Consider the following sinusoidal signal with the fundamental frequency f 0 f0​ of 4 kHz: g ( t ) = 5 cos ⁡ ( 2 π f 0 t ) = 5 cos ⁡ ( 800 π t ) . (i) The sinusoidal signal is sampled at a sampling rate f s fs​ of 6000 samples/s and reconstructed with an ideal LPF with the following transfer function: H 1 ( ω ) = { 1 / 6000 ∣ ω ∣ ≤ 6000 π 0 e l s e w h e r e . Determine the reconstructed signal. (ii) Repeat (i) for a sampling rate f s fs​ of 12 000 samples/s and an ideal LPF with the following transfer function: H 2 ( ω ) = { 1 / 12 000 ∣ ω ∣ ≤ 12 000 π 0 e l s e w h e r e .