|
|
High Precision |
Ordinary Rounding |
New Method |
|
n |
a(n) |
a'o(n) |
a'(n) |
|
0 |
32765.0156 |
32765 |
32766 |
|
1 |
21386.3712 |
21386 |
21387 |
|
2 |
992.9455 |
993 |
993 |
|
3 |
-6826.4739 |
-6826 |
-6827 |
|
4 |
-941.9129 |
-942 |
-943 |
|
5 |
3753.0633 |
3753 |
3752 |
|
6 |
862.0648 |
862 |
862 |
|
7 |
-2346.7999 |
-2347 |
-2346 |
|
8 |
-760.4611 |
-760 |
-760 |
|
9 |
1522.7395 |
1523 |
1522 |
|
10 |
645.6166 |
646 |
644 |
|
11 |
-986.6937 |
-987 |
-988 |
|
12 |
-526.4166 |
-526 |
-527 |
|
13 |
624.1586 |
624 |
624 |
|
14 |
411.0701 |
411 |
411 |
|
15 |
-378.5124 |
-379 |
-379 |
|
16 |
-306.2520 |
-306 |
-307 |
|
17 |
215.8401 |
216 |
215 |
|
18 |
216.5513 |
217 |
216 |
|
19 |
-112.6784 |
-113 |
-113 |
|
20 |
-144.2876 |
-144 |
-145 |
|
21 |
51.3508 |
51 |
50 |
|
22 |
89.6510 |
90 |
88 |
|
23 |
-18.1667 |
-18 |
-19 |
|
24 |
-51.1279 |
-51 |
-51 |
|
25 |
2.6714 |
3 |
3 |
|
26 |
26.0694 |
26 |
26 |
|
27 |
2.7570 |
3 |
3 |
|
28 |
-11.3053 |
-11 |
-10 |
|
29 |
-3.2459 |
-3 |
-1 |
|
30 |
3.8829 |
4 |
6 |
|
31 |
2.4990 |
2 |
4 |
|
32 |
0.0785 |
0 |
1 |
|
33 |
-0.2136 |
0 |
0 |
|
Max Ripple |
|||
|
Pass band |
0.0005dB |
0.0011dB |
0.0035dB |
|
Stop band |
-132.1dB |
-79.7dB |
-97.7dB |
This symmetrical low-pass FIR filter is designed for factor 2 decimation (down sampling). The high precision coefficients are scaled so that the center coefficient is close to 2^15.
The pass band is [0; 0.2] and the stop band is [0.3; 0.5] relative to the sampling frequency.
The table below shows the result of ordinary rounding (round to nearest) and the best result from 100 trials using the new method (with coefficients b1= b2 =1.96285 and b3 = 1).