Maximum Error Quantization
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How To Reduce Quantization Error
down vote favorite 1 I have an formula for this "Maximum Quantization Error" but i dont know what it is based in. Its just thrown in my study material without further explanation. It is defined as: $$Q = \dfrac {\Delta x}{2^{N+1}}$$ where $N$ is the number of bits used for quantization in a analog to digital conversion, and $\Delta x$ is, in portuguese "Faixa de Excursão do Sinal", I don't know what would be the correct translation, but I quantization error in a/d converter bet on something like "Signal Excursion Band". I know, its a strange name. Can someone help me with this? What is this $\Delta x$? Sorry for my bad english, it isnt my native language. adc quantization share|improve this question edited Apr 29 '14 at 17:07 jojek♦ 6,71241444 asked Apr 29 '14 at 15:19 Diedre 20115 Evidently you are learning the basics. Speaking as a retired EE; real designs are a lot more complicated. The answer below is idealized for discussion. While not wrong, there are large confounding terms in physical implementation. –rrogers Dec 30 '15 at 14:42 add a comment| 1 Answer 1 active oldest votes up vote 4 down vote accepted When you quantize a signal, you introduce and error which can be defined as $$q[n] = x_q[n]-x[n]$$ where $q[n]$ is the quantization error, $x[n]$ the original signal, and $x_q[n]$ of the quantized signal. The maximum quantization error is simply $max(\left | q \right |)$, the absolute maximum of this error function. Dx in this definition seems to be the range of the input signal so we could rewrite this as $$Q = \frac{max(x)-min(x)}{2^{N+1}}$$ Let's look at a quick example. Let's assume you have a signal that's uniformly distributed between -1 and +1 and you want to quantize this with 3 bits. You have a total 8 of quantizaton steps which would map to [-1 -.75 -.5 -25 0 .25 .5 .75]. T
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 how to calculate quantization step size signals coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, dB 1
Quantization Error Percentage
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 Error Ppt
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 http://dsp.stackexchange.com/questions/15925/what-is-maximum-quantization-error 92 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 http://www.skillbank.co.uk/SignalConversion/snr.htm measured by 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 sign
iclicker Registration Check Grades Honors Section Step-By-Step Examples ECE110 BLOG Suggested Reading Online Flashcards Video Channel ECE 110 Course Notes Sampling and Quantization https://courses.engr.illinois.edu/ece110/fa2016/content/courseNotes/files/?samplingAndQuantization Learn It! Required Analog and Digital Signals Sampling Nyquist Sampling Rate Quantization Unit Conversion Explore More Learn It! Analog and Digital SignalsDigital signals are more resilient against noise than analog signals. An analog signal exists throughout a continuous interval of time and/or takes on a continuous range of values. A sinusoidal signal (also called a pure quantization error tone in acoustics) has both of these properties. Figure 1 Fig. 1: Analog signal. This signal $v(t)=\cos(2\pi ft)$ could be a perfect analog recording of a pure tone of frequency $f$ Hz. If $f=440 \text{ Hz}$, this tone is the musical note $A$ above middle $C$, to which orchestras often tune their instruments. The period $T=1/f$ quantization error in is the duration of one full oscillation. In reality, electrical recordings suffer from noise that unavoidably degrades the signal. The more a recording is transferred from one analog format to another, the more it loses fidelity to the original.
Figure 2 Fig. 2: Noisy analog signal. Noise degrades the sinusoidal signal in Fig. 1. It is often impossible to recover the original signal exactly from the noisy version. A digital signal is a sequence of discrete symbols. If these symbols are zeros and ones, we call them bits. As such, a digital signal is neither continuous in time nor continuous in its range of values. and, therefore, cannot perfectly represent arbitrary analog signals. On the other hand, digital signals are resilient against noise. Figure 3 Fig. 3: Analog transmission of a digital signal. Consider a digital signal $100110$ converted to an analog signal for radio transmission. The received signal suffers from noise, but given sufficient bit duration $T_b$, it is still easy to read off the oribe down. Please try the request again. Your cache administrator is webmaster. Generated Thu, 20 Oct 2016 10:53:14 GMT by s_wx1202 (squid/3.5.20)