Handbook for Sound Engineers

958 Chapter 25

Much as the simple DAC, asserting a bit causes a corre-
spondingly binary weighted current to be output.

25.18.2.2 Reconstruction Filters

All the earlier comments about antialiasing filters apply
here, too. As well as the required audio—up to 20 kHz
in bandwidth—coming out of the DAC there are a host
of other products, the most unappealing and closest in
spectral terms being a mirror image of the audio
centered on the sampling frequency and descending in
frequency; a 20 kHz audio signal sampled at 48 kHz
will be output from the DAC along with an image at
28 kHz (sample frequency minus audio). Heterodyning
strikes again; there will also be an image at 68 kHz
(sample frequency plus audio), and in all likelihood
more sets of images centered on harmonics of the
sampling frequency. The most dangerous sonically
though is that first inverse image.

25.18.2.3 Oversampling

Enter a filter every bit as precipitous as the one needed
at the front end. Every bit as nasty, too. Solutions other
than good, well-designed filters come from the digital
domain; oversampling, for one. One approach is to
intersperse an interpolation filter between the processor
and DAC. This digital filter reconstructs the audio but at
a higher sample rate; the smoothing of the filter effec-
tively creates more sample points between the few actu-
ally being issued by the digital source (DSP). If a
guessed digital word is inserted between each of the real
ones, the effective sampling rate becomes doubled and,
in practice, the DAC is working twice as hard and fast
outputting analog.
Here is the good part. If the sampling rate is doubled,
the heterodyning images start that much higher up in
frequency; following the earlier example through, a
20 kHz signal’s first inverse image is now going to be at
76 kHz (96 kHz minus 20 kHz) instead of 28 kHz as
before. The immediate benefit is in the relaxation of the
reconstruction filter—it can be much less steep and

pushed up in frequency somewhat away from the audio

band.

The oversampling process can be carried on even

further; four times, eight times, even sixteen times and

more with greater oversampling rates commonly used,

pushing the undesired products correspondingly higher

in frequency and so dramatically relaxing reconstruc-

tion filter requirements. The fact that fifteen out of

sixteen samples may be filter guesses belies the fact that

it isn’t those that improve the audible performance—it

is the absence of brutal analog filtering that makes all

the difference. Exactly the same conditions apply here

to the application of higher (96+ kHz) sample rates,

simply with the intent of pushing antialiasing filter

effects out of audibility, as in A/D converters.

25.18.2.4 Sigma-Delta DACs

Sigma-delta DACs oversample to the same degree (64,

256, or beyond) as their previously described A/D

brothers and the corresponding increase in frequency of

the reconstruction filter dramatically simplifies their

implementation. Most D/As in proaudio are now

sigma-deltas, although conventional laddertypes are still

in wide use, and especially where higher than normal

audio speed is required (such as in a broadcast stereo

encoder). Again, latency is the only major drawback to

this type; the processing delay again depends on sample

rate and the particular device and its filter length, but is

generally around a millisecond. This, of course, means

that a system using sigma-deltas at both ends (ADC and

DAC) can potentially have a latency of a couple of

milliseconds or so; this can be a bust in some applica-

tions.

25.18.3 Sample-Rate converters (SRCs)

A big problem facing digital audio system designers in

the early days was combining sources from different

machinery that, unless heroics were performed and all

the system’s machinery was phase and word-clock

synchronized, almost certainly were all running at

Figure 25-128. An R/2R digital to analog conversion ladder.

Reference voltage 2R 2R 2R 2R 2R 2R 2R

R R R R R R R R

Off On

Most significant bit

Binary weighted

output current

Least significant bit