CN107193785A - A kind of waveform fitting method and device based on cubic spline interpolation - Google Patents
A kind of waveform fitting method and device based on cubic spline interpolation Download PDFInfo
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Abstract
The invention discloses a kind of waveform fitting method based on cubic spline interpolation, device and high-speed interpolation waveform fitting device, this method includes：The point of second predetermined number after the point and tail point of first predetermined number before the tail point and tail point of previous cubic spline interpolation unit in two adjacent cubic spline interpolation units is fitted to multinomial, the First Boundary Condition of tail point is used as using the corresponding first derivative of tail point；The point of second predetermined number after the point and head-end of first predetermined number before the head-end and head-end of latter cubic spline interpolation unit is fitted to multinomial, the second boundary of head-end is used as using the corresponding first derivative of head-end；The boundary condition of phase near point is determined according to equal First Boundary Condition and second boundary, two adjacent cubic spline interpolation units are connected；So as to ensure that the head and the tail of cubic spline interpolation unit are continuous, the operation of FPGA continuous productive processes can be realized, high wave-form refresh rate is reached, can preferably recover waveform.
Description
Technical field
The present invention relates to data processing field, more particularly to a kind of waveform fitting method based on cubic spline interpolation, dress
Put and high-speed interpolation waveform fitting device.
Background technology
Stored digital measuring instrument during the work of base gear, because real-time sampling rate is often inadequate, is only capable of collection letter when fast
Number a small number of sampling points, for reconstruction signal, it is necessary to enter row interpolation.And the process of interpolation is needed by FPGA (Field-
Programmable Gate Array, field programmable gate array) hardware realizes continuous productive process, so as to reach higher waveform
Refresh rate.Conventional interpolation method has closest interpolation, linear interpolation and Sine Interpolation at present.
In the prior art, closest interpolation, linear interpolation and Sine Interpolation can only recover very well to some specific waveforms,
Closest interpolation, linear interpolation have preferable effect to square wave and triangular wave, and the recovery effects to sine wave are poor, and sinusoidal
Interpolation then contrast.And cubic spline interpolation has preferable recovery effects to various types of signal.But realized for FPGA hardware
The high refresh rate of waveform, will consider computational efficiency problem, it is necessary to divide some module arithmetics, but existing each cubic spline interpolation unit
Often there is discontinuous problem in the presence of head and the tail, it is difficult to realize FPGA continuous productive processes.Therefore, how cubic spline interpolation is solved
Head and the tail border discontinuous problem, realizes FPGA continuous productive processes, be now urgent need to resolve the problem of.
The content of the invention
It is an object of the invention to provide a kind of waveform fitting method based on cubic spline interpolation, device and high-speed interpolation ripple
Shape is fitted device, so that the head and the tail border of adjacent cubic spline interpolation unit is continuous, realizes that FPGA continuous productive processes are operated, lifting is used
Experience at family.
In order to solve the above technical problems, the present invention provides a kind of waveform fitting method based on cubic spline interpolation, application
In high-speed interpolation waveform fitting device, including：
By the tail point of previous cubic spline interpolation unit in two adjacent cubic spline interpolation units and the tail end
The point of the second predetermined number is fitted to multinomial after the point and the tail point of preceding first predetermined number of point, with the tail point pair
The first derivative answered as the tail point First Boundary Condition；
By the head-end of latter cubic spline interpolation unit in two adjacent cubic spline interpolation units with it is described
The point of second predetermined number is fitted to multinomial after the point and the head-end of first predetermined number before head-end, with
The corresponding first derivative of the head-end as the head-end second boundary；Wherein, the tail point and the head
End points is the phase near point of two adjacent cubic spline interpolation units；
The boundary condition of the phase near point is determined according to the equal First Boundary Condition and the second boundary,
Two adjacent cubic spline interpolation units of connection.
Optionally, the tail point by previous cubic spline interpolation unit in two adjacent cubic spline interpolation units
Multinomial is fitted to the point of the second predetermined number after the point and the tail point of the first predetermined number before the tail point, specifically
For：
Wherein, a is first predetermined number, and b is second predetermined number.
Optionally, it is described that the phase near point is determined according to the equal First Boundary Condition and the second boundary
Boundary condition, be specially：
The First Boundary Condition is equal to equal to the second boundary is equal
Optionally, this method also includes：
By the head-end of previous cubic spline interpolation unit described in two adjacent cubic spline interpolation units and
The head-end of the latter cubic spline interpolation unit is with the point of first predetermined number before itself and from described after one's death the
The point of two predetermined numbers is fitted to multinomial.
Optionally, first predetermined number and second predetermined number are equal.
In addition, present invention also offers a kind of waveform fitting device based on cubic spline interpolation, applied to high-speed interpolation
Waveform fitting device, including：
First processing module, for by previous cubic spline interpolation unit in two adjacent cubic spline interpolation units
Tail point and the point of the second predetermined number after the point and the tail point of the first predetermined number before the tail point are fitted to multinomial
Formula, the First Boundary Condition of the tail point is used as using the corresponding first derivative of the tail point；
Second processing module, for by latter cubic spline interpolation list in two adjacent cubic spline interpolation units
The head-end of member and second predetermined number after the point and the head-end of first predetermined number before the head-end
Point is fitted to multinomial, and the second boundary of the head-end is used as using the corresponding first derivative of the head-end；Wherein, institute
State the phase near point of tail point and the head-end for two adjacent cubic spline interpolation units；
Link block is described close for being determined according to the equal First Boundary Condition and the second boundary
The boundary condition of point, connects two adjacent cubic spline interpolation units.
Optionally, the multinomial that the first processing module is fitted to, be specially：
Wherein, a is first predetermined number, and b is second predetermined number.
Optionally, the device also includes：
3rd processing module, for previous cubic spline described in two adjacent cubic spline interpolation units to be inserted
The head-end of value cell and the head-end of the latter cubic spline interpolation unit with first predetermined number before itself
Put and be fitted to multinomial from the point of second predetermined number after one's death.
Present invention also offers a kind of high-speed interpolation waveform fitting device, including：
Processor, for by the tail point of previous cubic spline interpolation unit in two adjacent cubic spline interpolation units
Multinomial is fitted to the point of the second predetermined number after the point and the tail point of the first predetermined number before the tail point, with institute
The corresponding first derivative of tail point is stated as the First Boundary Condition of the tail point；Two adjacent cubic splines are inserted
The head-end of latter cubic spline interpolation unit and the point of first predetermined number before the head-end and described in value cell
The point of second predetermined number is fitted to multinomial after head-end, and the head is used as using the corresponding first derivative of the head-end
The second boundary of end points；Wherein, the tail point and the head-end are two adjacent cubic spline interpolation lists
The phase near point of member；The perimeter strip of the phase near point is determined according to the equal First Boundary Condition and the second boundary
Part, connects two adjacent cubic spline interpolation units；
Follower, for the waveform of two adjacent cubic spline interpolation units to be exported.
A kind of waveform fitting method based on cubic spline interpolation provided by the present invention, intends applied to high-speed interpolation waveform
Clutch, including：By the tail point of previous cubic spline interpolation unit in two adjacent cubic spline interpolation units and the tail
The point of the second predetermined number is fitted to multinomial after the point and the tail point of the first predetermined number before end points, with the tail point
Corresponding first derivative as the tail point First Boundary Condition；By in two adjacent cubic spline interpolation units
Before the head-end and the head-end of latter cubic spline interpolation unit after the point and the head-end of first predetermined number
The point of second predetermined number is fitted to multinomial, and using the corresponding first derivative of the head-end as the head-end
Two boundary conditions；Wherein, the tail point and the head-end are the close of two adjacent cubic spline interpolation units
Point；The boundary condition of the phase near point is determined according to the equal First Boundary Condition and the second boundary, is connected
Two adjacent cubic spline interpolation units；
It can be seen that, the head and the tail border of the invention by using the adjacent cubic spline interpolation unit of fitting of a polynomial, with head and the tail point
Corresponding first derivative makes adjacent cubic spline interpolation unit connect as the cubic spline interpolation boundary condition, it is ensured that
The head and the tail of cubic spline interpolation unit are continuous, with smooth transition naturally cubic spline interpolation unit can be enable to realize FPGA
The operation of continuous productive process, has reached high wave-form refresh rate, and can preferably recover waveform, improves Consumer's Experience.In addition, this
Invention additionally provides a kind of waveform fitting device based on cubic spline interpolation and high-speed interpolation waveform fitting device, equally with upper
State beneficial effect.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
There is the accompanying drawing used required in technology description to be briefly described, it should be apparent that, drawings in the following description are only this
The embodiment of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can also basis
The accompanying drawing of offer obtains other accompanying drawings.
A kind of flow chart for waveform fitting method based on cubic spline interpolation that Fig. 1 is provided by the embodiment of the present invention；
The flow for another waveform fitting method based on cubic spline interpolation that Fig. 2 is provided by the embodiment of the present invention
Figure；
Three samples of another waveform fitting method based on cubic spline interpolation that Fig. 3 is provided by the embodiment of the present invention
The exemplary plot of bar interpolating unit；
A kind of structure chart for waveform fitting device based on cubic spline interpolation that Fig. 4 is provided by the embodiment of the present invention；
A kind of structure chart for high-speed interpolation waveform fitting device that Fig. 5 is provided by the embodiment of the present invention.
Embodiment
To make the purpose, technical scheme and advantage of the embodiment of the present invention clearer, below in conjunction with the embodiment of the present invention
In accompanying drawing, the technical scheme in the embodiment of the present invention is clearly and completely described, it is clear that described embodiment is
A part of embodiment of the present invention, rather than whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art
The every other embodiment obtained under the premise of creative work is not made, belongs to the scope of protection of the invention.
It refer to Fig. 1, a kind of waveform fitting method based on cubic spline interpolation that Fig. 1 is provided by the embodiment of the present invention
Flow chart.This method is applied to high-speed interpolation waveform fitting device, can include：
Step 101：By the tail point of previous cubic spline interpolation unit in two adjacent cubic spline interpolation units with
The point of the second predetermined number is fitted to multinomial after the point and the tail point of the first predetermined number before the tail point, with described
The corresponding first derivative of tail point as the tail point First Boundary Condition.
Wherein, cubic spline interpolation principle can be：
, can be as shown in formula (1) for several discrete points：
SPL is segmentation composition, there is n+1 point, and common n interval, is made up of n Si, can be as shown in formula (2)：
Every section of curve is made up of cubic polynomial respectively, can be as shown in formula (3)：
Si(x)=ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3, i=0,1 ... n-1 (3)
The resolution principle of cubic spline interpolation can be：SPL need to meet following condition：
Real discrete point, can be as shown in formula (4) at the head and the tail of every section of curve：
Si(xi)=yi (4)
0 rank, 1 rank and 2 ranks are continuous from beginning to end for every section of curve, can be as shown in formula (5)：
Head and the tail end points is characteristic boundaries, there is free boundary, fixed boundary, three kinds of not a node border, due to free boundary and
Not a node border is it cannot be guaranteed that the adjacent smooth transition naturally of cubic spline interpolation unit phase near point.And fixed boundary is passed through necessarily
Operation, can enable the smooth transition naturally of head and the tail end points of adjacent cubic spline interpolation unit, therefore can set head and the tail
The derivative of two-end-point is specified.
Order
It can be obtained by formula (1) and formula (7)：
By xiAnd yiData can be in the hope of seeking m by formula (8), then substitute into formula (5), can be in the hope of ai、bi、ciAnd di.By xi<
x<xi+1Y=S can be obtained by corresponding to corresponding cubic polynomiali(x)。
It should be noted that can be solved for each cubic spline interpolation unit by above-mentioned resolution principle, with
The corresponding first derivative of tail point of previous cubic spline interpolation unit is used as tail in two adjacent cubic spline interpolation units
The First Boundary Condition of end points, can be the order as shown in formula (6)In formula, B1For above-mentioned first border
Condition.
For by the tail point and tail end of previous cubic spline interpolation unit in two adjacent cubic spline interpolation units
The point of the second predetermined number is fitted to multinomial after the point and tail point of preceding first predetermined number of point, can be specially：
In formula, a is above-mentioned first predetermined number, and b is above-mentioned second predetermined number.
Can be in the hope of：
It is understood that two cubic spline interpolation units adjacent in this step can be each phase in FPGA hardware
Adjacent cubic spline interpolation unit, the adjacent cubic spline interpolation unit of each two can carry out this step.
For the specific setting of above-mentioned first predetermined number and the second predetermined number, that is, chosen during polynomial fitting
Before tail point closest to the tail point point number and tail point after closest to the tail point point number, Ke Yiyou
Designer or user are voluntarily set according to practical scene and user's request, and the present embodiment is unrestricted to this.It is preferred that,
Calculate for convenience, the first predetermined number and the second predetermined number can be set to equal numerical value.
Step 102：By the head end of latter cubic spline interpolation unit in two adjacent cubic spline interpolation units
Point and the point of second predetermined number after the point and the head-end of first predetermined number before the head-end are fitted to
Multinomial, the second boundary of the head-end is used as using the corresponding first derivative of the head-end；Wherein, the tail point
With the phase near point that the head-end is two adjacent cubic spline interpolation units.
It is understood that by the resolution principle of above-mentioned cubic spline interpolation, with two adjacent cubic spline interpolations
The corresponding first derivative of head-end of latter cubic spline interpolation unit, can be with as the second boundary of head-end in unit
As shown in formula (6), to makeIn formula, A2For second boundary.
It should be noted that by the head end of latter cubic spline interpolation unit in two adjacent cubic spline interpolation units
Point and the point of the second predetermined number after the point and head-end of the first predetermined number before head-end are fitted to multinomial, can pass through step
Rapid 101 identical mode is generated such as the multinomial of formula (9), may finally be tried to achieve：
Step 103：The phase near point is determined according to the equal First Boundary Condition and the second boundary
Boundary condition, connects two adjacent cubic spline interpolation units.
Wherein, it is equal with second boundary according to First Boundary Condition, can be in the hope of：The phase near point of two adjacent cubic spline interpolation units is determined
Boundary condition, that is, it may insure the sample of the previous cubic spline interpolation unit in two adjacent cubic spline interpolation units
The SPL of bar curve and latter cubic spline interpolation unit can be smooth naturally excessive in phase near point.
It is understood that for FPGA hardware, as long as before ensuring in two neighboring cubic spline interpolation unit
The head-end of the tail point of one cubic spline interpolation unit and latter cubic spline interpolation unit and respective preceding first predetermined number
Point and each after the point of the second predetermined number be fitted to multinomial, that is, adjacent cubic spline interpolation unit phase near point with
If if preceding do and rear do is fitted to multinomial, just can reach the purpose of the present embodiment, all adjacent two three can be made
Secondary spline interpolation unit is respectively provided with the predetermined number of identical first and the second predetermined number, is inserted if any 3 adjacent cubic splines
Value cell, first adjacent cubic spline interpolation unit and the phase near point of second cubic spline interpolation unit and preceding 2 points
Multinomial is fitted to rear 2 points, second adjacent cubic spline interpolation unit and the 3rd cubic spline interpolation unit
Phase near point is fitted to multinomial with preceding 2 points and rear 2 points；Two all adjacent cubic spline interpolation units can also be made equal
Different the first predetermined numbers and the second predetermined number are set, if any 3 adjacent cubic spline interpolation units, adjacent first
The phase near point of individual cubic spline interpolation unit and second cubic spline interpolation unit is fitted to many with preceding 2 points and rear 2 points
Formula, the phase near point and preceding 1 point of adjacent second cubic spline interpolation unit and the 3rd cubic spline interpolation unit and
1 point is fitted to multinomial afterwards；It is pre- that two cubic spline interpolation units that part can also be made adjacent are respectively provided with different first
Determine number and the second predetermined number.The present embodiment is unrestricted to this.
In the present embodiment, the embodiment of the present invention by using the adjacent cubic spline interpolation unit of fitting of a polynomial head and the tail side
Boundary, to put corresponding first derivative from beginning to end as the cubic spline interpolation boundary condition, makes adjacent cubic spline interpolation unit
Connection, it is ensured that the head and the tail of cubic spline interpolation unit are continuous, can make cubic spline interpolation unit with smooth transition naturally
The operation of FPGA continuous productive processes can be realized, high wave-form refresh rate has been reached, and can preferably recover waveform, user is improved
Experience.
It refer to Fig. 2 and Fig. 3, another waveform based on cubic spline interpolation that Fig. 2 is provided by the embodiment of the present invention
The flow chart of approximating method；Another waveform fitting side based on cubic spline interpolation that Fig. 3 is provided by the embodiment of the present invention
The exemplary plot of the cubic spline interpolation unit of method.This method is applied to high-speed interpolation waveform fitting device, can include：
Step 201：By the head-end and tail point of each cubic spline interpolation unit in adjacent cubic spline interpolation unit
Multinomial is fitted to the point of respective front and rear each 3rd predetermined number.
Wherein, this step can be to make the head-end and tail point of cubic spline interpolation unit all adjacent in FPGA equal
Multinomial is fitted to the point of respective front and rear each 3rd predetermined number, can conveniently calculate and ensure to be fitted the standard system of waveform
One.
Exemplified by four sample point datas in Fig. 3, i.e. the above-mentioned cubic spline interpolation unit of two neighboring FPGA module
Phase near point be the 6th point, take can be obtained with the 6th knock type (9) polynomial fitting at first 2 points and latter 2 points：
Step 202：The border of cubic spline interpolation unit is used as using each self-corresponding first derivative of head-end and tail point
Condition.
It is understood that this step can be such as calculating by way of Chinese style (6) above.Such as FPGA interpolation lists in Fig. 3
Member 1, which can obtain tail end boundary condition B1, FPGA interpolating unit 2, can obtain head end boundary condition A2.
Step 203：According to the tail point of the previous cubic spline interpolation unit of two adjacent cubic spline interpolation units
Boundary condition it is equal with the boundary condition of the head-end of latter cubic spline interpolation unit, connect it is adjacent two described three times
Spline interpolation unit.
Boundary condition such as the 6th point in Fig. 3 can pass throughIt is determined that after, FPGA
The batten on the 6 to 9th point that interpolating unit 1 generates SPL and FPGA interpolating units 2 generation on the 3 to 6th point is bent
Line, being capable of smooth natural transition on 6 borders.
In the present embodiment, the embodiment of the present invention is by by each cubic spline interpolation list in adjacent cubic spline interpolation unit
The point of the head-end and tail point of member and each front and rear each 3rd predetermined number is fitted to multinomial, can more facilitate calculating should
Multinomial simultaneously ensures that the standard for being fitted waveform is more unified.
It refer to Fig. 4, a kind of waveform fitting device based on cubic spline interpolation that Fig. 4 is provided by the embodiment of the present invention
Structure chart.The device is applied to high-speed interpolation waveform fitting device, can include：
First processing module 100, for by previous cubic spline interpolation list in two adjacent cubic spline interpolation units
The tail point and the point of the second predetermined number after the point and the tail point of the first predetermined number before the tail point of member are fitted to
Multinomial, the First Boundary Condition of the tail point is used as using the corresponding first derivative of the tail point.
Second processing module 200, for latter cubic spline in two adjacent cubic spline interpolation units to be inserted
The head-end of value cell makes a reservation for individual with after the point and the head-end of first predetermined number before the head-end described second
Several points are fitted to multinomial, and the second boundary of the head-end is used as using the corresponding first derivative of the head-end；Its
In, the tail point and the phase near point that the head-end is two adjacent cubic spline interpolation units.
Link block 300, described in being determined according to the equal First Boundary Condition and the second boundary
The boundary condition of phase near point, connects two adjacent cubic spline interpolation units.
Optionally, the multinomial that the first processing module 100 is fitted to, be specially：
Wherein, a is first predetermined number, and b is second predetermined number.
Optionally, the device can also include：
3rd processing module, for previous cubic spline described in two adjacent cubic spline interpolation units to be inserted
The head-end of value cell and the head-end of the latter cubic spline interpolation unit with first predetermined number before itself
Put and be fitted to multinomial from the point of second predetermined number after one's death.
In the present embodiment, the embodiment of the present invention by using the adjacent cubic spline interpolation unit of fitting of a polynomial head and the tail
Border, to put corresponding first derivative from beginning to end as the cubic spline interpolation boundary condition, makes adjacent cubic spline interpolation list
Member connection, it is ensured that the head and the tail of cubic spline interpolation unit are continuous, can make cubic spline interpolation unit with smooth transition naturally
The operation of FPGA continuous productive processes can be realized, high wave-form refresh rate has been reached, and can preferably recover waveform, user is improved
Experience.
It refer to Fig. 5, a kind of structure chart for high-speed interpolation waveform fitting device that Fig. 5 is provided by the embodiment of the present invention.Should
High-speed interpolation waveform fitting device can include：
Processor 10, for by the tail end of previous cubic spline interpolation unit in two adjacent cubic spline interpolation units
Point and the point of the second predetermined number after the point and the tail point of the first predetermined number before the tail point are fitted to multinomial, with
The corresponding first derivative of the tail point as the tail point First Boundary Condition；By two adjacent cubic splines
Point and institute of the head-end of latter cubic spline interpolation unit with first predetermined number before the head-end in interpolating unit
The point for stating second predetermined number after head-end is fitted to multinomial, using the corresponding first derivative of the head-end as described
The second boundary of head-end；Wherein, the tail point and the head-end are two adjacent cubic spline interpolations
The phase near point of unit；The border of the phase near point is determined according to the equal First Boundary Condition and the second boundary
Condition, connects two adjacent cubic spline interpolation units.
Follower 20, for the waveform of two adjacent cubic spline interpolation units to be exported.
In the present embodiment, the embodiment of the present invention by using the adjacent cubic spline interpolation unit of fitting of a polynomial head and the tail side
Boundary, to put corresponding first derivative from beginning to end as the cubic spline interpolation boundary condition, makes adjacent cubic spline interpolation unit
Connection, it is ensured that the head and the tail of cubic spline interpolation unit are continuous, can enable cubic spline interpolation unit with smooth transition naturally
The operation of FPGA continuous productive processes is enough realized, high wave-form refresh rate has been reached, and can preferably recover waveform, user's body is improved
Test.
The embodiment of each in specification is described by the way of progressive, and what each embodiment was stressed is and other realities
Apply the difference of example, between each embodiment identical similar portion mutually referring to.For device disclosed in embodiment and
For high-speed interpolation waveform fitting device, because it is corresponded to the method disclosed in Example, so description is fairly simple, it is related
Part is referring to method part illustration.
Professional further appreciates that, with reference to the unit of each example of the embodiments described herein description
And algorithm steps, can be realized with electronic hardware, computer software or the combination of the two, in order to clearly demonstrate hardware and
The interchangeability of software, generally describes the composition and step of each example according to function in the above description.These
Function is performed with hardware or software mode actually, depending on the application-specific and design constraint of technical scheme.Specialty
Technical staff can realize described function to each specific application using distinct methods, but this realization should not
Think beyond the scope of this invention.
Directly it can be held with reference to the step of the method or algorithm that the embodiments described herein is described with hardware, processor
Capable software module, or the two combination are implemented.Software module can be placed in random access memory (RAM), internal memory, read-only deposit
Reservoir (ROM), electrically programmable ROM, electrically erasable ROM, register, hard disk, moveable magnetic disc, CD-ROM or technology
In any other form of storage medium well known in field.
Above to the waveform fitting method provided by the present invention based on cubic spline interpolation, device and high-speed interpolation waveform
Fitting device is described in detail.Specific case used herein is set forth to the principle and embodiment of the present invention,
The explanation of above example is only intended to the method and its core concept for helping to understand the present invention.It should be pointed out that for this technology
For the those of ordinary skill in field, under the premise without departing from the principles of the invention, some improve can also be carried out to the present invention
And modification, these are improved and modification is also fallen into the protection domain of the claims in the present invention.
Claims (9)
1. a kind of waveform fitting method based on cubic spline interpolation, applied to high-speed interpolation waveform fitting device, it is characterised in that
Including：
Before the tail point of previous cubic spline interpolation unit in two adjacent cubic spline interpolation units and the tail point
The point of the second predetermined number is fitted to multinomial after the point and the tail point of first predetermined number, corresponding with the tail point
First derivative as the tail point First Boundary Condition；
By the head-end of latter cubic spline interpolation unit in two adjacent cubic spline interpolation units and the head end
The point of second predetermined number is fitted to multinomial after the point and the head-end of first predetermined number before point, with described
The corresponding first derivative of head-end as the head-end second boundary；Wherein, the tail point and the head-end
For the phase near point of two adjacent cubic spline interpolation units；
The boundary condition of the phase near point is determined according to the equal First Boundary Condition and the second boundary, is connected
Two adjacent cubic spline interpolation units.
2. the waveform fitting method according to claim 1 based on cubic spline interpolation, it is characterised in that it is described will be adjacent
Two cubic spline interpolation units in previous cubic spline interpolation unit tail point and the tail point before first predetermined
The point of the second predetermined number is fitted to multinomial after several points and the tail point, is specially：
Wherein, a is first predetermined number, and b is second predetermined number.
3. the waveform fitting method according to claim 2 based on cubic spline interpolation, it is characterised in that described according to phase
Deng the First Boundary Condition and the second boundary determine the boundary condition of the phase near point, be specially：
The First Boundary Condition is equal to equal to the second boundary is equal
4. the waveform fitting method based on cubic spline interpolation according to any one of claims 1 to 3, it is characterised in that
Also include：
By the head-end of previous cubic spline interpolation unit described in two adjacent cubic spline interpolation units and described
The head-end of latter cubic spline interpolation unit is with the point of first predetermined number before itself and from described second pre- after one's death
The point for determining number is fitted to multinomial.
5. the waveform fitting method according to claim 4 based on cubic spline interpolation, it is characterised in that described first is pre-
Determine number and second predetermined number is equal.
6. a kind of waveform fitting device based on cubic spline interpolation, applied to high-speed interpolation waveform fitting device, it is characterised in that
Including：
First processing module, for by the tail end of previous cubic spline interpolation unit in two adjacent cubic spline interpolation units
Point and the point of the second predetermined number after the point and the tail point of the first predetermined number before the tail point are fitted to multinomial, with
The corresponding first derivative of the tail point as the tail point First Boundary Condition；
Second processing module, for by latter cubic spline interpolation unit in two adjacent cubic spline interpolation units
The point of head-end and second predetermined number after the point and the head-end of first predetermined number before the head-end is intended
Multinomial is synthesized, the second boundary of the head-end is used as using the corresponding first derivative of the head-end；Wherein, the tail
End points and the phase near point that the head-end is two adjacent cubic spline interpolation units；
Link block, for determining the phase near point according to the equal First Boundary Condition and the second boundary
Boundary condition, connects two adjacent cubic spline interpolation units.
7. the waveform fitting device according to claim 6 based on cubic spline interpolation, it is characterised in that at described first
Manage module fits into multinomial, be specially：
Wherein, a is first predetermined number, and b is second predetermined number.
8. the waveform fitting device based on cubic spline interpolation according to claim 6 or 7, it is characterised in that also include：
3rd processing module, for by previous cubic spline interpolation list described in two adjacent cubic spline interpolation units
Member head-end and the latter cubic spline interpolation unit head-end with itself before first predetermined number point and
Multinomial is fitted to from the point of second predetermined number after one's death.
9. a kind of high-speed interpolation waveform fitting device, it is characterised in that including：
Processor, for by the tail point of previous cubic spline interpolation unit and institute in two adjacent cubic spline interpolation units
The point for stating the second predetermined number after the point and the tail point of the first predetermined number before tail point is fitted to multinomial, with the tail
The corresponding first derivative of end points as the tail point First Boundary Condition；By two adjacent cubic spline interpolation lists
The point and the head end of the head-end of latter cubic spline interpolation unit and first predetermined number before the head-end in member
The point of second predetermined number is fitted to multinomial after point, and the head-end is used as using the corresponding first derivative of the head-end
Second boundary；Wherein, the tail point and the head-end are two adjacent cubic spline interpolation units
Phase near point；The boundary condition of the phase near point is determined according to the equal First Boundary Condition and the second boundary,
Two adjacent cubic spline interpolation units of connection；
Follower, for the waveform of two adjacent cubic spline interpolation units to be exported.
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