I am digitally filtering a signal that is streaming live. The goal is to reduce the filter delay as much as possible while maintaining the quality of some measurements based on the filtered signal. For legacy reasons, the system was built with a low-pass and high-pass FIR filter in series - each filter has the same number of taps (kernel size), $n$.
I realized though, we are no longer constrained to these and could implement a single FIR band-pass filter. If I can reduce number of filter taps involved from $2n$ that will reduce the delay. My question is: is it possible to design this band-pass filter with fewer taps (a smaller kernel) than the combined taps (kernels) of the LPF/HPFs while achieving the same performance?
My initial thought is FIR filtering is a convolution operation, and thus linear + associative. That means you can construct the band pass kernel by convolving the LPF + HPF kernels. I'm unsure how to interpret this in terms of taps/kernel size because the convolution in some sense assumes an infinite kernel.