An FIR filter has a system function  H(z) = 0.05z² + 0.5z + 1 + 0.5z⁻¹ + 0.05z⁻².

(a) Find the magnitude |H(e^jω)| and phase response ∠H(e^jω) at frequencies ω = 0, π/2 and π. Sketch each of these responses for – π ≤ ω < π, and indicate the type of filter.

(b) Determine the impulse response h[n] and indicate if the filter is  causal.

(c) If H(z) is non-causal, how would you make it causal? What would  be the effect of your procedure on the magnitude and the phase responses obtained before? Explain and plot the magnitude and  phase of your causal filter.