In a PCM system, an input signal m₁ (t) = 8 cos(2000πt) volts. It is required to design a uniform quantizer with a maximum quantization error of 0.1 volts. 1) What is the minimum number of bits required to characterize the output levels? 2) What is the actual maximum quantization error if that minimum number of bits are fully utilized? 3) Assume a mid-rise quantizer is used. Assume also a sampling rate that is 50% above the Nyquist rate, with the first samples taken at t = 0 seconds. Sketch the quantizer output staircase waveform for one complete cycle of the input.

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In a PCM system, an input signal m₁(t) 8 cos(2000πt) volts. It is required to design a uniform quantizer
with a maximum quantization error of 0.1 volts.
1) What is the minimum number of bits required to characterize the output levels?
2) What is the actual maximum quantization error if that minimum number of bits are fully utilized?
3) Assume a mid-rise quantizer is used. Assume also a sampling rate that is 50% above the Nyquist
rate, with the first samples taken at t = 0 seconds.
Sketch the quantizer output staircase waveform for one complete cycle of the input.
4) Another signal m₂(t) = 6 cos(4000πt) is multiplexed with m₁(t) using TDM. Draw a suitable
frame structure, indicating the duration of each time slot and which signal sample is transmitted
per time slot. Assume that m₂(t) is sampled at a sampling rate double its Nyquist rate.
Transcribed Image Text:= In a PCM system, an input signal m₁(t) 8 cos(2000πt) volts. It is required to design a uniform quantizer with a maximum quantization error of 0.1 volts. 1) What is the minimum number of bits required to characterize the output levels? 2) What is the actual maximum quantization error if that minimum number of bits are fully utilized? 3) Assume a mid-rise quantizer is used. Assume also a sampling rate that is 50% above the Nyquist rate, with the first samples taken at t = 0 seconds. Sketch the quantizer output staircase waveform for one complete cycle of the input. 4) Another signal m₂(t) = 6 cos(4000πt) is multiplexed with m₁(t) using TDM. Draw a suitable frame structure, indicating the duration of each time slot and which signal sample is transmitted per time slot. Assume that m₂(t) is sampled at a sampling rate double its Nyquist rate.
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