Suppose that we have a signal X(t), of which its samples X follow a uniform PDF over the range (-3,7). We are sampling a second signal Y(t), of which its samples follow the function Y = (X − 1) 2 . We want to quantize Y(t) with a uniform PCM scheme, by using the maximum bit number possible and a step size bigger than 1. a) Derive the PDF of Y. b) What is the maximum bit number we can use? c) What is the corresponding step size?
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
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Suppose that we have a signal X(t), of which its samples X follow a uniform PDF over the range (-3,7). We are sampling a second signal Y(t), of which its samples follow the
function Y = (X − 1)
2
. We want to quantize Y(t) with a uniform PCM scheme, by
using the maximum bit number possible and a step size bigger than 1.
a) Derive the PDF of Y.
b) What is the maximum bit number we can use?
c) What is the corresponding step size?
d) Calculate the SQNR of this quantization process
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