Mean Square Value Of 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 of merit for the quantization error formula process of analog to digital conversion. In this conversion process, analog signals in a
Mean Square Quantization Error Formula
continuous range of values are converted to a discrete set of values by comparing them with a sequence of thresholds. quantization error example 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 distribution on the input values) is the expected
Quantization Error In Pcm
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 density function for the input analog values is p ( x ) {\displaystyle how to reduce quantization error 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 Data Conversion Website Quantization Error and Signal - to - Noise Ratio calculations The signal to noise ratio of a quantized signal is 2+6*(no of bits), as shown in the following table. Resolution and Signal to Noise Ratio for signals coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, dB 1 2 0.5 8 2 4 0.25 14 3 8 0.125 20 4 16 0.0625 26 5 32 0.03125 32 6 64 0.01563 quantization step size formula 38 7 128 0.00781 44 8 256 0.00391 50 9 512 0.00195 56 10 1024 0.00098 62 11 2048 0.00048 68 12 4096 0.00024 74 13 8192 0.00012 80 14 16384 0.00006 86 15 32768 0.00003 92 https://en.wikipedia.org/wiki/Mean_square_quantization_error 16 65536 0.00001 98 These values are for a signal matched to the full-scale range of the converter. If a signal with a range of 5V is measured by an 8 bit ADC with a range of 10V then only 7 bits are effectively in use, and a signal to noise ratio of 44 rather than 50 will apply. Proof: Suppose that the instantaneous value of the input voltage is measured by http://www.skillbank.co.uk/SignalConversion/snr.htm an ADC with a Full Scale Range of Vfs volts, and a resolution of n bits. The real value can change through a range of q = Vfs / 2n volts without a change in measured value occurring. The value of the measured signal is Vm = Vs - e, where Vm is the measured value, Vs is the actual value, and e is the error. The maximum value of error in the measured signal is emax = (1/2)(Vfs / 2n) or emax = q/2 since q = Vfs / 2n The RMS value of quantization error voltage is whence The Signal to Noise Ratio (SNR) is defined as It is normally quoted on a logarithmic scale, in deciBels ( dB ). or The RMS signal voltage is then The error, or quantization noise signal is Thus the signal - to - noise ratio in dB. is since Vfs = 2n q, then which simplifies to N.B. This equation is true only if the input signal is exactly matched to the Full Scale Range of the converter. For signals whose amplitude is less than the FSR the Signal - to - Noise Ratio will be reduced. Download a .pdf file of the analysis of quantization error and signal to noise ratio be down. Please try the request again. Your cache administrator is webmaster. Generated Wed, 19 Oct 2016 00:42:27 GMT by s_ac4 (squid/3.5.20)Quantization Error In Analog To Digital Conversion
Quantization Level