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AD9786

Rev. B | Page 31 of 56

Interpolation Modes

Table 28. Interpolation Modes

INTERP[1]

INTERP[0]

Mode

No interpolation

×2 interpolation

×4 interpolation

×8 interpolation

Interpolation is the process of increasing the number of points

in a time domain waveform by approximating points between

the input data points on a uniform time grid. This produces

a higher output data rate. Applied to an interpolation DAC,

a digital interpolation filter is used to approximate the interpolated

points, having an output data rate increased by the interpolation

factor. Interpolation filter responses are achieved by cascading

individual digital filter banks, whose filter coefficients are given in

Table 23, Table 24, and Table 25. Filter responses are shown in

Figure 57, which shows the interpolation filters of the AD9786

under different interpolation rates, normalized to the input data

rate, fSIN.

The digital filter’s frequency domain response exhibits symmetry

about half the output data rate and dc. It causes images of the

input data to be shaped by the interpolation filter’s frequency

response. This has the advantage of causing input data images

that fall in the stop band of the digital filter to be rejected by

the stop-band attenuation of the interpolation filter, while input

data images falling in the interpolation filter pass band are passed.

In band-limited applications, the images at the output |of the

DAC must be limited by an analog reconstruction filter. The

complexity of the analog reconstruction filter is determined by

the proximity of the closest image to the required signal band.

Higher interpolation rates yield larger stop-band regions,

suppressing more input images and resulting in a much relaxed

analog reconstruction filter.

A DAC shapes its output with a sinc function, having a null at

the sampling frequency of the DAC. The higher the DAC sam-

pling rate compared to the input signal bandwidth, the less the

DAC sinc function shapes the output. The higher the

interpolation rate, the more input data images fall in the

interpolation filter stop band and are rejected; the bandwidth

between passed images is larger with higher interpolation

factors. The sinc function shaping is also reduced with a higher

interpolation factor.

Table 29. Sinc Shaping at Band Edge of Interpolation Filters

Mode

Sinc Shaping

@ 0.43 fSIN (dB)

Bandwidth to First Image

No interpolation

–2.8241

fSIN

×2 interpolation

–0.6708

2 fSIN

×4 interpolation

–0.1657

4 fSIN

×8 interpolation

–0.0413

8 fSIN

–8

–6

–4

–2

–0

–150

–100

–50

–8

–6

–4

–2

–150

–100

–50

–8

–6

–4

–2

–150

–100

–50

–8

–6

–4

–2

–150

–100

–50

NO INTERPOLATION

×4 INTERPOLATION

×2 INTERPOLATION

×8 INTERPOLATION

SINC RESPONSE

fSIN

INTERP[1] = 1

INTERP[0] = 1

INTERP[1] = 1

INTERP[0] = 0

INTERP[1] = 0

INTERP[0] = 1

INTERP[1] = 0

INTERP[0] = 0

Figure 57. Interpolation Modes

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