Question 1
An audio sound system from HUAWEI has the spatial audio feature to give surrounding sound effects. Assuming there is an audio input signal with a fundamental frequency of 8 KHz and fifth harmonics with a signal strength of 1 volt and 0.5 volts respectively. It passes through the antialiasing filter before it goes through the 10-bit 2’s complement ADC of the system to process
the audio signal fidelity. It is being processed by the system before passes through an audio the amplifier that has a volume gain of 2 but it also produces an additional 2 nd and 4 th harmonics at
0.05 V and 0.025 V at the output respectively.

(a) Execute the calculation of anti-aliasing filter sampling frequency and its bandwidth. Hence, plot the ideal bandwidth spectrum of the filter.
(5 marks)

(b) Analyse the ADC quantization level that is required to cover the full voltage swing of 5 V peak-to-peak of the audio input signal. Hence, obtain its quantization error range with the rounding rule being used in the ADC conversion.
(6 marks)

(c) Analyse the ADC binary representation for an instantaneous audio input signal of -2.2 V.
(8 marks)

(d) Describe the audio performance through the calculation of the total harmonic distortion (THD) at the output of the amplifier in percentage. Hence, plot the amplitude spectrum of the output of the amplifier.