AD9772AST datasheet(12/30 Pages) AD

12 / 30 page

REV. 0

AD9772

–12–

Referring to Figure 23, the “new” 1st 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

– fFUNDAMENTAL. 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 reconstruc-

tion filter is increased, thus reducing the complexity of the ana-

log filter. Furthermore, the sin(x)/x roll-off over the original

input data passband (i.e., dc to fDATA/2) is significantly reduced.

As previously mentioned, the 2

× interpolation filter can be con-

verted into a high pass response, thus suppressing the “funda-

mental” while passing the “original” 1st image occurring at

fDATA – fFUNDAMENTAL. Figure 24 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

INTERPOLATION FILTER

fDATA

INPUT DATA LATCH

fDATA

DAC

fDATA

DAC'S SIN (X)/X

RESPONSE

1ST IMAGE

SUPPRESSED

1STIMAGE

fDATA

fFUNDAMENTAL DIGITAL

FILTER

RESPONSE

NEW

1STIMAGE

fDATA

fFUNDAMENTAL

FREQUENCY

DOMAIN

1/ 2

fDATA

TIME

DOMAIN

Figure 23. Time and Frequency Domain Example of Low-Pass 2

× Digital Interpolation Filter

INTERPOLATION FILTER

fDATA

INPUT DATA LATCH

fDATA

DAC

fDATA

DAC'S SIN (X)/X

RESPONSE

1ST IMAGE

SUPPRESSED

fFUNDAMENTAL

fDATA

DIGITAL

FILTER

RESPONSE

UPPER AND

LOWER IMAGE

fDATA

fFUNDAMENTAL

FREQUENCY

DOMAIN

1/ 2

fDATA

TIME

DOMAIN

Figure 24. Time and Frequency Domain Example of High-Pass 2

× Digital Interpolation Filter

exactly fDATA/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,

this also corresponds into 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” 1st image now occurs at

fDATA + fFUNDAMENTAL. A reduced transition region of 2

fFUNDAMENTAL exists for image selection, thus mandating that

the fFUNDAMENTAL be placed sufficiently high for practical filter-

ing purposes in direct IF applications. Also, the “lower sideband

images” occurring at fDATA – fFUNDAMENTAL and its multiples

(i.e., N

× f

DATA – fFUNDAMENTAL) experience a frequency inver-

sion while the “upper sideband images” occurring at fDATA +

fFUNDAMENTAL and its multiples (i.e., N

× f

DATA + fFUNDAMENTAL)

do not.

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