I am trying to design a general purpose 8-tap FIR filter. What is the general range of coefficients for any application? is it from [-1 to 1] or [0 to 1] ...? This filter will be used in interpolation applications with no signal gain.
Filter coefficients in general are not only positive, therefore you shall consider the range [-1, 1] for the normalized coefficients of your generic FIR.
An smooth interpolation filter probably may have a positive coefficients only, but not in general. A bandfilter or a highpass in contrast must have bipolar coefficients to block DC. There are some basic theorems in signal theory regarding even and odd time functions in relation to their fourier transforms, they also should give insights to symmetry properties of FIR coefficient series.