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.
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.
Probability of Error
This topic is widely taught in many undergraduate and postgraduate degree courses of:
Step by step
Solved in 6 steps with 9 images