I am trying to calculate Bits width for each stage of a cic filter using prune method. I came across @Rick Lyons Matlab script to calculate Bit width for CIC prune(https://www.dsprelated.com/showcode/269.php). However, I see Bj (Number of least significant bits that can be truncated at the input of a filter stage) to be negative. Can some one suggest why this happening? Below are the details of the filter configurations and the result obtained from the Matlab script:
N = 5, R = 128, M = 1, Bin = 8, Bout = 24
Num of Bits Growth Due To CIC Filter Gain = 35
Num of Accumulator Bits With No Truncation = 43
Stage(j) Bj Accum (adder) width
1 -14 57
2 -7 50
3 -1 44
4 5 38
5 10 33
6 13 30
7 14 29
8 15 28
9 16 27
1e+01 16 27
1e+01 19 24 (final truncation)
I haven't looked a Rick'code but you certainly don't need more bits than 43 at any given stage. I would guess a negative Bj value is really a 0, so here your first 3 accumulators would be the full 43 bit long.
Thank you for the reply. I tried with full 43 bits for stages where Bj is negative. I see a difference of 1LSB between a pruning and CIC filter designed without prune.
1 lsb error is probably what you should expect. You'll always get up to 1 lsb since there is truncation.
So, if truncation is replaced by rounding would they match?
This is discussed in the original Hogenauer paper. If I remember right some of the stages benefit from rounding, but for others floor() was just as good (or something along those lines).
However you'll always get up to 1-lsb error. This isn't much different than implementing the CIC as an FIR where you would truncate inside the accumulators.
gretzteam is correct in his first Oct. 17th comment. At the end of my text accompanying my MATLAB code at:
"Warning: It's possible, for
certain combinations of
N, R, M, Bin, and Bout, that negative values of Bj are computed, particularly when
RM is a small number, and Bout>Bin. When using the following Matlab
code, if you compute a negative value of
Bj then that value should be ignored
and no truncation should performed at that
Thank Rick Lyons.
Hi singh2426v. You're welcome, and Good Luck with your CIC filter work.