Mean Square Quantization Error

	Mean Square Quantization Error Mean square quantization error (MSQE) is a figure of merit for the process of analog to digital conversion. In this conversion process, analog signals in a continuous range of values are converted to a discrete set of values by comparing them with a sequence of thresholds. 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 value of the square of the quantization errors. Mathematically, suppose that the lower threshold for inputs that generate the quantized value q_i is t_, that the upper threshold is t_i, that there are k levels of quantization, and that the probability density function In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Figure Of Merit A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives. Examples Clock rate of a CPU Calories per serving Contrast ratio of an LCD Frequency response of a speaker * Fill factor of a solar cell * Resolution of the image sensor in a digital camera Measure of the detection performance of a sonar system, defined as the propagation loss for which a 50% detection probability is achieved Noise figure of a radio receiver The thermoelectric figure of merit, ''zT'', a material constant proportional to the efficiency of a thermoelectric couple made with the material The figure of merit of digital-to-analog converter, calculated as (power dissipation)/(2ENOB × effective bandwidth) /Hz* Luminous efficacy of lighting Profit of a company Residual noise remaining after compensation in an aeromagnetic survey Battery life of a laptop computer [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]
picture info	Analog-to-digital Converter In electronics, an analog-to-digital converter (ADC, 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 a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, 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). These typically take the form of metal–oxide–semiconductor (MOS) mixed-signal integrated circuit chips that integrate both analog and digital circuits. A digital-to-analog converter (DAC) performs the reverse function; it converts a digital s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Interval (mathematics) In mathematics, a (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set. For example, the set of numbers satisfying is an interval which contains , , and all numbers in between. Other examples of intervals are the set of numbers such that , the set of all real numbers \R, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton (set of one element). Real intervals play an important role in the theory of integration, because they are the simplest sets whose "length" (or "measure" or "size") is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the Borel measure and eventually to the Lebesgue measure. Intervals are central to interval arithmetic, a general numerical computing technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Probability Distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a rando ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Expected Value In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Probability Density Function In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. In a more precise sense, the PDF is used to specify the probability of the random variable falling ''within a particular range of values'', as opposed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]