How can quantum gravity help explain the origin of the universe?.. This is the question on a gable wall on the Ormeau Embankment in Belfast that the Political Commentator Malachi O Doherty asks himself every day.. The answer is Convovulation, my own theory of the nature of reality beyond the quantum, and of course, quantum gravity..This is an extension of the Convolution theorem which has had many practical applications today. I hope that this will give some help in explaining the Genesis Enigma in our own time of how God created the universe. We already think we know When? and Why? but no-one seems to know How?. In essence I believe that when He created Light He created it, not as Wave or as Particle but as Convovulation.
In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated. Convolution is similar to cross-correlation. It has applications that include probability, statistics, computer vision, image and signal processing, electrical engineering and differential equations.
The convolution can be defined for functions on groups other than Euclidian space. For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. And discrete convolution can be defined for functions on the set of integers. Generalizations of convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing. Computing the inverse of the convolution operation is known as deconvolution.
Convolution and related operations are found in many applications in science, engineering and mathematics.
- In image processing… In digital image processing convolutional filtering plays an important role in many important algorithms in edge detection and related processes.
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- In optics, an out-of-focus photograph is a convolution of the sharp image with a lens function. The photographic term for this is bokeh.
- In image processing applications such as adding blurring.
- In digital data processing
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- In analytical chemistry, Savitzsky-Golay smoothing filters are used for the analysis of spectroscopic data. They can improve signal-to-noise ratio with minimal distortion of the spectra.
- In statistics, a weighted moving average is a convolution.
- In acoustics, reverberation is the convolution of the original sound with echos from objects surrounding the sound source.
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- In digital signal processing, convolution is used to map the impulse response of a real room on a digital audio signal.
- In electronic music convolution is the imposition of a spectral or rhythmic structure on a sound. Often this envelope or structure is taken from another sound. The convolution of two signals is the filtering of one through the other.
- In electrical engineering, the convolution of one function (the input-signal) with a second function (the impulse-response) gives the output of a linear time-invariant system (LTI). At any given moment, the output is an accumulated effect of all the prior values of the input function, with the most recent values typically having the most influence (expressed as a multiplicative factor). The impulse response function provides that factor as a function of the elapsed time since each input value occurred.
- In physics wherever there is a linear system with a “superposition principle”, a convolution operation makes an appearance. For instance, in spectroscopy line broadening due to the Doppler effect on its own gives a Gaussian spectral line shape and collision broadening alone gives a Lorentzian line shape. When both effects are operative, the line shape is a convolution of Gaussian and Lorentzian, a Voigt function.
- In Time-resolved fluorescence spectroscopy, the excitation signal can be treated as a chain of delta pulses, and the measured fluorescence is a sum of exponential decays from each delta pulse.
- In computational fluid dynamics, the large eddy stimulation (LES) turbulence model uses the convolution operation to lower the range of length scales necessary in computation thereby reducing computational cost.
- In probability theory, the probability distribution of the sum of two independent random variables is the convolution of their individual distributions.
- In kernel density estimation, a distribution is estimated from sample points by convolution with a kernel, such as an isotropic Gaussian. (Diggle 1995).
- In radiotherapy treatment planning systems, most part of all modern codes of calculation applies a convolution-superposition algorithm..