sin

π f/fs

π f/fs

TLC32040C, TLC32040I, TLC32041C, TLC32041I

ANALOG INTERFACE CIRCUITS

SLAS014E – SEPTEMBER 1987 – REVISED MAY 1995

17

POST OFFICE BOX 655303

(sin x) / x roll-off for a zero-order hold function

The (sin x) / x roll-off for the AIC DAC zero-order hold function at a band-edge frequency of 3000 Hz for the

various sampling rates is shown in the table below.

Table 3.

(sin x) / x Roll-Off

20 log

fs (Hz)

(f = 3000 Hz)

s ()

(f

3000 Hz)

(dB)

(dB)

7200

– 2.64

8000

– 2.11

9600

– 1.44

14400

– 0.63

19200

– 0.35

The actual AIC (sin x) / x roll-off is slightly less than the above figures, because the AIC has less than a 100%

duty cycle hold interval.

correction filter

To compensate for the (sin x) / x roll-off of the AIC, a first-order correction filter shown below, is recommended.

u(i + 1)

(1 – p1)P2

+

+

z – 1

y(i + 1)

p1

The difference equation for this correction filter is:

where the constant p1 determines the pole locations.

The resulting squared magnitude transfer function is:

1

* 2p1 cos(2 p f f

+