I would like to appy multiple filters to a signal at once. Let's assume I got two frequency bands I want to extract. I compute a Butterworth Filter for 300-500Hz and one for 700-800Hz. I would like to combine those filters into a single filter and apply it to the signal. The resulting signal should contain only frequencies in range 300-500Hz and 700-800Hz.
I assume that if the filters are FIR (finite impulse response) filters I just need to add them. Using that single filter, I apply a convolution to the signal. Is that correct?
I am pretty lost if it gets to IIR (Infinite impulse response) filters which are - as I understand - divisions of polynoms in a radial space I do not understand. How can I combine two IIR filters?
Kind regards, Thomy800