IIR filter and phase shift [closed]

1. Do FIR filters have phase shift?
2. Why do IIR filters not have linear phase?
3. Can IIR filter linear phase?
4. Why are IIR filters not stable?
5. Is phase response important for filters?

Do FIR filters have phase shift?

The FIR filters have a phase response that traces out a straight line. Both of these FIR filters exhibit linear phase [1][2]. This means that those sinusoidal components are given a constant phase shift and that the phase shift is constant relative to each frequency.

Why do IIR filters not have linear phase?

For an IIR filter to satisfy the linear phase condition, both the poles and zeros would need to have mirror images outside the unit circle of the z-plane. However, poles outside the unit circle ⇒ unstable. Therefore, a causal, stable IIR cannot have linear phase.

Can IIR filter linear phase?

It is well known that causal Finite Impulse Response (FIR) filters can be designed to have linear phase. However, Infinite Impulse Response (IIR) filters can have linear phase only in the noncausal case (Mitra, 2006; Vaidyanathan, 1993; Vaidyanathan and Chen, 1998), (the phase response can be 0 or π).

Why are IIR filters not stable?

(a) Stable IIR filter, (b) The same IIR filter becomes unstable due to rounding effects. , one poles lie exactly on the unit circle (ie, it is just out of the region of stability) and hence it is an unstable IIR filter.

Is phase response important for filters?

While filters are designed primarily for their amplitude response, the phase response can be important in some applications. For purposes of review, the transfer function of an active filter is actually the cascade of the filter transfer function and the amplifier transfer function (see Figure 1).