### TABLE IX Run times in seconds for direct form filter

1997

Cited by 5

### Table 1: Nominal and truncated filter coefficients for direct form implemen- tation.

### Table 2. The best reduction choices for the FRM filter with overall order approximately equal to the direct form, for the numerical example.

"... In PAGE 3: ... Using a standard minimax FIR design for the prototype filter, we obtain the results presented at the first line of Table 1. By using a FRM design, we see that the best reduction scenario which leads to an order of 320 is as given in Table2 . The comparison is presented in Table 1.... ..."

### Table 1 - Comparing the noise performance of the minimum noise type III structure to the noise performance of two versions of the direct form error spectrum shaping structure.

"... In PAGE 5: ...Table 1 - Comparing the noise performance of the minimum noise type III structure to the noise performance of two versions of the direct form error spectrum shaping structure. In Table1 , it is also included an elliptic filter that accomplishes the same specifications considered when designing the two filters of Figs. 3, 4, 5 and 6.... In PAGE 5: ... In both cases, they vary 40 % of their optimal value. From Table1 , one can notice that the signal to noise ratio of the optimum error spectrum shaping structure is much better than the signal to noise ratio of the minimum noise type III structure. However, the optimum error spectrum shaping structure is much likely to sustain limit cycles, for narrow bandwidth filters, what justified proposing its adaptive version (Macedo Jr.... ..."

### Table 1 - Comparing the noise performance of the minimum noise type III structure to the noise performance of two versions of the direct form error spectrum shaping structure.

"... In PAGE 5: ...Table 1 - Comparing the noise performance of the minimum noise type III structure to the noise performance of two versions of the direct form error spectrum shaping structure. In Table1 , it is also included an elliptic filter that accomplishes the same specifications considered when designing the two filters of Figs. 3, 4, 5 and 6.... In PAGE 5: ... In both cases, they vary 40 % of their optimal value. From Table1 , one can notice that the signal to noise ratio of the optimum error spectrum shaping structure is much better than the signal to noise ratio of the minimum noise type III structure. However, the optimum error spectrum shaping structure is much likely to sustain limit cycles, for narrow bandwidth filters, what justified proposing its adaptive version (Macedo Jr.... ..."

### Table 1 - Comparing the noise performance of the minimum noise type III structure to the noise performance of two versions of the direct form error spectrum shaping structure.

"... In PAGE 4: ... For doing that, the structures are simulated considering fixed- point two-complement arithmetic implementation with 16 bits wordlength, from which 15 bits are used for representing the mantissa of the signal and filter coefficients. Table1 shows the resulting signal to... In PAGE 4: ...Table 1 - Comparing the noise performance of the minimum noise type III structure to the noise performance of two versions of the direct form error spectrum shaping structure. In Table1 , it is also included an elliptic filter with the same specifications of the filters in Figures 3, 4 5 and 6. By its turn, the two implementations of the error spectrum shaping structure used are the optimal one [13] and the adaptive one [14].... In PAGE 4: ... In both cases, they vary 40 % of their optimal value. From Table1 , one can notice that the signal to noise ratio of the optimum error spectrum shaping structure Figure 5: Noise results for the Chebyschev example under L2 scaling. Figure 6.... ..."

### Table 1. Synthesis results comparing average power consumed in a multiplier in folding 65-tap, 129-tap bandpass FIR filters on to an architecture with a given number of multipliers and adders. Several scenarios are compared which include folding begining from a direct-form filter DFG and folding from a transpose filter DFG with varying unfolding factors to uncover common data-operands. Coefficient reordering is also resorted to in all the cases in an attempt to further reduce power consumption in the multipliers.

2000

"... In PAGE 4: ... The multiplier used in our simulations was a 16 16 Booth-recoded Wallace-Tree multiplier. The results of our simulation are tabulated in Table1 . Table 1 presents a compar- ison of average power consumed in a multiplier for folding from a transpose FIR filter DFG with various unfolding factors for a given number of hardware multipliers and adders.... ..."

Cited by 2

### Table 2: The number of multipliers, two-input adders, and branches.

1999

"... In PAGE 4: ...other forms: (1) the balanced state-space realization [1], (2) Agarwal and Burrus structure [3], (3) Diniz and Antoniou structure [4], and (4) direct form II. Table2 also compares the computational complexity of those filter structures with respect to the number of multipliers, two-input adders, and branches of these filters. The computational complexity roughly provides an indication of its cost of implementa- tion.... ..."

Cited by 2

### Table 2.8 Total transition activity for folded direct form FIR lter Signal Measured Estimated % Error

1999

### Table 1: The characteristics and experimental results of the examples used to demonstrate the effective- ness of the new approach. cp - critical path length

"... In PAGE 16: ... 6 Experimental Results We applied our approach to design for functional test pattern execution on a set of 10 industrial examples. Table1 provides the characteristics of the considered designs and presents the experimental results for the designs. The examples are the following: second order Volterra filter, third order Volterra filter, 12th order IIR filter, DAC (NEC digital-to-analog converter for audio applications), LMS audio formatter (NEC design for communication), Avenhaus direct-form filter, Avenhaus cascade-form filter, Avenhaus parallel-form filter, Avenhaus continued-fraction filter, and Avenhaus ladder filter.... ..."