An audio earpiece has a spatial audio feature that can track human head movement to give surround sound effects. Assuming you are listening to the audio that is streaming from your laptop to your earpiece, the audio signal has a fundamental component of 4 KHz and its second harmonics at 0.25 V and 0.125 V respectively. It passes through the anti-aliasing filter before it goes through the 8 bits 2's complement ADC inside the earpiece to process the audio signal fidelity. The processed audio signal goes through an amplifier with a volume gain of 3 and produces additional 4thand 5thharmonics at 0.075 V and 0.05 V respectively.

(a) Execute the calculation of both sampling frequency and bandwidth of the anti-aliasing filter. Hence, plot the 3 dB bandwidth spectrum.

(b) Analyse the quantization level that is required to cover the full voltage swing of 2 V peak-to-peak of the spatial audio input signal at the earpiece. Hence, obtain the quantization error range with the truncation rule being used in the conversion process of ADC.

(c) Analyse the ADC binary representation for an instantaneous audio input signal of -0.6 V.

(d) Describe the quality of the earpiece audio performance by calculating its total harmonic distortion (THD) at the amplifier output in percentage. Hence, plot the amplitude spectrum of the amplifier at the output.