Stability Condition in Terms of the Pole Locations A causal LTI digital filter is BIBO stable if and only if its impulse response h[n] is absolutely summable, i.e., We now develop a stability condition in terms of the pole locations of the transfer function H(z)
The simple filters discussed so far are characterized either by a single passband and/or a single stopband There are applications where filters with multiple passbands and stopbands are required The comb filter is an example of such filters