Question 2
(a) Given that a Macbook Pro laptop is receiving a music stream and passes this music to an audio multiplicative mixer apple software inside the system. This music has three signal components with frequency at Middle C note and its third and fifth harmonics with amplitude of 3 volts, 2 volts, and 1 volt peaks respectively.
(i) Obtain the Middle C Note frequency and its respective harmonic of the music stream where 𝑝 = 60. Hence, describe the frequency spectrum for the music stream. Hint: 𝑝 = 69 + 12 𝑙𝑜𝑔2 (
𝑓 440) 𝐻𝑧
(4 marks)
(ii) The music stream passes through the multiplicative mixer apple software. It produces various beat frequencies among each other. Explain the mixing
process by calculating the mixed and beat frequencies.
(8 marks)
(iii) Analyse through plotting the amplitude spectrum of the output of the
multiplicative mixer in Question 2(a)(ii). Clearly indicate the beat frequencies
in the plot.
(4 marks)

(b) Given that amplitude modulation (AM) technology is being used to broadcast the audio music stream via Wi-Fi technology. The audio modulating signal is given as 𝑏(𝑡) = 1 + 8 cos(2𝜋𝑓𝑡) V where 𝑓 is the fifth harmonics frequency in the music stream in Question 2a (i). The carrier is given as 𝑝(𝑡) = 5 cos(10000000000𝜋𝑡) V.
(i) Derive and analyse through plotting the frequency spectrum of the modulated signal.
(6 marks)
(ii) Determine the receiver carrier frequency used and determine the bandwidth of the recovering filter to recover the modulating signal.