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Quantization

Quantization. Prof. Siripong Potisuk. Analog-to-Digital Conversion. Discretize the independent variable or time of an analog signal ( Sampling ) Discretize the dependent variable or amplitude of an analog signal by rounding off to the nearest integer ( Quantization )

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Quantization

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  1. Quantization Prof. Siripong Potisuk

  2. Analog-to-Digital Conversion • Discretize the independent variable or time of an analog signal (Sampling) • Discretize the dependent variable or amplitude of an analog signal by rounding off to the nearest integer (Quantization) • Each quantization level represented using binary encoding scheme (Encoding)

  3. Analog-to-Digital Conversion (A/D)

  4. Quantizer Input-output Characteristic Passing a discrete-time signal through a piecewise constant staircase type function

  5. Quantization Level • Suppose the value of x[n] ranges over the interval [xmin, xmax]. The spacing between adjacent quantization level or step size is where L = number of quantization levels N = number of binary bits used to represent the value of x[n]

  6. Quantization Error • Also known as quantization noise • Modeled as a random variable uniformly distributed over the interval [-D/2, D/2] with probability density p(x) = 1/D. • The average power of the quantization noise is

  7. Example • Suppose the amplitude of a discrete-time signal x[n] is constrained to lie in the interval [-10, 10]. If the average power of the quantization noise is to be less than 0.001, what is the minimum number of bits that are needed to represent the value of x[n]?

  8. Example Assuming that a 3-bit A/D converter accepts input ranging from 0 to 5 volts, determine: (a) number of quantization levels; (b) step size of the quantizer (resolution); (c) quantization level when the analog voltage is 3.2 volts; (d) binary code produced by the A/D converter; (e) the quantization error for the 3.2-V input.

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