![]() However they all take the form of a ‘mini wave’, fading to zero quickly. Rather than being a wave that goes on forever, like sin() or cos(), wavelets are a short ‘burst’ of waves that quickly die away, like the picture below:īecause there are very few rules about what defines a wavelet, there are hundreds of different types. In doing this they are opening up a new way to make sense of signals, which is the bread and butter of Information Engineering.Īt their most basic, wavelets are quite literally ‘mini waves’. ![]() What’s interesting about wavelets is that they are starting to undermine a staple mathematical technique in Engineering: the Fourier Transform. S2CID 18118758.Wavelets have recently migrated from Maths to Engineering, with Information Engineers starting to explore the potential of this field in signal processing, data compression and noise reduction. "Minimum uncertainty for antisymmetric wave functions". "An optimal entropic uncertainty relation in a two-dimensional Hilbert space". "Entropic uncertainty relations and locking: Tight bounds for mutually unbiased bases". "Generalized entropic uncertainty relations" (PDF). Physica A: Statistical Mechanics and Its Applications. "On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles". "One-parameter class of uncertainty relations based on entropy power". Smith, Extensions of the Heisenberg–Weil inequality. An inequality in the theory of Fourier integrals. "Formulation of the uncertainty relations in terms of the Rényi entropies". "An Entropy-based Uncertainty Principle for a Locally Compact Abelian Group" (PDF). ^ Ozaydin, Murad Przebinda, Tomasz (2004).The Many-Worlds Interpretation of Quantum Mechanics: the theory of the universal wave function. Any probability density function has a radially decreasing equimeasurable "rearrangement" whose variance is less (up to translation) than any other rearrangement of the function and there exist rearrangements of arbitrarily high variance, (all having the same entropy.) The same is not true of variance, however. Any two equimeasurable probability density functions have the same Shannon entropy, and in fact the same Rényi entropy, of any order. G ( y ) ≈ ∫ − ∞ ∞ exp ( − 2 π i x y ) f ( x ) d x, f ( x ) ≈ ∫ − ∞ ∞ exp ( 2 π i x y ) g ( y ) d y, In 1957, Hirschman considered a function f and its Fourier transform g such that This is stronger than the usual statement of the uncertainty principle in terms of the product of standard deviations. It turns out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |