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This question already has an answer here:

if we have linear phase FIR filter $H(z)$ which is causal and stable can $\frac{1}{H(z)}$ be causal and stable ?

can it be causal without been stable ?

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marked as duplicate by lennon310, robert bristow-johnson, MBaz, jojek Oct 8 '17 at 16:49

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For 1/H(z) to be causal, it must not have more zeroes than poles. Therefore, H(z) must not have more poles than zeroes.

If H(z) has linear phase, then it must have zeroes either in the unitary circle or simultaneously inside and outside of it. Therefore, 1/H(z) can't be stable if H(z) has linear phase.

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