AD1896 Analog Devices, AD1896 Datasheet - Page 16

• Manufacturer Part Number: AD1896
• Description: 192 kHz Stereo Asynchronous Sample Rate Converter
• Manufacturer: Analog Devices

AD1896
ASRC FUNCTIONAL OVERVIEW
THEORY OF OPERATION
Asynchronous sample rate conversion is converting data from
one clock source at some sample rate to another clock source at
the same or different sample rate. The simplest approach to
asynchronous sample rate conversion is the use of a zero-order
hold between two samplers shown in Figure 4. In an asynchro-
nous system T2 is never equal to T1 nor is the ratio between T2
and T1 rational. As a result, samples at f
dropped producing an error in the resampling process. The
frequency domain shows the wide side lobes that result from
this error when the sampling of f
attenuated images from the sin(x)/x nature of the zero-order
hold. The images at f
are infinitely attenuated. Since the ratio of T2 to T1 is an irra-
tional number, the error resulting from the resampling at f
can never be eliminated. However, the error can be signifi-
cantly reduced through interpolation of the input data at f
The AD1896 is conceptually interpolated by a factor of 2
THE CONCEPTUAL HIGH INTERPOLATION MODEL
Interpolation of the input data by a factor of 2
(2
both the time domain and the frequency domain of interpolation
by a factor of 2
involve the steps of zero-stuffing (2
20
–1) samples between each f
FREQUENCY RESPONSE OF f
HOLD SPECTRUM
IN
f
S_IN
= 1/T1
20
SPECTRUM OF ZERO-ORDER HOLD OUTPUT
. Conceptually, interpolation by 2
S_IN
SPECTRUM OF f
SIN(X)/X OF ZERO-ORDER HOLD
, dc signal images, of the zero-order hold
ORIGINAL SIGNAL
SAMPLED AT f
ZERO-ORDER
f
S_OUT
S_OUT
HOLD
CONVOLVED WITH ZERO-ORDER
S_OUT
S_OUT
S_IN
20
S_IN
sample. Figure 5 shows
SAMPLING
is convolved with the
–1) number of samples
S_OUT
f
S_OUT
20
will be repeated or
= 1/T2
involves placing
OUT
2
20
f
S_OUT
would
S_OUT
S_IN
20
.
.
between each f
signal with a digital low-pass filter to suppress the images. In the
time domain it can be seen that f
sample from the zero-order hold as opposed to the nearest f
sample in the case of no interpolation. This significantly reduces
the resampling error.
In the frequency domain shown in Figure 6 the interpolation
expands the frequency axis of the zero-order hold. The images
from the interpolation can be sufficiently attenuated by a good
low-pass filter. The images from the zero-order hold are now
pushed by a factor of 2
of the zero-order hold, which is f
zero-order hold are the determining factor for the fidelity of the
output at f
the zero-order hold frequency response, maximum image =
sin (π × F/f
worst-case image which would be 2
f
The following worst-case images would appear for f
192 kHz:
S_INTERP
IN
Image at f
Image at f
f
S_IN
is f
S_OUT
S_INTERP
S_INTERP
S_INTERP
S_IN
INTERPOLATE
TIME DOMAIN OF f
TIME DOMAIN OUTPUT OF THE LOW-PASS FILTER
TIME DOMAIN OF f
TIME DOMAIN OF THE ZERO-ORDER HOLD OUTPUT
S_IN
BY N
. The worst-case images can be computed from
× 2
)/(π × F/f
sample and convolving this interpolated
20
– 96 kHz = –125.1 dB
+ 96 kHz = –125.1 dB
.
20
closer to the infinite attenuation point
S_IN
S_OUT
S_INTERP
LOW-PASS
FILTER
SAMPLES
S_OUT
RESAMPLING
S_IN
). F is the frequency of the
20
× 2
selects the closest f
× f
20
S_IN
. The images at the
ZERO-ORDER
HOLD
± f
S_IN
/2 , and
S_IN
S_IN
f
S_OUT
=
S_IN
× 2
OUT
20