At some point back when the dinosaurs roamed the Earth and I was in
high school, I borrowed my first digital signal processing book from a friend.
I later went on to an engineering education and master's thesis about DSP,
but the very basics of DSP never stop to fascinate me. Today, I wanted to
write something about one of them and how it affects audio processing in
Nageru (and finally, how Debian's policies put me in a bit of a bind on
this issue).
DSP texts tend to obscure profound truths with large amounts of maths,
so I'll try to present a somewhat less general result that doesn't require
going into the mathematical details. That rule is:
Adding a signal to weighted, delayed copies of itself is a filtering operation.
(It's simple, but ignoring it will have sinister effects, as we'll see later.)
Let's see exactly what that means with a motivating example. Let's say that
I have a signal where I want to get rid of (or rather, reduce) high frequencies.
The simplest way I can think of is to add every neighboring sample; that is,
set y
n = x
n + x
n-1. For each sample, we
add the previous sample, ie., the signal as it was one sample ago.
(We ignore what happens at the edges; the common
convention is to assume signals extend out to infinity with zeros.)
What effect will this have? We can figure it out with some trigonometry,
but let's just demonstrate it by plotting instead: We assume 48 kHz sample rate
(which means that our one-sample delay is 20.83 s) and a 22 kHz
note (definitely treble!), and plot the signal with one-sample delay
(the x axis is sample number):
As you can see, the resulting signal is a new signal of the same frequency
(which is always true; linear filtering can never create new frequencies,
just boost or dampen existing ones), but with much lower amplitude.
The signal and the delayed version of it end up cancelling each other mostly
out. Also note that there signal has changed
phase; the resulting signal
has been a bit delayed compared to the original.
Now let's look at a 50 Hz signal (turn on your bass face). We need to zoom out a bit to see
full 50 Hz cycles:
The original signal and the delayed one overlap almost exactly! For a lower
frequency, the one-sample delay means almost nothing (since the waveform is
varying so slowly), and thus, in this case, the resulting signal is amplified,
not dampened. (The signal has changed phase here, too actually exactly as much
in terms of real time but we don't really see it, because we've zoomed out.)
Real signals are not pure sines, but they can be seen as sums of many sines
(another fundamental DSP result), and since filtering is a linear operation,
it affects those sines independently. In other words, we now have a very
simple filter that will amplify low frequencies and dampen high frequencies
(and delay the entire signal a little bit). We can do this for all
frequencies from 0 to 24000 Hz; let's ask Octave to do it for us:
(Of course, in a real filter, we'd probably multiply the result with 0.5
to leave the bass untouched instead of boosting it, but it doesn't really
change anything. A real filter would have a lot more coefficients, though,
and they wouldn't all be the same!)
Let's now turn to a problem that will at first seem different: Combining
audio from multiple different time sources. For instance, when mixing video,
you could have input from two different cameras or sounds card and would want
to combine them (say, a source playing music and then some audience sound
from a camera). However, unless you are lucky enough to have a professional-grade setup
where everything runs off the same clock (and separate clock source cables
run to every device), they won't be in sync; sample clocks are good, but they are
not perfect, and they have e.g. some temperature variance. Say we have really
good clocks and they only differ by 0.01%; this means that after an hour of
streaming, we have 360 ms delay, completely ruining lip sync!
This means we'll need to resample at least one of the sources to match the
other; that is, play one of them faster or slower than it came in originally.
There are two problems here: How do you determine how much to resample
the signals, and how do we resample them?
The former is a difficult problem in its own right; about every algorithm
not backed in solid control theory
is doomed to fail in one way or another, and when they fail, it's extremely
annoying to listen to. Nageru follows
a 2012 paper by Fons Adriaensen;
GStreamer does well, something else. It fails pretty badly in a number of
cases; see e.g.
this 2015 master's thesis
that tries to patch it up. However, let's ignore this part of the problem
for now and focus on the resampling.
So let's look at the case where we've determined we have a signal and need to
play it 0.01% faster (or slower); in a real situation, this number would vary
a bit (clocks are not even consistently wrong). This means that at some point,
we want to output sample number 3000 and that corresponds to input sample
number 3000.3, ie., we need to figure out what's between two input samples.
As with so many other things, there's a way to do this that's simple, obvious
and wrong, namely linear interpolation.
The basis of linear interpolation is to look at the two neighboring samples
and weigh them according to the position we want. If we need sample 3000.3,
we calculate y = 0.7 x
3000 + 0.3 x
3001 (don't switch
the two coefficients!), or, if we want to save one multiplication and get
better numerical behavior, we can use the equivalent
y = x
3000 + 0.3 (x
3001 - x
3000).
And if we need sample 5000.5, we take y = 0.5 x
5000 + 0.5 x
5001. And after a while, we'll be back on integer samples; output sample
10001 corresponds to x
10000 exactly.
By now, I guess it should be obvious what's going on: We're creating a filter!
Linear interpolation will inevitably result in high frequencies being
dampened; and even worse, we are creating a
time-varying filter, which means
that the amount of dampening will vary over time. This manifests itself as
a kind of high-frequency flutter , where the amount of flutter depends on
the relative resampling frequencies. There's also cubic resampling (which
can mean any of several different algorithms), but it only really reduces
the problem, it doesn't really solve it.
The proper way of interpolating depends a lot on exactly what you want
(e.g., whether you intend to change the rate quickly or not);
this paper
lays out a bunch of them, and was the paper that originally made me understand
why linear interpolation is so bad. Nageru outsources this problem to
zita-resampler,
again by Fons Adriaensen; it yields extremely high-quality resampling
under controlled delay, through a relatively common technique known as
polyphase filters.
Unfortunately, doing this kind of calculations takes CPU. Not a lot of CPU,
but Nageru runs in rather CPU-challenged environments (ultraportable laptops
where the GPU wants most of the TDP, and the CPU has to go down to the
lowest frequency), and it is moving in a direction where it needs to resample
many more channels (more on the later), so every bit of CPU helps. So I coded
up an SSE optimization of the inner loop for a particular common case
(stereo signals) and sent it in for upstream inclusion. (It made the
code 2.7 times as fast without any structural changes or reducing precision,
which is pretty much what you can expect from SSE.)
Unfortunately, after a productive discussion, suddenly upstream went silent.
I tried pinging, pinging again, and after half a year pinging again, but to
no avail. I
filed the patch in Debian's BTS,
but the maintainer understandably is reluctant to carry a delta against upstream.
I also can't embed a copy; Debian policy would dictate that I build against
the system's zita-resampler. I could work around it by
rewriting zita-resampler until it looks nothing like the original, which
might be a good idea anyway if I wanted to squeeze out the last drops of speed;
there are AVX optimizations to be had in addition to SSE, and the structure
as-is isn't ideal for SSE optimizations (although some of the changes I have
in mind would have to be offset against increased L1 cache footprint,
so careful benchmarking would be needed). But in a sense, it feels like just
working around a policy that's there for good reason. So like I said, I'm
in a bit of a bind. Maybe I should just buy a faster laptop.
Oh, and how does GStreamer solve this? Well, it doesn't use linear interpolation.
It does something even worse it uses nearest neighbor. Gah.
Update: I was asked to clarify that this is about the audio resampling done
by the GStreamer audio sink to sync signals, not in the audioresample element, which solves
a related but different problem (static sample rate conversion).
The audioresample element supports a number of different resampling methods;
I haven't evaluated them.
There's one set of these controls for each bus. (This is the expanded view; there's
also a compact view that has only the meters and the fader, which is what
you'll typically want to use during the run itself the expanded view is for
setup and tweaking.) A bus in Nageru is a pair of channels (left/right),
sourced from a video capture or ALSA card. The channel mapping is flexible;
my USB sound card has 18 channels, for instance, and you can use that to make
several buses. Each bus has a name (here I named it very creatively Main ,
but in a real setting you might want something like Blue microphone or
Speaker PC ), which is just for convenience; it doesn't mean much.
The most important parts of the mix are given the most screen estate,
so even though the way through the signal chain is left-to-right
top-to-bottom, I'll go over it in the opposite direction.
By far the most important part is the audio level, so the fader naturally is
very prominent. (Note that the scale is nonlinear; you want more resolution
in the most important area.) Changing a fader with the mouse or keyboard is
possible, and probably most people will be doing that, but Nageru will also
support USB faders. These usually speak MIDI, for historical reasons, and
there are some UI challenges when they're all so different, but you can get
really small ones if you want to get that tactile feel without blowing up
your budget or getting a bigger backpack.
Then there's the meter to the left of that. Nageru already has R128 level
meters in the mastering section (not shown here, but generally unchanged from
1.3.0), and those are kept as-is, but for each bus, you don't want to know loudness; you want to know
recording levels, so you want a peak meter, not a loudness meter. In particular, you don't want the bus to send clipped data
to the master (which would happen if you set it too high); Nageru can handle
this situation pretty well (unlike most digital mixers, it mixes in
full 32-bit floating-point so there's no internal clipping, and there's a limiter on the master by default),
but it's still not a good place to be in, so you can see that being marked
in red in this example. The meter doubles as an input peak check during
setup; if you turn off all the effects and set the fader to neutral, you can
see if the input hits peak or not, and then adjust it down. (Also, you can
see here that I only have audio in the left channel; I'd better check my
connections, or perhaps just use mono, by setting the right channel on the
bus mapping to the same input as the left one.)
The compressor (now moved from the mastering section to each bus) should be
well-known for those using 1.3.0, but in this view, it also has a reduction
meter, so that you can see whether it kicks in or not. Most casual users
would want to just leave the gain staging and compressor settings alone, but
a skilled audio engineer will know how to adjust these to each speaker's
antics (some speak at a pretty even volume and thus can get a bit of
headroom, while some are much more variable and need tighter settings).
Finally (or, well, first), there's the EQ section. The lo-cut is again
well-known from 1.3.0 (the cutoff frequency is the same across all buses),
but there's now also a simple three-band EQ per bus. Simply ask the speaker
to talk normally for a bit, and tweak the controls until it sounds good.
People have different voices and different ways of holding the microphone,
and if you have a reasonable ear, you can use the EQ to your advantage to
make them sound a little more even on the stream. Either that, or just
put it in neutral, and the entire EQ code will be bypassed.
The code is making pretty good progress; all the DSP stuff is done
(save for some optimizations I want to do in zita-resampler, now that
the discussion flow is started again),
and in theory, one could use it already as-is. However, there's a fair
amount of gnarly support code that still needs to be written: In particular,
I need to do some refactoring to support ALSA hotplug (you don't want
your entire stream to go down just because an USB soundcard dropped out
for a split second), and similarly some serialization of saving/loading
bus mappings. It's not exactly rocket science, but all the code still needs
to be written, and there are a number of corner cases to think of.
If you want to peek, the code is in the
multichannel_audio
branch, but beware; I rebase/squash it pretty frequently, so if you pull
from it, expect frequent git breakage.
Here is my monthly update covering what I have been doing in the free software world (
During this year s 
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