FIR Linear Phase Condition

A FIR filter is linear-phase if (and only if) its coefficients are symmetrical around the center coefficient, that is, the first coefficient is the same as the last; the second is the same as the next-to-last, etc.

1. Do all FIR filters have linear phase?
2. What are the conditions to be satisfied for constant phase delay in linear phase FIR filters?
3. What is linear FIR filter?
4. Which one of the following FIR system has linear phase response?

Do all FIR filters have linear phase?

No! FIR filters are NOT always linear phase. The acronym 'FIR" only tells you that the impulse response is finite in duration, nothing more and nothing less. So called "minimum phase" FIR filters are not linear phase.

What are the conditions to be satisfied for constant phase delay in linear phase FIR filters?

For a FIR system to have a linear phase the condition for impulse response is h(n)=±h(M−1−n)⋅ If h(n)=h(M−1−n) then the FIR is symmetrical around and if h(n)=−h(M−1−n) then the FIR is anti symmetrical around the centre coefficient.

What is linear FIR filter?

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.

Which one of the following FIR system has linear phase response?

Answer (Detailed Solution Below) Option 1 : FIR filter can have an exact linear phase.