Handbook for Sound Engineers

974 Chapter 25

enough noise, the gate opens (actually it relieves 14 dB
of attenuation, which is enough to make stage spill go
away enough), and the limiter almost immediately takes
over, keeping the voice at a manageable, consistent
level for the mix. Note the 3 dB of makeup gain. Lest
one is concerned that this combination is far too
unsubtle for quieter songs, remember that this is a
digital process and in the context of a programmable
console can be (and is) reprogrammed to suit on a
song-by-song or even section-by-section within a song.

25.22.3 Inadequate Samples for Limiters

By and large, Mr. Shannon and Mr. Nyquist did great
jobs. Digital audio works really well and it is indeed
possible to reconstruct an indistinguishable result from
a source through a system sampling barely twice as high
as audio bandwidth. But there are a couple of places
where a limited number of samples trips up—In partic-
ular, attempting to sense the peak of a signal, as one
attempts to do with limiters and gates, both of which
need to respond accurately to them.
Unfairly and unreasonably (since it isn’t terribly
relevant to most real audio) we’ll consider first the
example of Fs/2—half the sample rate. With only two
samples per cycle of sampled signal it is entirely
possible for the two samples to miss the signal alto-
gether, if they happen to occur at zero-crossing points of
the applied audio signal. But, then again, they might hit
the jackpot at the crests.
More realistically, look at the two extreme cases of
Fs/4, or 12 kHz for a 48 kHz sample rate, in Fig.
25-145. Nobody is arguing that 12 kHz isn’t audible, yet
here is a case where there can be as much as 3 dB error
in sensing a level. There are similar, if far less serious
points of error dotted throughout the audio spectrum
(e.g., Fs/8, 6 kHz etc., or anywhere else where Fs is
divided by an even number). Now, to be completely fair,
under any reasonable circumstance this effect would not
be excited and certainly not be audible, since an exactly

12 kHz tone in isolation is not by and large terribly

common or useful—And would be a far-reached argu-

ment in support of a blanket increase in sampling rates

for digital audio. However, in the specific case of

attempting to peak-sense audio levels, one comes across

these spot frequencies with too little effort. This is a

reconstruction error, or more precisely, an error due to

the samples not explicitly describing the signal but

relying on a later reconstruction filter to fill in the gaps.

Back to analog, the signal reconstructs just fine! This is

just a hint of the occasional disconnect between the two

domains.

A second—and actually practically more worri-

some—reconstruction error effect is if through clipping

or heavy dynamics processing a pair of adjacent-in-time

samples are made full-scale, a downstream reconstruc-

tion filter will cause a significant overshoot beyond full

scale in the recovered analog signal. This can cause

clipping in the following analog stages if insufficient

head room is allowed, and a nasty surprise to anyone

who thinks full scale is the most one can see out of a

digital system!

By way of a slightly different practical example of

sampling oddities, it was noticed that digital limiters

seemed to respond differently each time to a snare-drum

impulse; sometimes they’d catch it hard, sometimes

they wouldn’t. In comparison an analog limiter just,

well, caught it. Now, snare drum is pretty evil, a nasty

big initial short spike. On analysis, sometimes the spike

was adequately described by the limited number of

samples, sometimes it blew through the gaps. There

wasn’t much difference, between 3 and 6 dB in captured

peak level, but that is plenty enough a difference to be

audible and, more to the point here, plenty enough to

invalidate the devices as peak limiters!

Oversampling—i.e. making the sample rate twice or

even more times higher—has the effect of pushing the

worst of the reconstruction-error potholes out of the

relevant audio band. Even though one is operating on

Figure 25-144. Soft-knee limiter and gate characteristics.

Audio precision compress level (dbu) vs measured genampl (dbu) 06 apr 101 15:20:0

Soft-knee limiter and gate characteristics I/P gain at 50 dB; gate opens at limiter nominal knee at 50 ( 20 dBFS), clips at 30 (0 dBFS). 60 ( 30 dBFS),

10.000

5.000

0.0

5.000

10.00

15.00

20.00

25.00

30.00

65.0 60.0 

55.0 50.0 45.0 40.0 35.0 30.0 25.0

Figure 25-145. Sampling Irregularity at Fs/4 (12 kHz); possi-

ble 3 dB error.

A. Lucky.

Sample: 1 2 3 4

Value:+1 0 

10

(^1234)
+0.707 +0.707 0.707 0.707
B. Unlucky.