Quantisation Error In The A D Process
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In electronics, an analog-to-digital converter (ADC, A/D, A–D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering quantization error formula a digital camera, into a digital signal. An ADC may also
Quantization Noise
provide an isolated measurement such as an electronic device that converts an input analog voltage or current to quantization of signals a digital number proportional to the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, what is quantization but there are other possibilities. There are several ADC architectures. Due to the complexity and the need for precisely matched components, all but the most specialized ADCs are implemented as integrated circuits (ICs). A digital-to-analog converter (DAC) performs the reverse function; it converts a digital signal into an analog signal. Contents 1 Explanation 1.1 Resolution 1.1.1 Quantization error
Quantization Error Example
1.1.2 Dither 1.1.3 Non-linearity 1.2 Jitter 1.3 Sampling rate 1.3.1 Aliasing 1.3.2 Oversampling 1.4 Relative speed and precision 1.5 Sliding scale principle 2 Types 2.1 Direct-conversion 2.2 Successive approximation 2.3 Ramp-compare 2.4 Wilkinson 2.5 Integrating 2.6 Delta-encoded 2.7 Pipeline 2.8 Sigma-delta 2.9 Time-interleaved 2.10 Intermediate FM stage 2.11 Other types 3 Commercial 4 Applications 4.1 Music recording 4.2 Digital signal processing 4.3 Scientific instruments 4.4 Rotary encoder 5 Electrical symbol 6 Testing 7 See also 8 Notes 9 References 10 Further reading 11 External links Explanation[edit] The conversion involves quantization of the input, so it necessarily introduces a small amount of error. Furthermore, instead of continuously performing the conversion, an ADC does the conversion periodically, sampling the input. The result is a sequence of digital values that have been converted from a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal. An ADC is defined by its bandwidth and its signal-to-noise ratio. The bandwidth of an ADC is characterized primarily by its sampling rate. The dynamic range of
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Quantization Error In Pcm
Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top What is “Maximum Quantization Error”? up vote 2 down vote favorite 1 I have an formula https://en.wikipedia.org/wiki/Analog-to-digital_converter 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 bet on something like "Signal Excursion Band". I know, its a strange http://dsp.stackexchange.com/questions/15925/what-is-maximum-quantization-error 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♦ 6,71041444 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]. The difference between steps is 0.25. If you round during quantization the maximum error will be half of that (i.e. 0.125). Now let's try t
& SoCs Operating Systems Power Optimization Programming Languages & Tools Prototyping & Development Real-time & Performance Real-world Applications Safety & Security System Integration Essentials & Education Products News http://www.embedded.com/design/real-time-and-performance/4007558/DSP-Tricks-Reducing-A-D-Converter-Quantization-Noise Source Code Library Webinars Courses Tech Papers Community Insights Forums Events http://www.medicine.mcgill.ca/physio/vlab/biomed_signals/atodvlab.htm Archives ESP / ESD Magazine Newsletters Videos Collections About Us About Embedded Contact Us Newsletters Advertising Editorial Contributions Site Map Home> Real-time & Performance Development Centers > Design How-To DSP Tricks: Reducing A/D Converter Quantization Noise Richard G. Lyons April 22, 2008 Tweet Save to quantization error My Library Follow Comments Richard G. LyonsApril 22, 2008 To reduce or eliminate the ill effects of quantization noise in analog-to-digital (A/D) converters, . DSP practitioners can use two tricks to reduce converter quantization noise. Those schemes are called oversampling and dithering. Oversampling. The process of oversampling to reduce A/D converter quantization noise is straightforward. We merely quantisation error in sample an analog signal at an fs sample rate higher than the minimum rate needed to satisfy the Nyquist criterion (twice the analog signal's bandwidth), and then lowpass filter. What could be simpler? The theory behind oversampling is based on the assumption that an A/D converter's total quantization noise power (variance) is the converter's least significant bit (lsb) value squared over 12, or The next assumption is: the quantization noise values are truly random, and in the frequency domain the quantization noise has a flat spectrum. (These assumptions are valid if the A/D converter is being driven by an analog signal that covers most of the converter's analog input voltage range, and is not highly periodic.) Next we consider the notion of quantization noise power spectral density (PSD), a frequency-domain characterization of quantization noise measured in noise power per hertz as shown in Figure 13"17 below. Thus we can consider the idea that quantization noise can be represented as a certain amount of power (watts, if we wis
stored in a computer for further processing. Analogue signals are "real world" signals - for example physiological signals such as electroencephalogram, electrocardiogram or electrooculogram. In order for them to be stored and manipulated by a computer, these signals must be converted into a discrete digital form the computer can understand. An example of an A/D board which performs the analogue to digital conversion. This board is placed inside the computer where it communicates with the rest of the computer hardware and software. An alternate way to acquire a signal is to use an integrated device which comprises the electronics necessary to acquire as well as amplify the signals (shown to the right). Powerlab* recording system has an A/D board as well as amplifiers and communicates with the computer through its USB port. (ADInstruments)* Using A/D conversion and a computer to analyze data has many advantages over older non-computerized methods. Computer data is easily transported and manipulated. Computer analysis of signals is far more efficient than analysis by hand and paper. Most importantly, real-time analysis can be performed - this means that signals can be analyzed as they are acquired during the course of an experiment Sampling Consider the signal shown in the figure which is part of an electroencephalogram. It is an analogue signal, since it is continuously changing in time. Any arbitrarily given value that is within the range of the signal can be obtained simply by measuring electrical activity at the right point in time. The object of A/D conversion is to convert this signal into a digital representation, and this is done by sampling the signal. A digital signal is a sampled signal, obtained by sampling the analogue signal at discrete points in time. These points are usually evenly spaced in time, with the time between being referred to as the sampling interval. In the figure, the sampling interval is 2.5 milliseconds, with samples being taken at the times indicated by the red dots on the waveform. The electronic circuit that carries out the process of sampling the signal and A/D conversion is called an analogue-to-digital converter (ADC). Being an electronic device, it requires an electrical signal at its input. Thus the first step in the process of A/D conversion is to convert the analogue (non-voltage) signal into an analogue voltage signal. The device that carries out this function is called a transducer. For signals which are inherently voltages such as the electrocardiogram from