Problem
1. A time series sound wave x(t) has a fundamental frequency component at 2 kHz with an amplitude of 2 Volts. It is picked up and then gone through a non-linear amplifier that resulted in the second and third order harmonics at 1 Volt and 0.5 Volt respectively. The output of the amplifier is input to anti-aliasing filter of a linear PCM system. The output of the filter is then eventually fed to an 8-bit 2's complement ADC of the PCM system.
2. Execute the Nyquist sampling rate of the anti-aliasing filter.
3. Determine the ADC's quantization step that will cover the voltage swing of 3 Volts peak-to-peak of the input signal. Hence, obtain the ADC's quantization error range if truncation rule is used.
4. Obtain the binary representation for a given sound signal input having an instantaneous input of -1.3 Volts with the obtained quantization step in part (3).