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(4000rt) 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.
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(4000rt) 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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Quantization and Resolution
Quantization is a methodology of carrying out signal modulation by the process of mapping input values from an infinitely long set of continuous values to a smaller set of finite values. Quantization forms the basic algorithm for lossy compression algorithms and represents a given analog signal into digital signals. In other words, these algorithms form the base of an analog-to-digital converter. Devices that process the algorithm of quantization are known as a quantizer. These devices aid in rounding off (approximation) the errors of an input function called the quantized value.
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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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