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quantization error adc converter Allons, Tennessee

Analog-to-digital converter (ADC)[edit] Outside the realm of signal processing, this category may simply be called rounding or scalar quantization. For simple rounding to the nearest integer, the step size Δ {\displaystyle \Delta } is equal to 1. This generalization results in the Linde–Buzo–Gray (LBG) or k-means classifier optimization methods. Iterative optimization approaches can be used to find solutions in other cases.[8][19][20] Note that the reconstruction values { y k } k = 1 M {\displaystyle \{y_{k}\}_{k=1}^{M}} affect only the distortion

Embedded Systems Design. Currently,[when?] frequencies up to 300MHz are possible.[8] For a successive-approximation ADC, the conversion time scales with the logarithm of the resolution, e.g. Slow on-chip 8, 10, 12, or 16 bit analog-to-digital converters are common in microcontrollers. If a preamplifier has been used prior to A/D conversion, the noise introduced by the amplifier can be an important contributing factor towards the overall SNR.

doi:10.1109/29.17498 References[edit] Sayood, Khalid (2005), Introduction to Data Compression, Third Edition, Morgan Kaufmann, ISBN978-0-12-620862-7 Jayant, Nikil S.; Noll, Peter (1984), Digital Coding of Waveforms: Principles and Applications to Speech and Video, If you round during quantization the maximum error will be half of that (i.e. 0.125). A key observation is that rate R {\displaystyle R} depends on the decision boundaries { b k } k = 1 M − 1 {\displaystyle \{b_{k}\}_{k=1}^{M-1}} and the codeword lengths { Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply.

doi:10.1109/TIT.1972.1054906 ^ Toby Berger, "Minimum Entropy Quantizers and Permutation Codes", IEEE Transactions on Information Theory, Vol. But both types of approximation errors can, in theory, be made arbitrarily small by good design. ShareThis View My Stats Visitors Designed By Blogtipsntricks. The difference between the original signal and the reconstructed signal is the quantization error and, in this simple quantization scheme, is a deterministic function of the input signal.

David (1977), Analog & Digital Communication, John Wiley, ISBN978-0-471-32661-8 Stein, Seymour; Jones, J. For the second step, the input voltage is compared to 4 V (midpoint of 0–8). Best ECE certificate training courses to get an opportunities in core companies So many ECE studying or completed engineering graduated people has confusion in mind that what type of the courses asked 2 years ago viewed 11405 times active 1 year ago Blog Stack Overflow Podcast #92 - The Guerilla Guide to Interviewing Related 1Is it theoretically possible to perfectly quantize a

The analysis of quantization involves studying the amount of data (typically measured in digits or bits or bit rate) that is used to represent the output of the quantizer, and studying Commercial ADCs often have several inputs that feed the same converter, usually through an analog multiplexer. All rights reserved. Figure 7: Integral nonlinearity error Because nonlinearity in measurement will cause distortion, INL will also affect the dynamic performance of an ADC.

The ADC specifications that describe this type of accuracy are offset error, full-scale error, differential nonlinearity (DNL), and integral nonlinearity (INL). Nonlinearity Ideally, each code width (LSB) on an ADC's transfer function should be uniform in size. of position : One Salary: Rs. 20,000/- per month (inclusive of all) Age ... doi:10.1109/18.532878 ^ Bernard Widrow, "A study of rough amplitude quantization by means of Nyquist sampling theory", IRE Trans.

IT-14, No. 5, pp. 676–683, Sept. 1968. A quantizer designed for this purpose may be quite different and more elaborate in design than an ordinary rounding operation. This can be observed as uneven spacing of the code "steps" or transition boundaries on the ADC's transfer-function plot. An ADC with a typical 2 LSB INL may yield higher INL error than expected, making a 12-bit ADC effectively a 10-bit ADC--caveat emptor!

An encoder might output a Gray code. Most commonly, these discrete values are represented as fixed-point words (either proportional to the waveform values or companded) or floating-point words. The set of possible input values may be infinitely large, and may possibly be continuous and therefore uncountable (such as the set of all real numbers, or all real numbers within is 1/256 of the full signal range, or about 0.4%.

This distortion is created after the anti-aliasing filter, and if these distortions are above 1/2 the sample rate they will alias back into the band of interest. The two parts of the ADC may be widely separated, with the frequency signal passed through an opto-isolator or transmitted wirelessly. In more elaborate quantization designs, both the forward and inverse quantization stages may be substantially more complex. Although r k {\displaystyle r_{k}} may depend on k {\displaystyle k} in general, and can be chosen to fulfill the optimality condition described below, it is often simply set to a

In Figure 8, the fundamental frequency is the input signal frequency. For example, a 16-bit ADC has a maximum signal-to-noise ratio of 6.02 × 16 = 96.3dB. Neuhoff, "Quantization", IEEE Transactions on Information Theory, Vol. In some designs, rather than optimizing for a particular number of classification regions M {\displaystyle M} , the quantizer design problem may include optimization of the value of M {\displaystyle M}

Quantization error models[edit] In the typical case, the original signal is much larger than one least significant bit (LSB). Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Figure 10: FFT showing harmonic distortion (Equation 5) The magnitude of harmonic distortion diminishes at high frequencies to the point that its magnitude is less than the noise floor or is Commercial converters usually have ±0.5 to ±1.5 LSB error in their output.

The noise is non-linear and signal-dependent.