Posted: August 26th, 2022

An audio earpiece such as Apple Airpods Pro

Question 1

An audio earpiece such as Apple Airpods Pro has spatial audio feature that can track human head movement to give surround sound effect. Assuming you are listening to the audio that is streaming from the Macbook Pro 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 4th and 5th harmonics 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. Analyze the quantization level that is needed to cover the full voltage swing of 2 V peak-to-peak of the spatial audio input signal at the earpiece. So, use the truncation rule used in the ADC conversion process to figure out the range of quantization errors.

(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.

Question 2

(a) A YouTube music is streaming online from the Internet to a computer that is equipped with an audio multiplicative mixer software. The music has three signal components with frequency of 4 kHz, 9 kHz, and 19 kHz with amplitude of 4 V, 2 V and 1 V peaks respectively.

(i) Describe the frequency spectrum for the music.

(ii) The music passes through the computer’s multiplicative mixer software. It produces various beat frequencies among each other. Explain the mixing process by calculating the beat frequencies.

(iii) Analyse through illustration on the amplitude spectrum of the output of the multiplicative mixer in Question 2(a)(ii). Hence, indicate the beat frequencies in the plot.

(b) An amplitude modulation (AM) technology is used where the audio music signal is broadcasting to the ship for crew entertainment via skywave propagation. The audio modulating signal is given as (𝑡) = 1 + 8 cos(20000𝜋𝑡) V while the carrier is given as 𝑝(𝑡) = 5 cos(20000000𝜋𝑡) + 5 cos(30000000𝜋𝑡) V.

(i) Derive and analyse through illustration on the frequency spectrum of the spatial modulated signal.

(ii) Determine the receiver carrier and derive the bandwidth of the recovering filter in order to recover the modulating signal.

Question 3

(a) Discuss with illustration on the principle of critical band and frequency masking.

(b) The Blue-ray sampling rate is 192 kHz and 24 bits coding are employed to record 1000 minutes of two channel stereo uncompressed song. Execute the calculation to analyse the number of Blue-ray required to store the songs, assuming a DVD size is 25 GB.

(c) MIDI protocol is used to demonstrate the application of audio technology in multimedia. A set of MIDI subroutines is being attached below. They can be used in a C-language program to control MIDI device. The subroutine parameters can be specified in the MIDI specification in Appendix I and all parameter values must be in hexadecimal format. Please use the subroutines to do the following operations.

Question 4

System Start and select song number 11 at starting point at a count of 200
(3 marks) Channel 10 plays low piano A note for 2000 ms at maximum volume and then middle volume. (3 marks) Channel 12 plays note at 7040 Hz for 1000 ms at quarter volume and then middle volume following formula to obtain pitch value given as P = 69 + 12log2(f/440). (3 marks) Channel 15 plays note at 3520 Hz for 3000 ms at middle loudness and then silent following formula to obtain pitch value given as P = 69 + 12log2(f/440).

(a) Discuss and illustrate early reflection and late reverberation. Hence explain the critical distance.

(b) Analyse the power difference (PD) reduction in dB at the receiver for two sound signals that have travelled 5 m and 25 m respectively. Assume uniform media transmission. Explain what is the consequence when both direct blocked and reflected sound signal are totally out of phase with each other but equal in strength. Name ONE (1) application that use this feature.

(c) Assume a human wear a spatial audio tracking earpiece that tracks the head movement with respect to the sound source. The sound source is transmitting music signal at 50 degrees at the right with respect to the centre of the human. Obtain the Inter-aural delay (ITD) of sound waves, assuming the distance between two ears is 30 cm. Analyse the differentiating capability of the ear with the calculated ITD. Assume the speed of sound wave in air is 340 m/s.

(d) To create sound echoes, reverberation filter is used to produce various reflection sound. Its output response is given as (𝑛)=𝑥(𝑛−1)−𝑔∗𝑦(𝑛−2) where 𝑥(𝑛) is the input power level sequence of {12, 12, 9, 8, -2, -1, -1, -6…0} and 𝑔 is the coefficient that determines the decay level of reverberation with a value of 0.2. Draw the Infinite Impulse Response (IIR) filter implementation of the above filter and determine the output at 9 seconds. Assume input and output remains 0 when 𝑛 = 0 and n is an integer.

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