It is nearly impossible to design a linearphase IIR transfer function It is always possible to design an FIR transfer function with an exact linear-phase response Consider a causal FIR transfer function H(z) of length N+1, i.e., of order N:
The output y[n] of a frequency-selective LTI discrete-time system with a frequency response exhibits some delay relative to the input x[n] caused by the nonzero phase response of the system
BIBO Stability Condition - A discrete-time LTI system is BIBO stable if the output sequence {y[n]} remains bounded for any bounded input sequence{x[n]}
