How do we make consideration on the precision on filter?

[boeysue]

In fixed-point filter domain,how can we make the decision of the precision on input /output and multiplicand and addition?In floating points, I have already built the exact magnitude response of the filter,but I have no idea about the presicion on fixed point math. If anyone have some opions or suggestion plz tell me,

 

[brmadhukar]

Hi,
you need to know the input width of the signal. (1-bit/8-bits/12-bits). Based on the output precision required, and the number of additions present, you may compute the quantization. You can also use dynamic range as an input to this. Hope this helps.
B R M

 

[boeysue]

Hi:
If I must use multistage filter,how to determine the intermediate precision of the filter?
Best regards..

 

[zorro]

Hi boeysue,

there are several problems:
- accuracy in the frequency response due to quantization of coeffiencients,
- stability due to numerical rounding (avoid limit cycles),
- signal-to-quantization-noise ratio,
- scaling in order of best use of dynamic range,
Using IIR filters, it is better to use cascaded 2nd order cells instead of higher order sections
The book of Oppenheim and Schafer has a very good traetment of these problems.
Regards

Z

 

[boeysue]

Oppen's book is hard to read. Is any book easier for this topic?

 

[ye.hui]

in matlab, you can use quantization functions in filter design toolbox to analyse the fixed-point filters. it is very convenient.

 

[boeysue]

Should it be experimental exercise ? Or It can be based on thereotical theorem?
Is there any paper talked about it?Thanks for answering that!..

 

[spweda]

It is a combination of the math analysis and the computer simulation. For the theoretical analysis, it is assumed that the quantization noise is the white noise. Based on the FIR filter, you could calculate the spectrum density and the nosie power. For the simulation part, you could sweep the quantization level and check the spectrum of the output and compare it with the spectrum of the float-point.

 

[boeysue]

In real implementation,is the sum of product is to add all product at one time or to add one and another sequentially???These two way seems to have different precision..Plz help..