FIR filter coefficient scaling and downscaling

Your filter input range is 0 ~ 4095.

scale your coeffs so that their sum = 4096

coeff = round(4096*coeff/sum(coeff));

Then discard 12 LSBs (bit 11:0) giving you unity gain (output 0 ~ 4095);

Discard remaing 4 MSBs(bit 27:24). you may insert flag/saturate if bit 24 gets that occasional hit at extremes.

Hi Kaz,

Thanks for your reply.

The Fir compiler has floating point, fixed point and Integer coefficients. For the calculation in your previous post:

coeff = round(4096*coeff/sum(coeff));

should I be using the integer coefficients that are output to the text file by fir compiler when i generate the filter? or the fixed point coefficients?

I have tried to use coeff = (4096*coeff/sum(coeff)); without rounding with the integer coefficients. The sum of resultant coeffs is 4096. And then I copied these scaled coefficients into a text file and used Import coefficient of fir compiler.

The new Integer coefficients that the compiler generates are less than 12 bits but their sum is greater than 12 bits.

I am not sure how the hardware implementation works, but i assume it uses the integer coefficients, So for DC signal value the output will be equal to sum of integer coefficients which is greater than 12bits.

Is that true? Once again thanks for replying to my question.

I regret I don't know about specifics of Altera FIR compiler. I referred to general concepts of filtering.

I always think of signed representation for a filter's input/output and don't really understand what unsigned means or is it converted to signed invisibley.

The rule for fixed point (incidentally it is sort of integer) is that what you mentioned:

DC output = 4095*h0 + 4095*h1 + ...etc = 4095(ho+h1+...etc). hence if sum of coeffs = 4096 then your output = 4095*4096 then divide back by 4096(truncate 12 bits) and your output becomes 4095.

The only exceptions are those input patterns that = DC level but with pattern that negates the sign of some coeffs resulting in a sum larger than actual sum of signed coeffs !

I think the best thing is to try and see how FIR implements the output scaling

through simulation.

The sum of coeff is 51519. Do you think some thing is not set right in the fir compiler setting. I am using the following settings:

Input Number System : unsigned binary

Input Bit Width: 12

Coeffecients scaling: Auto

Bit width 12

Structure: fully Parallel filter.

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The sum of coeff is 51519. Do you think some thing is not set right in the fir compiler setting.

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I guess it's normal operation of the FIR compiler, but it ends up in a DC gain that's not a power of two, so you can't get a gain of 1 by just adjusting the number of bits. Provided, that the coefficients are now using the full range, you can use manual scaling to the next smaller power of two, 32768.

IMHO you should replace sum(coefs) with sum(abs(coefs)) everywhere, and the algorithm will work a lot better.

Read a book on convolution and you will find out why.