AD9772EB datasheet(12/32 Pages) AD

12 / 32 page

REV. A

AD9772A

–12–

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

fDATA – 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

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 fDATA/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

fDATA – fFUNDAMENTAL. 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 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

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 fDATA +

fFUNDAMENTAL. A reduced transition region of 2

fFUNDAMENTAL

exists for image selection, thus mandating that the fFUNDAMENTAL

be placed sufficiently high for practical filtering purposes in direct

IF applications. Also, the “lower sideband images” occurring at

fDATA – fFUNDAMENTAL and its multiples (i.e., N

fDATA –

fFUNDAMENTAL) experience a frequency inversion while the “upper

sideband images” occurring at fDATA + fFUNDAMENTAL and its mul-

tiples (i.e., N

fDATA + fFUNDAMENTAL) do not.

fDATA

DAC

fDATA

1ST IMAGE

SUPPRESSED

1STIMAGE

fDATA

fFUNDAMENTAL DIGITAL

FILTER

RESPONSE

NEW

1STIMAGE

fDATA

fFUNDAMENTAL

FREQUENCY

DOMAIN

1/ 2

fDATA

TIME

DOMAIN

INPUT DATA

LATCH

INTERPOLATION

FILTER

DAC'S SIN (X)/X

RESPONSE

Figure 5. Time and Frequency Domain Example of Low-Pass 2

Digital Interpolation Filter

fDATA

1ST IMAGE

SUPPRESSED

fFUNDAMENTAL

fDATA

DIGITAL

FILTER

RESPONSE

UPPER AND

LOWER IMAGE

fDATA

fFUNDAMENTAL

FREQUENCY

DOMAIN

1/ 2

fDATA

TIME

DOMAIN

DAC

INPUT DATA

LATCH

INTERPOLATION

FILTER

DAC'S SIN (X)/X

RESPONSE

Figure 6. Time and Frequency Domain Example of High-Pass 2

Digital Interpolation Filter

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