Originally Posted by sfogg
If you have a 10-tap FIR filter (which is rather small by audio standards), each sample undergoes 10 additions and 10 multplications. For a naive algorithm, that requires a little more than 2*10*n, or 20*n bits. For 32-bit integers, that's over 640 bits per sample.
This is not correct. Let's say your samples are 16 bits and the filter coefficients are 32 bits. Then a multiplication results in 48 bits. Additions only add 1 bit, so 10 additions add 2log10=3.32 bits.
The total number of bits without rounding for the 10-tap FIR filter is 52.