Datasheet

AD9772A
Rev. C | Page 18 of 40
In many band-limited applications, the images from the
reconstruction process must be suppressed by an analog filter
following the DAC. The complexity of this analog filter is typically
determined by the proximity of the desired fundamental to the
first image and the required amount of image suppression.
Adding to the complexity of this analog filter is the requirement
of compensating for the sin(x)/x response of the DAC.
Referring to
Figure 27, the new first image associated with the
higher data rate of the DAC after interpolation is pushed out
further relative to the input signal, because 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 value of the sin(x)/x roll-
off divided by the original input data pass band (that is, 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 28 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 half-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. Because the even coefficients have an integer
value of 0 (see
Table 5), this process simplifies into inverting the
center coefficient of the low-pass filter (that is, inverting H(18)).
Note that this also corresponds to inverting the peak of the
impulse response shown in
Figure 4. The resulting high-pass
frequency response becomes the frequency inverted mirror
image of the low-pass filter response shown in
Figure 5.
Note that the new first image 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. In addition, the lower sideband images occurring
at f
DATA
− f
FUNDAMENTAL
and its multiples (that is, N × f
DATA
−
f
FUNDAMENTAL
) experience a frequency inversion while the upper
sideband images occurring at f
DATA
+ f
FUNDAMENTAL
and its multiples
(that is, N × f
DATA
+ f
FUNDAMENTAL
) do not.
2×
DAC
2 × f
DATA
f
DATA
FIRST IMAGE
SUPPRESSED
FIRST IMAGE
2 × f
DATA
f
DATA
DIGITAL
FILTER
RESPONSE
NEW
FIRST IMAGE
2 × f
DATA
f
DATA
f
FUNDAMENTAL
f
FUNDAMENTAL
FREQUENCY
DOMAIN
1/ 2 × f
DATA
1/ f
DATA
TIME
DOMAIN
INPUT DATA
LATCH
2× INTERPOLATION
FILTER
DAC SIN(x)/x
RESPONSE
2 ×
f
DATA
f
DATA
02253-027
Figure 27. Time and Frequency Domain Example of Low-Pass 2× Digital Interpolation Filter
f
FUNDAMENTAL
FREQUENCY
DOMAIN
TIME
DOMAIN
2×
DAC
2 ×
f
DATA
f
DATA
FIRST IMAGE
SUPPRESSED
f
FUNDAMENTAL
2 × f
DATA
f
DATA
DIGITAL
FILTER
RESPONSE
UPPER AND
LOWER IMAGE
2 ×
f
DATA
f
DATA
1/2 × f
DATA
1/ f
DATA
INPUT DATA
LATCH
2× INTERPOLATION
FILTER
DAC SIN(x)/x
RESPONSE
2 ×
f
DATA
f
DATA
02253-028
Figure 28. Time and Frequency Domain Example of High-Pass 2× Digital Interpolation Filter