AD7225LR datasheet(17/24 Pages) AD

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AD7225

Rev. C | Page 17 of 24

APPLICATIONS INFORMATION

Xn – 1

Xn – 2

Xn – 3

FILTER

INPUT

y(n)

FILTER

OUTPUT

AD7225

QUAD DAC

AD585

SHA

AD7225

QUAD DAC

AD7820

ADC

INPUT

SAMPLES

AM29520

TLC

DELAYED

INPUT

SAMPLES

AD584

REF

10V

VREF

AM7224

DAC

VOUT

VREF

VREFA

VOUTA

VREFA

VOUTA

VREFA

VOUTA

VREFA

VOUTA

TAP WEIGHT

GAIN SET

VOUTA

VOUTB

VOUTC

VOUTD

ACCUMULATOR

OUTPUT

FILTER

OUTPUT

Figure 20. Programmable Transversal Filter

PROGRAMMABLE TRANSVERSAL FILTER

A discrete time filter can be described by either multiplication

in the frequency domain or by convolution in the time domain:

( )

( ) ( )

∑

−

The convolution sum can be implemented using the special struc-

ture known as the transversal filter (see Figure 21). It consists

of an N-stage delay line with N taps weighted by N coefficients,

the resulting products being accumulated to form the output.

The tap weights or coefficients hk are the nonzero elements of

the impulse response and therefore determine the filter transfer

function. A particular filter frequency response is realized by

setting the coefficients to the appropriate values. This property

leads to the implementation of transversal filters whose fre-

quency response is programmable.

Xn – 1

Xn – 2

Xn – N + 1

hN – 1

N –1

Xn – N

FILTER

INPUT

Xn – k + 1

yn =

k = 1

FILTER

OUTPUT

Figure 21. Transversal Filter

A four-tap programmable transversal filter can be implemented

using the AD7225 (see Figure 20). The input signal is first sampled

and converted to allow the tapped delay line function to be

provided by the AM29520. The multiplication of delayed input

samples by fixed, programmable up weights is accomplished by

the AD7225, the four coefficients or reference inputs being set

by the digital codes stored in the AD7226. The resultant products

are accumulated to yield the convolution sum output sample,

which is held by the AD585.

–100

–90

–80

–70

–60

–50

–40

–30

–20

–10

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

NORMALIZED FREQUENCY (f/fS)

h1 = 0.117

h2 = 0.417

h3 = 0.417

h4 = 0.417

Figure 22. Predicted (Theoretical) Response

–100

–90

–80

–70

–60

–50

–40

–30

–20

–10

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

FREQUENCY (f/fS)

h1 (DAC A) = 00011110

h2 (DAC B) = 01101011

h3 (DAC C) = 01101011

h4 (DAC D) = 00011110

Figure 23. Actual Response

Low-pass, band-pass, and high-pass filters can be synthesized

using this arrangement. The particular up weights needed for

any desired transfer function can be obtained using the standard

Remez exchange algorithm. Figure 22 shows the theoretical

low-pass frequency response produced by a four-tap transversal

filter with the coefficients indicated. Although the theoretical

prediction does not take into account the quantization of the

input samples and the truncation of the coefficients, neverthe-

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