Datasheet
REV. B
AD1895
–16–
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 asyn-
chronous sample rate conversion is the use of a zero-order hold
between two samplers as shown in Figure 4. In an asynchronous
system, T2 is never equal to T1 nor is the ratio between T2 and
T1 rational. As a result, samples at f
S_OUT
will be repeated or
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
S_OUT
is convolved with the attenuated
images from the sin(x)/x nature of the zero-order hold. The images
at f
S_IN
, dc signal images, of the zero-order hold are infinitely
attenuated. Since the ratio of T2 to T1 is an irrational number,
the error resulting from the resampling at f
S_OUT
can never be
eliminated. However, the error can be significantly reduced
through interpolation of the input data at f
S_IN
. The AD1895 is
conceptually interpolated by a factor of 2
20
.
ZERO-ORDER
HOLD
IN
OUT
f
S_IN
= 1/T1 f
S_OUT
= 1/T2
ORIGINAL SIGNAL
SAMPLED AT
f
S_IN
SIN(X)/X OF ZERO-ORDER HOLD
SPECTRUM OF ZERO-ORDER HOLD OUTPUT
SPECTRUM OF
f
S_OUT
SAMPLING
f
S_OUT
2
f
S_OUT
FREQUENCY RESPONSE OF f
S_OUT
CONVOLVED WITH ZERO-ORDER
HOLD SPECTRUM
Figure 4. Zero-Order Hold Being Used by f
S_OUT
to
Resample Data from f
S_IN
THE CONCEPTUAL HIGH INTERPOLATION MODEL
Interpolation of the input data by a factor of 2
20
involves placing
(2
20
–1) samples between each f
S_IN
sample. Figure 5 shows
both the time domain and the frequency domain of interpolation
by a factor of 2
20
. Conceptually, interpolation by 2
20
would
involve the steps of zero-stuffing (2
20
–1) a number of samples
between each f
S_IN
sample and convolving this interpolated signal
with a digital low-pass filter to suppress the images. In the time
domain, it can be seen that f
S_OUT
selects the closest f
S_IN
× 2
20
sample from the zero-order hold as opposed to the nearest f
S_IN
sample in the case of no interpolation. This significantly reduces
the resampling error.
IN OUT
f
S_IN
f
S_OUT
TIME DOMAIN OF f
S_IN
SAMPLES
TIME DOMAIN OUTPUT OF THE LOW-PASS FILTER
TIME DOMAIN OF
f
S_OUT
RESAMPLING
TIME DOMAIN OF THE ZERO-ORDER HOLD OUTPUT
INTERPOLATE
BY N
LOW-PASS
FILTER
ZERO-ORDER
HOLD
Figure 5. Time Domain of the Interpolation and Resampling
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
20
closer to the infinite attenuation point
of the zero-order hold, which is f
S_IN
× 2
20
. The images at the
zero-order hold are the determining factor for the fidelity of the
output at f
S_OUT
. The worst-case images can be computed from
the zero-order hold frequency response, maximum image =
sin (π × F/f
S_INTERP
)/(π × F/f
S_INTERP
). F is the frequency of the
worst-case image, which would be 2
20
× f
S_IN
± f
S_IN
/2 , and
f
S_INTERP
is f
S_IN
× 2
20
.
The following worst-case images would appear for f
S_IN
=
192 kHz:
Image at f
S_INTERP
– 96 kHz = –125.1 dB
Image at f
S_INTERP
+ 96 kHz = –125.1 dB