AD9772A
Referring to Figure 5, the “new” first image associated with the
DAC’s higher data rate after interpolation is “pushed” out fur-
ther relative to the input signal, since it now occurs at 2
f
DATA
– f
FUNDAMENTAL
. The “old” first image associated with the
lower DAC data rate before interpolation is suppressed by the
digital filter. As a result, the transition band for the analog
reconstruction filter is increased, thus reducing the complexity of the
analog filter. Furthermore, the sin(x)/x roll-off over the original
input data passband (i.e., dc to f
DATA
/2) is significantly reduced.
As previously mentioned, the 2 interpolation filter can be
converted into a high-pass response, thus suppressing the “fun-
damental” while passing the “original” first image occurring at
f
DATA
– f
FUNDAMENTAL
. Figure 6 shows the time and frequency
representation for a high-pass response of a discrete time sine
wave. This action can also be modeled as a “1/2 wave” digital
mixing process in which the impulse response of the low-pass
filter is digitally mixed with a square wave having a frequency
of exactly f
DATA
/2. Since the even coefficients have a zero value
(refer to Table I), this process simplifies into inverting the cen-
ter coefficient of the low-pass filter (i.e., invert H(18)). Note
that this also corresponds to inverting the peak of the impulse
response shown in Figure 2a. The resulting high-pass frequency
response becomes the frequency inverted mirror image of the
low-pass filter response shown in Figure 2b.
It is worth noting that the “new” first image now occurs at f
DATA
+
f
FUNDAMENTAL
. A reduced transition region of 2 f
FUNDAMENTAL
exists for image selection, thus mandating that the f
FUNDAMENTAL
be placed sufficiently high for practical filtering purposes in direct
IF applications. Also, the “lower sideband images” occurring at
f
DATA
– f
FUNDAMENTAL
and its multiples (i.e., N f
DATA
–
f
FUNDAMENTAL
) experience a frequency inversion while the “upper
sideband images” occurring at f
DATA
+ f
FUNDAMENTAL
and its mul-
tiples (i.e., N f
DATA
+ f
FUNDAMENTAL
) do not.
TIME
DOMAIN
1/ 2
f
DATA
1/
f
DATA
f
FUNDAMENTAL
1
ST
IMAGE
f
FUNDAMENTAL
DIGITAL
FILTER
RESPONSE
NEW
1
ST
IMAGE
DAC'S SIN (X)/X
RESPONSE
FREQUENCY
DOMAIN
f
DATA
2
f
DATA
f
DATA
SUPPRESSED
1
ST
IMAGE
2
2
f
DATA
f
DATA
2
f
DATA
INPUT DATA
LATCH
INTERPOLATION
FILTER
2
DAC
f
DATA
2
f
DATA
Figure 5. Time and Frequency Domain Example of Low-Pass 2
Digital Interpolation Filter
TIME
DOMAIN
1
/
2
f
DATA
1/
f
DATA
f
FUNDAMENTAL
1
ST
IMAGE
UPPER AND
LOWER IMAGE
DIGITAL
FILTER
RESPONSE
DAC'S SIN (X)/X
RESPONSE
FREQUENCY
DOMAIN
f
DATA
2
f
DATA
SUPPRESSED
f
DATA
2
f
DATA
f
DATA
2
f
DATA
f
FUNDAMENTAL
INPUT DATA
LATCH
2
INTERPOLATION
FILTER
2
DAC
f
DATA
2
f
DATA
Figure 6. Time and Frequency Domain Example of High-Pass 2
Digital Interpolation Filter
–12–
REV. A
AD [ ANALOG DEVICES ]
