after they received less than 2 percent of the $175
million earned by their CD sales. That was about 40 times less than the
profit that was divided among their management, production and record
companies." -- Courtney Love on the REAL piracy
BTW, when do
you apply windowing : before step 1, after step 3,
or both ? What is the FFT size ?
Before 1, the FFT is 2048 bins, 8x overlap.
11:26 a.m.
On Wed, Aug 11, 2004 at 10:44:01 +1000, Erik de Castro Lopo wrote:
On Wed, 11 Aug 2004 12:04:16 +0100
Steve Harris <S.W.Harris(a)ecs.soton.ac.uk> wrote:
What kind of window do you use?
Hanning (raised cosine). I did play with some others, but it didnt
make any substantial difference, so I went back to Hanning.
- Steve
BTW, when
do you apply windowing : before step 1, after step 3,
or both ? What is the FFT size ?
Before 1, the FFT is 2048 bins, 8x overlap.
10 Aug
10 Aug
9:47 a.m.
On Tue, 10 Aug 2004 10:53:39 +0100
Steve Harris <S.W.Harris(a)ecs.soton.ac.uk> wrote:
At the time I started working on jamin, LP filters
were the fashionable
thing in mastering software.
Its also relatively easy to linearize the phase of an IIR
filter by adding extra allpass sections.
Erik
--
+-----------------------------------------------------------+
Erik de Castro Lopo nospam(a)mega-nerd.com (Yes it's valid)
+-----------------------------------------------------------+
"The X-files is too optimistic. The truth is not out there."
-- Anthony Ord
11:40 a.m.
On Tue, Aug 10, 2004 at 09:32:08 +1000, Erik de Castro Lopo wrote:
On Tue, 10 Aug 2004 10:53:39 +0100
Steve Harris <S.W.Harris(a)ecs.soton.ac.uk> wrote:
Yes, but creating IIR filters with arbitrary freq responsonses is not
easy, at least not for me :)
- Steve
At the time I started working on jamin, LP
filters were the fashionable
thing in mastering software.
Its also relatively easy to linearize the phase of an IIR
filter by adding extra allpass sections.
7442
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7443
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16 comments
3 participants
participants (3)
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Alfons Adriaensen -
Erik de Castro Lopo -
Steve Harris