Consider an FIR filter h[n] of length L with real-valued coefficients. Suppose that L is an odd number. Furthermore, we assume the anti-symmetricity of the filter coefficients so that h[n] = −h[L − 1 − n]. 

(a) Show that the “continuous-phase” ϕ(ω) is written in the form of ωℓ ϕ0 for 2ℓ ∈ Z and ϕ0 ∈ {0, π2 }. Specify ℓ and ϕ0. 

(b) Show that h[n] has zero DC gain, that is, H(ej0 ) = L−1 X n=0 h[n] = 0. 

(c)  Show that h[n] has zero HF gain, that is, H(e jπ) = L−1 X n=0 h[n](−1)n = 0.

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