AD9772A-EB datasheet(18/40 Pages) AD

18 / 40 page

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×

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 value of the sin(x)/x roll-

off divided by the original input data pass band (that is, 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 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 fDATA/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 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. In addition, the lower sideband images occurring

at fDATA − fFUNDAMENTAL and its multiples (that is, N × fDATA −

fFUNDAMENTAL) experience a frequency inversion while the upper

sideband images occurring at fDATA + fFUNDAMENTAL and its multiples

(that is, N × fDATA + fFUNDAMENTAL) do not.

2×

DAC

2 ×

fDATA

FIRST IMAGE

SUPPRESSED

FIRST IMAGE

2 ×

fDATA

DIGITAL

FILTER

RESPONSE

NEW

FIRST IMAGE

2 ×

fDATA

fFUNDAMENTAL

FREQUENCY

DOMAIN

1/ 2 ×

fDATA

TIME

DOMAIN

INPUT DATA

LATCH

2× INTERPOLATION

FILTER

DAC SIN(x)/x

RESPONSE

2 ×

fDATA

Figure 27. Time and Frequency Domain Example of Low-Pass 2× Digital Interpolation Filter

fFUNDAMENTAL

FREQUENCY

DOMAIN

TIME

DOMAIN

2×

DAC

2 ×

fDATA

FIRST IMAGE

SUPPRESSED

fFUNDAMENTAL

2 ×

fDATA

DIGITAL

FILTER

RESPONSE

UPPER AND

LOWER IMAGE

2 ×

fDATA

1/2 ×

fDATA

INPUT DATA

LATCH

2× INTERPOLATION

FILTER

DAC SIN(x)/x

RESPONSE

2 ×

fDATA

Figure 28. Time and Frequency Domain Example of High-Pass 2× Digital Interpolation Filter

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