Dry vibration for two month, after the sugnak analysis, leaf vary a understanding again on the Fu that use in the processing procedure to digital signal, as to algorithmic summary of leaf under Fu.

It is a kind of very important algorithm of domain of digital signal processing that Fu LiYe varies. But what meanings does this algorithm have on earth?

Want, know Fu set up leaf, vary algorithmic meaning, should first understand Fu set up the intersection of leaf and meaning of principle. It shows that Fu sets up leaf principle: Any continuously metric sequence or signal, can all be expressed as the superposing limitlessly of the sine wave signal of different frequency. Until Fu that principle this creat set up transformation algorithm of the leaf and utilize the original signal that direct measurement gets, calculate the frequency, amplitude and phase place of different sine wave signals in this signal by way of totalizing.

And Fu set up leaf correspondent transformation algorithm Fu set up transformation algorithm of the leaf instead. This inverse transformation is a kind of totalizing dealt with, can convert the sine wave signal changed alone to a signal in this way too from essence.

So, we can say, Fu LiYe varies and converts the signal of time domain different to deal with originally to the easy analytic signal of frequency domain the frequency spectrum of the signal ,Can deal with, process the signal of these frequency domains with some tools. Can also utilize Fu to set up inverse transformation of leaf and convert the signal of these frequency domains to the signal of time domain finally.

According to eyes of modern mathematics, leaf it varies to be one special integral transform in the Fu. It can represent a certain function of meeting certain condition into a linear combination or total mark of the basis function of the sine. In the field of different research, leaf vary, have many kinds of different variant forms in the Fu, if the leaf is varied and the leaf is varied on dispersed Fu in the Fu continuously.

Fu sets up the leaf to vary and belong to and mediate the analytic content. ” Analyze ” Two words, can interpret as deep research. Look from literal about, ” Analyze ” Two words, reality is ” Make a careful and detailed analysis ” That is all. It passes the function correctly ” Make a careful and detailed analysis ” To reach the understanding and research thoroughly to the complicatedness function. In view of philosophy, ” Analyze the doctrine ” Sum ” Reduce the doctrine ” ,Just should be through achieving the goal of promoting to the appropriate analysis within the things to its essential understanding. For example modern atomic theory attempts to analyze the origins of all materials in the world as the atom, and the atom is only several hundred kinds, relative material world is abundant limitlessly, the analysis and classify, offer very fine means for know various property of thing undoubtedly.

In the field of mathematics, it is so too, though initial Fu sets up leaf analysis is as the analytic analytic tool of the hot course, but its way of thinking still has typical reductionism and analyzes the characteristic of the doctrine. ” Arbitrary” Function resolving through being certain,last the forms combineds linears of sine function, and the sine function is abundant research but relatively simple functions physically, this idea is very similar with the atomic theory idea on chemistry! The wonderful one is, modern mathematics finds it has spanking properties that Fu LiYe varies, make its working well and useful so, let people have to sigh over the mystery of the divine force that created the universe with feeling:

1. It is a linear operator that Fu LiYe varies, if entrust the appropriate norm, it or unitary operator;

2. Inverse transformation that LiYe Fu vary apt to find, form and vary very much similar;

3. The basis function of the sine is the proper function of differentiating, thus make the solving of the linear differential equation can be turned into the solving of the algebraic equation of constant coefficient. In the invariable physical system in the linearity, the frequency is an invariable property, thus the system can obtain to the response of complicated encouragement by making its response to different frequency sine signals up;

4. The famous convolution theorem is pointed out: Fu LiYe can melt to vary complicated convolution operation makes operation for simple product, thus has offered a kind of simple means to calculate the convolution;

5. Dispersed the intersection of a formal one and Fu set up leaf vary, can utilize the intersection of digital calculator and calculating fast .

Just because the above-mentioned good properties, leaf vary in physics, number theory, combinatorial mathematics, SIGPROC signal processing, probability, statistics, cryptology, acoustics, optics field having extensive application in the Fu.