CN108334685A - A kind of frequency spectrum refinement method of engineering truck vibration signal - Google Patents

A kind of frequency spectrum refinement method of engineering truck vibration signal Download PDF

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CN108334685A
CN108334685A CN201810072733.4A CN201810072733A CN108334685A CN 108334685 A CN108334685 A CN 108334685A CN 201810072733 A CN201810072733 A CN 201810072733A CN 108334685 A CN108334685 A CN 108334685A
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frequency
frequency spectrum
data
refinement
spectrum refinement
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CN108334685B (en
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董建超
王守银
李建冬
崔广志
高辉
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Beijing Machinery Equipment Research Institute
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Beijing Machinery Equipment Research Institute
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01HMEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M17/00Testing of vehicles
    • G01M17/007Wheeled or endless-tracked vehicles
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02Preprocessing

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  • Computer Hardware Design (AREA)
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  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)

Abstract

The present invention relates to a kind of frequency spectrum refinement methods of engineering truck vibration signal, include the following steps:Gathering project methods of vehicle vibration signal is filtered by the amplification of engineering truck vibration signal, by amplified vibration signal, the data integralization that filtering obtains is handled, the data frequency after calculating integralization obtains effective peak frequency, the difference on the frequency score value of calculating effective peak judges whether to need frequency spectrum refinement processing, signal to be treated is carried out to micronization processes, is reprocessed until all the sensors all completion processing.Using the above method, the bad defect of engineering truck vibration control effect can be solved, the vibration of engineering truck is reduced.

Description

A kind of frequency spectrum refinement method of engineering truck vibration signal
Technical field
The present invention relates to technical field of data processing more particularly to a kind of frequency spectrum refinement sides of engineering truck vibration signal Method.
Background technology
When engineering truck is travelled and is worked, when being run by the arbitrary excitation and mobile unit of road roughness influence Excitation, these excitations cause vehicle to vibrate by tire and suspension transmission, and excessive vibration can be to vehicle structure and staff Safety cause damages, need effectively to be controlled.The committed step of vibration control be exactly to vehicle vibration response signal into Line frequency spectrum analysis extracts frequency and phase information, to control or the passive control measure of targetedly taking the initiative, drop The vibration of low engineering truck.
Traditional spectrum signature extraction and analysis generally uses fast Fourier to change (FFT), obtains entire band limits Panoramic spectrum, however the operating mode of engineering truck is often in the changeable operating mode of unstable state, vibration response signal has frequency spectrum intensive Feature, this just need to intensive narrow band spectrum section carry out screening and micro-scale analysis.Using artificial processing method, exist The uncertain factors such as human error, this can lead to the omission of spectrum peak, so that the vibration control effect of engineering truck is big It gives a discount.
Invention content
In view of above-mentioned analysis, the present invention is intended to provide a kind of frequency spectrum refinement method of engineering truck vibration signal, Spectrum peak is caused to be omitted to solve existing artificial refining data so that the vibration control effect of engineering truck was had a greatly reduced quality Problem.
The purpose of the present invention is mainly achieved through the following technical solutions:
A kind of frequency spectrum refinement method of engineering truck vibration signal, which is characterized in that include the following steps:
Multiple acceleration transducer acquisition vibration signals are installed in engineering truck;
The vibration signal of acquisition is pre-processed, including signal enhanced processing and to amplified acceleration transducer signals It is filtered;
To the filtered data-signal of each acceleration transducer, data regularization is carried out, constitutes Regularization data;
According to the row of Regularization data to dimension serial number, the frequency spectrum per column data is calculated, effective peak of the column data is obtained It is worth frequency;
The difference on the frequency score value for calculating adjacent effective peak in the column data frequency spectrum judges whether to need to carry out at frequency spectrum refinement Reason is that then extraction needs to carry out the initial frequency of micronization processes frequency range and terminates frequency, carry out chirp z transform and preserve As a result, obtaining the zoom FFT of corresponding frequency band;It is no, directly preserve spectrum results.
Each column data is traversed, is handled to obtain the CZT of frequency spectrum refinement frequency range, and preserve result;Up to institute is in need The frequency range of refinement completes frequency spectrum refinement processing.
The present invention has the beneficial effect that:The frequency spectrum refinement method of this method utilizing works methods of vehicle vibration signal, to collecting Batch data processing, greatly improve data-handling efficiency so that vibration control effect promoting.
On the basis of said program, the present invention has also done following improvement:
Further, the multiple acceleration transducer is individually positioned in centre bit before the vehicle bridge left side of engineering truck, vehicle frame It sets and cab floor center.
Advantageous effect using above-mentioned further scheme is:The acceleration transducer of several different locations, energy are acquired respectively Variation must be vibrated by enough including each main vibration source so that data acquisition is more complete, and obtained data are more effective.
Further, the Signal Pretreatment includes:
It includes carrying out level-one amplification, high-pass filtering and two level amplification successively to do enhanced processing to the vibration signal of acquisition;
Amplified signal is removed by noise using low-pass filter.
Advantageous effect using above-mentioned further scheme is:After signal is amplified required multiple, many height can be superimposed Frequency noise need to can be filtered out high-frequency noise by the way of low-pass filtering, and influence of the noise to data is reduced;The first order is amplified Circuit obtains the zero-bit output voltage for having superposition sensor in output signal, amplifies to succeeding target for elimination zero-bit output voltage It influences, is needed before second order amplifier plus signal is isolated in a high-pass filtering circuit.
Further, described that data regularization is carried out to the filtered data-signal of each acceleration transducer, it constitutes Regularization data include:
The quantity of sensor gathered data after the filtering is M, that is, includes M length data vector different in size, and M is to pass Sensor quantity;Sampling number maximum value therein i.e. length maximum value is found, N is denoted as;
Zero padding processing is carried out to remaining M-1 data vector back so that the length of each data vector is N;
By after zero padding vector according to first row, secondary series ... m column arrange, constitute Regularization data.
Advantageous effect using above-mentioned further scheme is:By filtered data padding different in size, become regular The data of change preferably can do subsequent processing to each of which data.Maximum value data vector is chosen as length standard, was both protected The validity of all data has been protected, and has been wasted caused by preventing data length to be set as the definite value beyond each data length.
Further, the frequency spectrum calculated per column data includes:
Fast Fourier Transform (FFT) is carried out to the column data;
It takes absolute value to transformation results, obtains spectral magnitude.
Advantageous effect using above-mentioned further scheme is:Using Fast Fourier Transform (FFT), data effective spectrum is calculated Out, and by effective peak frequency it preserves, is made reference for the follow-up difference on the frequency score value that calculates.
Further, the effective peak frequency that obtains includes:
Using the maximum value of the spectral magnitude as the criterion of the row effective peak, when amplitude is higher than a times of maximum value, It is determined as that effective peak, the corresponding frequency values of extraction effective peak save as effective peak frequency sequence.
Advantageous effect using above-mentioned further scheme is:The condition of effective peak is set, can save effective frequency after Continuous refinement.
Further, described to judge whether to need to carry out frequency spectrum refinement processing, including sequence compares the difference on the frequency of effective peak The size of sub-sequence and primary frequency resolution ratio b multiple values, if difference on the frequency score value is all higher than or is equal to primary frequency resolution ratio b multiples Value is then not necessarily to carry out frequency spectrum refinement, directly preserves spectrum results;
If difference on the frequency score value is respectively less than primary frequency resolution ratio b multiple values, need to carry out frequency spectrum refinement.
Wherein, b value ranges are:3~5.
Advantageous effect using above-mentioned further scheme is:Frequency differential sequence and the primary frequency of effective peak compare, For judging there is whether frequency spectrum needs to refine, the process of the frequency spectrum refinement of unnecessary refinement is avoided.The value range that b is arranged is 3-5 is as refinement standard so that has not only met refinement and has required, but also has been wasted caused by not will produce excessively refinement.
Further, the initial frequency of the determining frequency spectrum refinement frequency range includes:
It when difference on the frequency score value is less than primary frequency resolution ratio b multiple values for the first time, extracts in the difference value, minuend corresponds to Initial frequency of the effective peak Frequency point as first segment frequency spectrum refinement frequency range.
Advantageous effect using above-mentioned further scheme is:It is made pair of difference on the frequency score value and primary frequency resolution ratio b multiple values Than judging frequency spectrum, whether there is still a need for refinements.To limit frequency spectrum refinement frequency initial range, reduce the frequency of unnecessary refinement Compose the process of refinement.
Further, the termination frequency of the determining frequency spectrum refinement frequency range includes:
If until the last one serial number of difference sequence, difference on the frequency score value are respectively less than primary frequency resolution ratio b multiple values, then carry Take the last one effective peak Frequency point as the termination frequency of this section of frequency spectrum refinement frequency range;Illustrate that the column data only has one section Frequency range needs to carry out frequency spectrum refinement;
If in comparison process, when frequency of occurrences difference value is more than primary frequency resolution ratio b multiple values, extracting the difference value In, termination frequency of the corresponding effective peak Frequency point of minuend as first segment frequency spectrum refinement frequency range.
Advantageous effect using above-mentioned further scheme is:When difference on the frequency score value is all higher than b times of primary frequency, you can stop Refinement, limits the range of refinement, to avoid unnecessary refinement.Using the method for automatic decision, artificial judgment is avoided The shortcomings that being easy to omit.
Further, described to carry out chirp z transform (CZT) according to the following formula, and preserve result;
Wherein:
X (n), fs are the column data and sample frequency of the operating mode after Regularization respectively;
fmin1,fmax1, initial frequency, the termination frequency of respectively this section frequency spectrum refinement frequency range;
R=(fmax1-fmin1)/Δ f, the points of this section of frequency spectrum refinement frequency range CZT;
R=0,1, R-1, the serial number of this section of frequency spectrum refinement frequency range CZT;
Δ f is the frequency resolution after frequency spectrum refinement.
Advantageous effect using above-mentioned further scheme is:To needing the frequencies of micronization processes in the way of linear transform Rate carries out micronization processes so that resolution ratio reduces, and achievees the purpose that refinement.
It in the present invention, can also be combined with each other between above-mentioned each technical solution, to realize more preferred assembled schemes.This Other feature and advantage of invention will illustrate in the following description, also, certain advantages can become from specification it is aobvious and It is clear to, or understand through the implementation of the invention.The purpose of the present invention and other advantages can by write specification, right Specifically noted structure is realized and is obtained in claim and attached drawing.
Description of the drawings
Attached drawing is only used for showing the purpose of specific embodiment, and is not considered as limitation of the present invention, in entire attached drawing In, identical reference mark indicates identical component.
Fig. 1 is a kind of system block diagram of the frequency spectrum refinement method of engineering truck vibration signal of the present invention;
Fig. 2 is that the effective peak of one column data of the specific embodiment of the invention screens schematic diagram;
Fig. 3 is that the effective peak of one column data of the specific embodiment of the invention screens close-up schematic view;
Fig. 4 is that the refinement frequency range of one column data of the specific embodiment of the invention judges schematic diagram;
Fig. 5 is that the frequency spectrum refinement of one column data of the specific embodiment of the invention handles schematic diagram;
Specific implementation mode
Specifically describing the preferred embodiment of the present invention below in conjunction with the accompanying drawings, wherein attached drawing constitutes the application part, and It is used to illustrate the principle of the present invention together with embodiments of the present invention, be not intended to limit the scope of the present invention.
The specific embodiment of the present invention, discloses a kind of frequency spectrum refinement method of engineering truck vibration signal, specifically Include the following steps:
Step 1, on the left of the vehicle bridge of engineering truck, the preceding center of vehicle frame and cab floor center difference Multiple acceleration transducers are placed, and collected acceleration signal is passed through into signal amplification circuit.
Specifically, signal amplification circuit is made of a two-stage amplifying circuit.Zero-bit is eliminated using bivalent high-pass filter The influence that output voltage amplifies succeeding target.
Amplified signal is filtered by step 2, removes denoising.
Specifically, the high-frequency noise generated after amplification is filtered out using low-pass filter.When signal is amplified required times After number, many high-frequency noises can be superimposed, need to be filtered out high-frequency noise by the way of low-pass filtering.
Filtered signal is imported into the workspaces MATLAB by step 3, is carried out at data Regularization to filtered signal Reason.
Preferably, the step 3 includes the following steps:
Step 301 is M to the quantity of sensor gathered data after the filtering, and M is the number of sensor, that is, includes M long Data vector different in size is spent, sampling number maximum value therein i.e. length maximum value is found, is denoted as N;
Step 302 carries out zero padding processing to remaining M-1 data vector back so that the length of each data vector It is N;
Step 303, by after zero padding vector according to first row, secondary series ... m column arrange, constitute Regularization data.
By data vector zero padding different in size, become the data of Regularization, after can preferably being done to each of which data Continuous processing.Maximum value data vector is chosen as preferred length standard, not only protects the validity of all data, but also prevent data Length is set as wasting caused by definite value.
Step 4, according to the row of Regularization data to dimension serial number, calculate the frequency spectrum of the column data first, obtain effective peak It is worth frequency;
Preferably, the frequency spectrum for calculating each column data, obtaining effective peak frequency includes:
Step 401 carries out Fast Fourier Transform (FFT) (FFT) to the data, as shown in Fig. 2, wherein Fig. 3 is the amplification of Fig. 2 Figure, it can thus be seen that the frequency at peak value is significantly larger than effective peak frequency, therefore needs micronization processes;
Step 402 takes absolute value to the result of FFT transform, obtains spectral magnitude;
Step 403 extracts criterion of the maximum value of spectral magnitude as effective peak, when amplitude is higher than a times of maximum value When, it is determined as that effective peak, the corresponding frequency values of extraction effective peak save as effective peak frequency sequence.
Preferably, a value ranges are 0.1~0.2.
By finding out effective peak-to-peak value frequency, as the reference value with the frequency spectrum for needing to refine.Subsequently to calculate frequency Difference value makes reference.Using Fast Fourier Transform (FFT), which is calculated, and effective peak frequency is protected It deposits, can be wasted caused by avoid all refining, improve efficiency.
Step 5, the difference on the frequency score value according to adjacent effective peak, judge whether the column data needs to carry out at frequency spectrum refinement Reason.
Specifically, if it is judged that need to carry out frequency spectrum refinement processing, then extraction needs to carry out micronization processes frequency range Initial frequency and terminate frequency, carry out chirp z transform and preserve as a result, obtain the zoom FFT of corresponding frequency band, tie Fruit is as shown in Figure 5;If it is judged that for woth no need to carry out frequency spectrum refinement processing, then spectrum results are directly preserved.
Specifically, the step 5 includes the following steps:
Step 501, the frequency differential sequence for calculating effective peak frequency sequence;
The size of step 502, the frequency differential sequence and primary frequency resolution ratio b multiple values of sequence comparison effective peak, such as Fruit difference on the frequency score value is all higher than primary frequency resolution ratio b multiple values, then is not necessarily to carry out frequency spectrum refinement, directly preserves spectrum results;It is no Then enter step 503.
Preferably, the value range of b is 3-5.
Step 503, the initial frequency for determining frequency spectrum refinement frequency range;
It when difference on the frequency score value is less than primary frequency resolution ratio b multiple values for the first time, extracts in the difference value, minuend corresponds to Initial frequency of the effective peak Frequency point as first segment frequency spectrum refinement frequency range, as shown in figure 4, the refinement frequency range judgement of data Utilize the difference value of frequency;
Step 504, the termination frequency for determining frequency spectrum refinement frequency range;
If until the last one serial number of difference sequence, difference on the frequency score value are respectively less than primary frequency resolution ratio b multiple values, then carry Take the last one effective peak Frequency point as the termination frequency of this section of frequency spectrum refinement frequency range;Illustrate that the column data only has one section Frequency range needs to carry out frequency spectrum refinement;
If in comparison process, when frequency of occurrences difference value is more than primary frequency resolution ratio b multiple values, extracting the difference value In, termination frequency of the corresponding effective peak Frequency point of minuend as first segment frequency spectrum refinement frequency range;
Step 505 repeats step 503,504, extracts the initial frequency of next section of frequency spectrum refinement frequency range and terminates frequency, directly To the last one serial number of difference sequence, the judgement of frequency spectrum refinement frequency range is completed;
Step 506, for each section of frequency spectrum refinement frequency range of each data in each operating mode after Regularization, according to Following formula calculates its chirp z transform (CZT), and preserves result;
Wherein:
X (n), fs are the column data and sample frequency of the operating mode after Regularization respectively;
fmin1,fmax1, initial frequency, the termination frequency of respectively this section frequency spectrum refinement frequency range;
R=(fmax1-fmin1)/Δ f, the points of this section of frequency spectrum refinement frequency range CZT;
R=0,1, R-1, the serial number of this section of frequency spectrum refinement frequency range CZT;
Δ f is the frequency resolution after frequency spectrum refinement, electedly, is traditionally arranged to be 10~20 times of former resolution ratio;
Step 507 continues step 506, calculates each section of frequency of each column data in each sensor after Regularization The CZT of spectrum refinement frequency range, and preserve result;Until each column data institute refinement in need frequency range completion frequency spectrum refinement at Reason.
In steps of 5, it is compared with primary frequency using the frequency differential sequence of effective peak, for judging whether there is frequency spectrum It needs refinement to limit the initial range of the frequency of frequency spectrum refinement and terminates range, avoid unnecessary thinning process.By second The frequency spectrum that section need to refine does refinement identical with first segment spectral method and judges, with the method for automatic decision, avoids and manually sentences The shortcomings that disconnected easy omission.To needing the frequency of micronization processes to carry out micronization processes in the way of linear transform so that point Resolution reduces, and achievees the effect that refinement.Using the method for automatic refinement batch processing, automatically processing the first operating mode second segment needs carefully The frequency range of change.
Step 6 traverses each sensor, is handled to obtain the CZT of frequency spectrum refinement frequency range, and preserve result;Until Refinement in need frequency range complete frequency spectrum refinement processing.
In conclusion an embodiment of the present invention provides a kind of frequency spectrum refinement method of engineering truck vibration signal, can solve Certainly the operating mode of engineering truck is often changeable in unstable state, and the prior art uses artificial processing method, and there are human errors etc. Uncertain factor, leads to the omission of spectrum peak, the defect that the vibration control effect of engineering truck is had a greatly reduced quality.Realize vibration letter Number being capable of batch and energy automatic business processing.
It will be understood by those skilled in the art that realizing all or part of flow of above-described embodiment method, meter can be passed through Calculation machine program is completed to instruct relevant hardware, and the program can be stored in computer readable storage medium.Wherein, institute It is disk, CD, read-only memory or random access memory etc. to state computer readable storage medium.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto, Any one skilled in the art in the technical scope disclosed by the present invention, the change or replacement that can be readily occurred in, It should be covered by the protection scope of the present invention.

Claims (10)

1. a kind of frequency spectrum refinement method of engineering truck vibration signal, which is characterized in that include the following steps:
Multiple acceleration transducer acquisition vibration signals are installed in engineering truck;
The vibration signal of acquisition is pre-processed, including signal enhanced processing and amplified acceleration transducer signals are filtered Wave processing;
To the filtered data-signal of each acceleration transducer, data regularization is carried out, constitutes Regularization data;
According to the row of Regularization data to dimension serial number, the frequency spectrum per column data is calculated, obtains the effective peak frequency of the column data Rate;
The difference on the frequency score value for calculating adjacent effective peak in the column data frequency spectrum judges whether to need to carry out frequency spectrum refinement processing, It is that then extraction needs to carry out the initial frequency of micronization processes frequency range and terminates frequency, carry out chirp z transform and preserve knot Fruit obtains the zoom FFT of corresponding frequency band;It is no, directly preserve spectrum results.
Each column data is traversed, is handled to obtain the CZT of frequency spectrum refinement frequency range, and preserve result;Until institute's refinement in need Frequency range complete frequency spectrum refinement processing.
2. the frequency spectrum refinement method of engineering truck vibration signal according to claim 1, which is characterized in that the multiple to add Velocity sensor is individually positioned in vehicle bridge left side, the preceding center of vehicle frame and the cab floor center of engineering truck.
3. the frequency spectrum refinement method of engineering truck vibration signal according to claim 1, which is characterized in that the signal is pre- Processing includes:
It includes carrying out level-one amplification, high-pass filtering and two level amplification successively to do enhanced processing to the vibration signal of acquisition;
It is filtered and amplified signal is removed by noise using low-pass filter.
4. the frequency spectrum refinement method of engineering truck vibration signal according to claim 1, which is characterized in that described to each The filtered data-signal of acceleration transducer carries out data regularization, constitutes Regularization data and includes:
The quantity of sensor gathered data after the filtering is M, that is, includes M length data vector different in size, M is sensor Quantity;Sampling number maximum value therein i.e. length maximum value is found, N is denoted as;
Zero padding processing is carried out to remaining M-1 data vector back so that the length of each data vector is N;
By after zero padding vector according to first row, secondary series ... m column arrange, constitute Regularization data.
5. the frequency spectrum refinement method of engineering truck vibration signal according to claim 1, which is characterized in that described to calculate often The frequency spectrum of column data includes:
Fast Fourier Transform (FFT) is carried out to the column data;
It takes absolute value to transformation results, obtains spectral magnitude.
6. the batch processing method that frequency spectrum according to claim 5 refines automatically, which is characterized in that described to obtain effective peak Frequency includes:
Using the maximum value of the spectral magnitude as the criterion of the row effective peak, when amplitude is higher than a times of maximum value, judgement For effective peak, the corresponding frequency values of extraction effective peak save as effective peak frequency sequence.
7. the batch processing method that frequency spectrum according to claim 1 refines automatically, which is characterized in that described to judge whether to need Carry out frequency spectrum refinement processing, including frequency differential sequence and the primary frequency resolution ratio b multiple values of sequence comparison effective peak is big It is small, if difference on the frequency score value is all higher than or is equal to primary frequency resolution ratio b multiple values, without carrying out frequency spectrum refinement, directly preserve Spectrum results;
If difference on the frequency score value is respectively less than primary frequency resolution ratio b multiple values, need to carry out frequency spectrum refinement.
Wherein, b value ranges are:3~5.
8. the batch processing method that frequency spectrum according to claim 7 refines automatically, which is characterized in that the determining frequency spectrum refinement The initial frequency of frequency range includes:
When difference on the frequency score value is less than primary frequency resolution ratio b multiple values for the first time, extract in the difference value, minuend is corresponding to be had Imitate initial frequency of the crest frequency point as first segment frequency spectrum refinement frequency range.
9. the batch processing method that frequency spectrum according to claim 8 refines automatically, which is characterized in that the determining frequency spectrum refinement The termination frequency of frequency range includes:
If until the last one serial number of difference sequence, difference on the frequency score value are respectively less than primary frequency resolution ratio b multiple values, then extract most Termination frequency of the latter effective peak Frequency point as this section of frequency spectrum refinement frequency range;Illustrate that the column data only has one section of frequency range It needs to carry out frequency spectrum refinement;
If in comparison process, when frequency of occurrences difference value is more than primary frequency resolution ratio b multiple values, extracted in the difference value, quilt Termination frequency of the corresponding effective peak Frequency point of subtrahend as first segment frequency spectrum refinement frequency range.
10. the batch processing method that frequency spectrum according to claim 9 refines automatically, which is characterized in that it is described according to the following formula into Row chirp z transform (CZT), and preserve result;
Wherein:
X (n), fs are the column data and sample frequency of the operating mode after Regularization respectively;
fmin1,fmax1, initial frequency, the termination frequency of respectively this section frequency spectrum refinement frequency range;
R=(fmax1-fmin1)/Δ f, the points of this section of frequency spectrum refinement frequency range CZT;
R=0,1 ... R-1, the serial number of this section of frequency spectrum refinement frequency range CZT;
Δ f is the frequency resolution after frequency spectrum refinement.
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