Quantized Error
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the original analog signal (green), the quantized signal (black dots), the signal reconstructed from the quantized signal (yellow) and quantization error formula the difference between the original signal and the reconstructed signal quantization noise power (red). The difference between the original signal and the reconstructed signal is the quantization error and, how to reduce quantization error in this simple quantization scheme, is a deterministic function of the input signal. Quantization, in mathematics and digital signal processing, is the process of mapping a
Quantization Error In Pcm
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 involves rounding. Quantization also forms the core of essentially all lossy quantization noise in pcm 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 is a many-to-few mapping, it is an inherently non-linear and irreversible process (i.e., because the same output value is shared by multiple input v
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 Learn It! Required Analog and Digital Signals quantization error example Sampling Nyquist Sampling Rate Quantization Unit Conversion Explore More Learn It! Analog
Signal To Quantization Noise Ratio
and Digital SignalsDigital signals are more resilient against noise than analog signals. An analog signal exists throughout a continuous
Quantization Error In Analog To Digital Conversion
interval of time and/or takes on a continuous range of values. A sinusoidal signal (also called a pure tone in acoustics) has both of these properties. Figure 1 Fig. 1: Analog signal. https://en.wikipedia.org/wiki/Quantization_(signal_processing) 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 $T=1/f$ is the duration of one full oscillation. In reality, electrical recordings suffer from noise that unavoidably degrades the signal. The more https://courses.engr.illinois.edu/ece110/fa2016/content/courseNotes/files/?samplingAndQuantization 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 original sequence $100110$ perfectly. Digital signals can be stored on digital media (like a compact disc) and manipulated on digital systems (like the integrated circuit in a CD player). This digital technology enables a variety of digital processing unavailable to analogTour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About http://dsp.stackexchange.com/questions/15925/what-is-maximum-quantization-error Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with us Signal Processing Questions Tags Users Badges Unanswered Ask Question _ Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. Join them; it only takes a minute: Sign up Here's how it works: Anybody quantization error 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 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: $$Q = \dfrac {\Delta quantization error in x}{2^{N+1}}$$ 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 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 |)