Step-1: Identify the specification of filter

$N=7 ∝=3 ω_c=-1\ltω\lt1$

Window Type: Hamming

Step-2: Calculate the Inverse Fourier Transform of H(ω)

$h_d (n)=\frac{1}{2π} ∫_{-ω_c}{(ω_c}H_d (ω) e^{jωn} dω$

$=\frac{1}{2π} ∫_{-1}^1e^{-j3ω} e^{jωn }d$

$=\frac{1}{2π} ∫_{-1}^1e^{j(n-3)ω} dω$

$=\frac{1}{2π} [e^{\frac{j(n-3)ω)}{(j(n-3))}}]_{-1}^1$

$=\frac{1}{(π(n-3))} [(e^{j(n-3)}-e^{\frac{-j(n-3)))}{2j}}]$

$h_d (n)=\frac{sin⁡(n-3)}{(π(n-3))}$

$h_d (0)=0.014=h_d (6)$ {by linear phase property}

$h_d (1)=0.144=h_d (5)$ …