16x interpolation using polyphase FIR - sum of the coefficients I have an issue with polyphase implementation during interpolation. Lets assume I have 256 taps long FIR lowpass sinc filter. In order to interpolate by a factor of 2 I do use two FIR filters (polyphase filter) out of the main one since I don't need to calculate zero stuffed samples. The same goes with interpolation by a factor of 4 in which case four sub-filters (polyphase filters) are used.

However, there is something which bothers me a lot and I don't know what to think about it - the sum of the coefficients within sub-filters should always equal to 1 (if the gain is 1). That is the case with polyphase filters for interpolation factors of 2 and 4. However, if I set interpolation to a factor of 8 or greater sum of coefficients within each polyphase does no longer create a correct sum (which should be close to 1).
Basically, you are up-sampling to a higher sample rate. The purpose of the interpolation filter is to eliminate the mirror-spectra, that you get from up-sampling and inserting zeros. 

You need to chose the cutoff frequency for the interpolation filter accordingly. If you upsample by two you want a cutoff of fs/4 (or thereabouts). If you want to upsample by 8, your cutoff frequency needs to be lower, i.e. fs/16.