Optimization of Number Representations - Signal Processing Systems - page 1306

Tabl e 7 Search sequences of performance/cost directed heuristic method
Word-length
ADC Filter DAC Performance SQNR(dB) Hardware cost Comment

11 16 11 34.27 8054 Minimum word-length

12 16 11 38.56 8254 Selected

11 17 11 34.83 8281

11 16 12 34.59 8256

13 16 11 39.65 8454

12 17 11 40.36 8481 Determined word-length

12 16 12 37.43 8456

Fig. 19 An LMS channel
identification system

performance is tested using binary decision, e.g. pass or fail, this method cannot be
used. The search sequences of this heuristic method for the first order recursive filter
is shown in Table 7 .

5.4 Optimization Example

The impulse response of a channel can be identified by using an adaptive digital
filter which adjusts the coefficients to minimize the channel modeling error. When
the word-length of the filter coefficients or the input data is not sufficient, the
system not only converges slowly but also the magnitude of error becomes large.
A power estimation block that measures the average power of the error signal after
some time-off period is employed as for the fixed-point performance measure [ 22 ]
(Fig. 19 ) .
When we apply the automatic grouping rules, the coefficient in each tap becomes
a separate group. In order to reduce the number of groups, the coefficients are
manually grouped by assigning a fixed-point attribute of “coef.” The grouping result
for each tap is shown in Fig. 20 .
The “tap in” and “tap out” signals are automatically grouped because they
are connected by a delay, and assigned to “u005.” The “sum in” and “sum out”
signals are also grouped, and assigned to the “u001” group. The integer word-
length, minimum word-length, and optimum word-length for each group of signals