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- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/03%3A_Compression/3.05%3A_Dynamic_Dictionary/3.5.01%3A_The_LZW_PatentIts advantages were quickly recognized, and it was used in a variety of compression schemes, including the Graphics Interchange Format GIF developed in 1987 by CompuServe (a national Internet Service ...Its advantages were quickly recognized, and it was used in a variety of compression schemes, including the Graphics Interchange Format GIF developed in 1987 by CompuServe (a national Internet Service Provider) for the purpose of reducing the size of image files in their computers. Web site developers were not sure if their use of GIF images made them responsible for paying royalties, and they were not amused at the thought of paying for every GIF image on their sites.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/06%3A_CommunicationsWe have been considering a model of an information handling system in which symbols from an input are encoded into bits, which are then sent across a “channel” to a receiver and get decoded back into ...We have been considering a model of an information handling system in which symbols from an input are encoded into bits, which are then sent across a “channel” to a receiver and get decoded back into symbols, as shown in Figure 6.1. We will model both the source and the channel in a little more detail, and then give three theorems relating to the source characteristics and the channel capacity.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/11%3A_Energy/11.03%3A_System_and_Environment/11.3.06%3A_Reversible_Energy_FlowWe saw previously that when a system is allowed to interact with its environment, total entropy generally increases. In this case it is not possible to restore the system and the environment to their ...We saw previously that when a system is allowed to interact with its environment, total entropy generally increases. In this case it is not possible to restore the system and the environment to their prior states by further mixing, because such a restoration would require a lower total entropy. Thus mixing in general is irreversible.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/00%3A_Front_Matter/02%3A_InfoPageThe LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the Californ...The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/06%3A_Communications/6.02%3A_Source_EntropyAs part of the source model, we assume that each symbol selection is independent of the other symbols chosen, so that the probability p(Ai) does not depend on what symbols have previously been ch...As part of the source model, we assume that each symbol selection is independent of the other symbols chosen, so that the probability p(Ai) does not depend on what symbols have previously been chosen (this model can, of course, be generalized in many ways). The information rate, in bits per second, is H•R where R is the rate at which the source selects the symbols, measured in symbols per second.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/12%3A_Temperature/12.01%3A_Temperature_ScalesThe same is true of 1/β, and indeed of any constant times 1/β. (Actually this statement is not true if one of the two values of β is positive and the other is negative; in this...The same is true of 1/β, and indeed of any constant times 1/β. (Actually this statement is not true if one of the two values of β is positive and the other is negative; in this case the resulting value of β is intermediate but the resulting value of 1/β is not.) Note that 1/β can, by using the formulas in Chapter 11, be interpreted as a small change in energy divided by the change in entropy that causes it, to within the scale factor kB.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/06%3A_Communications/6.04%3A_Channel_ModelIf the input is changed at a rate R less than W (or, equivalently, if the information supplied at the input is less than C) then the output can follow the input, and the output events can ...If the input is changed at a rate R less than W (or, equivalently, if the information supplied at the input is less than C) then the output can follow the input, and the output events can be used to infer the identity of the input symbols at that rate. If there is an attempt to change the input more rapidly, the channel cannot follow (since W is by definition the maximum rate at which changes at the input affect the output) and some of the input information is lost.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/10%3A_Physical_Systems/10.02%3A_Introduction_to_Quantum_MechanicsThen the left-hand side is identified as the total energy, and the right-hand side as the sum of the kinetic and potential energies (assuming the wave function is normalized so that the space integral...Then the left-hand side is identified as the total energy, and the right-hand side as the sum of the kinetic and potential energies (assuming the wave function is normalized so that the space integral of |ψ(r,t)|2 is 1, a property required for the interpretation in terms of a probability density).
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/02%3A_Codes/2.08%3A_Detail-_IP_AddressesTable 2.7 is an excerpt from IPv4, http://www.iana.org/assignments/ipv4-address-space (version 4, which is in the process of being phased out in favor of version 6). Each domain name is associated wit...Table 2.7 is an excerpt from IPv4, http://www.iana.org/assignments/ipv4-address-space (version 4, which is in the process of being phased out in favor of version 6). Each domain name is associated with a unique IP address, a numerical name consisiting of four blocks of up to three digits each, e.g. Later, parts of the address space were allocated to various other registries to manage for particular purposes or regions of the world.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/08%3A_Inference/8.02%3A_Principle_of_Maximum_Entropy_-_Simple_Form/8.2.06%3A_SummaryOne of these constraints is that the sum of the probabilities is 1. We then expressed the entropy in terms of the remaining variable. Finally, we found the value of the remaining variable for which th...One of these constraints is that the sum of the probabilities is 1. We then expressed the entropy in terms of the remaining variable. Finally, we found the value of the remaining variable for which the entropy is the largest. The result is a probability distribution that is consistent with the constraints but which has the largest possible uncertainty. This technique requires that the model for the system be known at the outset; the only thing not known is the probability distribution.
- https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Information_and_Entropy_(Penfield)/06%3A_Communications/6.03%3A_Source_Coding_TheoremSpecifically, the Source Coding Theorem states that the average information per symbol is always less than or equal to the average length of a codeword: \[\begin{align*} H \quad &= \quad \displaystyle...Specifically, the Source Coding Theorem states that the average information per symbol is always less than or equal to the average length of a codeword: H=∑ip(Ai)log2(1p(Ai))≤∑ip(Ai)log2(1p′(Ai))=∑ip(Ai)log22Li=∑ip(Ai)Li=L