Mean Square Quantization Error
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Please help to improve this article by introducing more precise citations. (August 2016) (Learn how and when to remove this template message) Mean square quantization error (MSQE) is a figure quantization error formula of merit for the process of analog to digital conversion. In this conversion
Uniform Quantization
process, analog signals in a continuous range of values are converted to a discrete set of values by comparing
Quantization Step Size Formula
them with a sequence of thresholds. The quantization error of a signal is the difference between the original continuous value and its discretization, and the mean square quantization error (given some probability
Quantization Error In Pcm
distribution on the input values) is the expected value of the square of the quantization errors. Mathematically, suppose that the lower threshold for inputs that generate the quantized value q i {\displaystyle q_{i}} is t i − 1 {\displaystyle t_{i-1}} , that the upper threshold is t i {\displaystyle t_{i}} , that there are k {\displaystyle k} levels of quantization, and that the probability uniform quantization pdf density function for the input analog values is p ( x ) {\displaystyle p(x)} . Let x ^ {\displaystyle {\hat {x}}} denote the quantized value corresponding to an input x {\displaystyle x} ; that is, x ^ {\displaystyle {\hat {x}}} is the value q i {\displaystyle q_{i}} for which t i − 1 ≤ x < t i {\displaystyle t_{i}-1\leq x the original analog signal (green), the quantized signal (black dots), the signal reconstructed from the difference between uniform and nonuniform quantization quantized signal (yellow) and the difference between the original signal quantization error definition and the reconstructed signal (red). The difference between the original signal and the reconstructed uniform quantization definition signal is the quantization error and, in this simple quantization scheme, is a deterministic function of the input signal. Quantization, in mathematics and digital signal https://en.wikipedia.org/wiki/Mean_square_quantization_error processing, is the process of mapping a large set of input values to a (countable) smaller set. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily https://en.wikipedia.org/wiki/Quantization_(signal_processing) involves rounding. Quantization also forms the core of essentially all lossy compression algorithms. The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer. Contents 1 Basic properties of quantization 2 Basic types of quantization 2.1 Analog-to-digital converter (ADC) 2.2 Rate–distortion optimization 3 Rounding example 4 Mid-riser and mid-tread uniform quantizers 5 Dead-zone quantizers 6 Granular distortion and overload distortion 7 The additive noise model for quantization error 8 Quantization error models 9 Quantization noise model 10 Rate–distortion quantizer design 11 Neglecting the entropy constraint: Lloyd–Max quantization 12 Uniform quantization and the 6 dB/bit approximation 13 Other fields 14 See also 15 Notes 16 References 17 External links Basic properties of quantization[edit] Because quantization i be down. Please try the request again. Your cache administrator is webmaster. Generated Thu, 20 Oct 2016 12:04:59 GMT by s_wx1062 (squid/3.5.20) be down. Please try the request again. Your cache administrator is webmaster. Generated Thu, 20 Oct 2016 12:04:59 GMT by s_wx1062 (squid/3.5.20)