Normalization is a way to simplify calculationdimensionThe expression of is transformed intoDimensionlessExpression for, becomingscalar。 This method is often used in many calculations.
Normalization is a dimensionless processing method, which makesabsolute valueBecome somethingRelative valueRelationship.Simplify calculation and reducemeasurementEffective methods.[1]For example, each frequency value in the filtercut-off frequencyAfter normalization, the frequency is the relative value of the cut-off frequency, and there is no dimension.Impedance toInternal resistance of power supplyAfter normalization, each impedance becomes a relativeImpedance value，“Ohms”This dimension is gone.After all kinds of operations are completed, everything in the anti normalization is restored.Nyquist frequency is often used in signal processing toolbox, which is defined assampling frequency The nyquist frequency is used for normalization in filter order selection and cut-off frequency design.For example, for a system with a sampling frequency of 500 hz, the normalized frequency of 400 hz is 400/500=0.8, and the normalized frequency range is between [0,1].If the normalized frequency is converted to angular frequency, the normalized frequency is multiplied by 2 * pi; if the normalized frequency is converted to hz, the normalized frequency is multiplied bysampling frequency Half of.
In general, the wave function is aComplex function。However, the probability density is aReal function, the sum of integrals in space is 1, which is calledprobability density function。So the probability of finding particles in the region is 1.
Since particles exist in space, the probability of finding particles in space is 1, so integrating in the whole space will result in 1.
If, from the analysisSchrodinger equationIf the probability of the wave function obtained is limited but not equal to 1, then the wave function can be multiplied by a constant to make the probability equal to 1.Or if there is an arbitrary constant in the wave function, you can set the value of this arbitrary constant so that the probability is equal to 1.[2]
application
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1. The complex impedance can be normalized as: Z=R+j ω L=R (1+j ω L/R) (the complex part becomes a pure number without any dimension).
2. Many operations in microwave, such as circuit analysis, signal system and electromagnetic wave transmission, can be processed in this way, which not only ensures the convenience of operations, but also highlights the essence of physical quantities.
3. In statistics, the specific role of normalization is to summarize unified samplesstatistical distribution Sex.Normalization between 0-1 is statisticalprobability distribution, normalization between - 1 -+1 is a statistical coordinate distribution.That is, the integral of the function in (- ∞,+∞) is 1.
A wave function expressing the quantum state of a particle must satisfyparticleSchrodinger equation.Since and can both satisfy the same Schrodinger equation, they must all express the samequantum state。If we do not use the normalized wave function, we can only knowprobabilityRelative size of;Otherwise, the absolute probability can be known by using the normalized wave function.This will provide a lot of convenience for the analysis of quantum problems.
Normalization in image processing
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reason
In the image, if you compare two pictures (style of two pictures: number of channels,data formatSame, size: resolution can be different)
1. When it is necessary to judge whether two pictures are the same when comparing their sizes;
2. When it is necessary to determine the position of a smaller picture in the larger picture.
At this time, we can useEuclidean distance As the judgment function, as follows:
(The foundation is the distance between two points in 2D:
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If D=0, the pictures are equal;Or a small picture has been found in the big picture.But the value range of the above D value is too wide, even reaching (0, positive infinity), which will exceedcomputerCalculation range of.Therefore, normalization is used.
Processing steps
one
Expand the similarity function to get:
2. It can be seen that only the second item is meaningful, because the values of the first and third items are fixed after the template is selected.For the Euclidean distance similarity function, the larger the value, the more dissimilar it is. That is, the smaller the value of the second term, the more dissimilar it is.
Normalize the second item:
Then when R (i, j) is 1, it means that the template is completely equal to the subgraph.
