Filter Output Size

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Rodney 2012-6-1

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https://ww2.mathworks.cn/matlabcentral/answers/40029-filter-output-size

Hi All.

I am attempting to realize a discrete-time FIR filter designed in MATLAB on an embedded target, and am having difficulty understanding how MATLAB has arrived at its stated output size of {34,17}.

In short, my filter has 64 symmetric coefficients that are {16,17} - ie the MSB weight is 0.25. My filter inputs are {16,0}, and the heart of my implementation is as follows.

 for (i = 0 ; i < 32 ; i++) {
     output += coefficient[i] * ( input[a] + input[b] );
 }

The values of the input index (ie 'a' and 'b') are not relevant to this discussion. The filter output is thus the sum of 32 of the following operations:

 {16,17} * ( {16,0} + {16,0} ) = {16,17} * {17,0}
                               = {33,17}

My problem is this - how did MATLAB get from this result to {34,17}, when I would of thought the output would need to be {39,17}. I have arrived at this number using the fact that for multiple additions, you need:

floor(log2(32))+1

extra bits, as per Ricardo Losada's brilliant book "Digital Filters in MATLAB". Can anyone explain what is going on - I am at somewhat of a loss.