CN111649817B - Distributed optical fiber vibration sensor system and mode identification method thereof - Google Patents
Distributed optical fiber vibration sensor system and mode identification method thereof Download PDFInfo
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Abstract
The invention provides a distributed optical fiber vibration sensor system and a mode identification method thereof, wherein the system comprises a distributed optical fiber vibration sensor, a feature extraction module and a mode classification module; after a coherent detection method is adopted for detecting the distributed optical fiber vibration sensor to obtain a vibration signal f [ theta ] to be classified at a vibration point, the characteristic extraction module is used for carrying out characteristic extraction on the vibration signal f [ theta ] to obtain intrusion event characteristic parameter data, the characteristic parameter data are sent to the pattern classification module, and then a classifier trained by the pattern recognition method is used for classifying intrusion events in a database of the pattern classification module, so that the intelligent pattern recognition of the distributed optical fiber vibration sensor is realized.
Description
Technical Field
The invention relates to the technical field of optical fiber vibration sensors, in particular to a distributed optical fiber vibration sensor system and a mode identification method thereof.
Background
With the continuous development of the optical communication industry in recent years, related optical devices are continuously updated and mature, and the application of optical fibers in the communication field is rapidly advanced. Meanwhile, the application of the optical fiber in the sensing detection field is gradually developed, and the optical fiber sensor is different from the traditional sensor in that the optical fiber sensor has the characteristics of electromagnetic interference resistance, safety, energy conservation, high sensitivity, small volume, easiness in laying and the like. The optical fiber can sense various external information such as external physical characteristics of stress, temperature, electromagnetic field, gas concentration and the like according to the characteristic change of the back scattering light of the pumping pulse light. The backward scattering light can be divided into Rayleigh scattering light, Brillouin scattering light and Raman scattering light according to frequency change, wherein the Rayleigh scattering light frequency is consistent with the detection pulse light, the power is strongest, the scattering distance is long, and the long-distance security detection device can be used for long-distance security detection. The optical fiber sensor can be divided into point type, quasi-distributed type and distributed type sensing according to sensing modes, the point type and quasi-distributed type sensing mainly aims at measuring characteristic parameters of important monitoring points, namely only can detect each point in an effective range, the sensing points mainly detect the optical fiber Bragg grating, and the optical fiber plays a role in transmitting light source information in the sensor. Different from distributed optical fiber sensing, the optical fiber is a transmission medium and a sensor, and can realize the whole-process characteristic information detection of the single-mode optical fiber. In addition, optic fibre is portable, light in weight, easy the buckling, can lay according to actual conditions according to geographical environment, guardrail shape and the environmental requirement of detection range, and the engineering of being convenient for is realized. In recent years, the Rayleigh scattering-based phase-sensitive optical time domain reflection distributed optical fiber sensing technology is well applied to the field of perimeter security detection, and intrusion events on an optical fiber laying area are monitored in real time by demodulating disturbance interference intensity changes of Rayleigh scattering light after optical pulses are demodulated.
It can be seen that the distributed optical fiber vibration sensor can effectively detect strain signals on an optical fiber laying area, but if the problem of intrusion event pattern recognition of a vibration point cannot be effectively solved, false alarm events are increased, and therefore security cost is increased. The optical fiber sensor is used for detecting the signals of the intrusion vibration points, extracting the characteristics from the signals and identifying the vibration type, so that not only can the security decision be assisted, but also the operation cost can be effectively reduced. The existing optical fiber sensing security system relies on feature direct extraction or Singular Value Decomposition (SVD) feature dimension reduction, and utilizes intrusion event feature vector learning to train a support vector machine or a neural network so as to realize classification. However, singular value decomposition is generally used for analyzing relevant information of two fields, and for analyzing respective correlation of two dimensions of a matrix, the singular value decomposition is commonly used for personalized recommendation, and SVD is also accompanied with the problem of high data computation amount. The neural network and the deep learning network are widely applied in the fields of computer vision, speech recognition and the like, and multi-target classification recognition can be realized by using the softmax layer of the neural network. However, training a neural network with a high recognition rate requires a large amount of supervised learning data, and the samples are usually in the tens of thousands or even millions. When the training data is insufficient, problems of under-fitting and the like are caused, and problems of super-parameter modulation, updating and maintenance caused by the insufficient training data also require relatively high cost, so that the output reaction time and the classification accuracy of the system are directly influenced. Therefore, a classifier method for small sample feature extraction and data noise reduction compression is required to be provided for the pattern recognition problem of the optical fiber sensor, so as to reduce the system operation amount, improve the pattern recognition rate and the response speed of the optical fiber sensor system, and assist security detection.
Disclosure of Invention
The invention aims to provide a distributed optical fiber vibration sensor system and a mode identification method thereof aiming at the defects of the prior art.
In order to achieve the above object, a first aspect of the present invention provides a pattern recognition method for a distributed optical fiber vibration sensor system, which first performs feature extraction on a vibration signal f [ θ ] to be classified at an acquired vibration point to obtain intrusion event feature parameter data:
according to different intrusion event types YiEach sample having at least 100 groups, each Mi(i ═ 1,2,3, … …);
preselected feature ai＝ai1，ai2…ainWherein a isiAiming at different intrusion scenes Y for the characteristic vector of the ith group of dataiAccording to a preselected characteristic a ═ a1，a2…anCollecting the characteristics of sample signals at abnormal vibration point of optical fiber sensor
Group (M/i. ltoreq. M)i(i is 1,2,3, … …)), obtaining m groups of characteristic vectors A of the sample signals at the abnormal vibration point of the optical fiber sensor1；
Averaging according to each column to obtain A2Calculating the covariance matrix A2 TA2Characteristic value λ of1、λ2…λi(i ≦ n) and corresponding normalized feature vector ξ1、ξ2…ξiWherein λ isjIs A2In xij(j ∈ (1, …, i)) the sum of variances after directional projection;
will be lambdajSorting from big to small, selecting the first k lambadas1、λ2…λk(k ≦ i) represents the sum of data variances corresponding to the principal direction of the feature, and the corresponding feature vector ξ1、ξ2…ξkComposition characteristic a ═ a1，a2…anζ ═ ξ (ξ) of the conversion matrix1、ξ2…ξk)n×kCompleting affine transformation of all the characteristic vectors in the main direction to obtain characteristic parameters A3＝(A1ζ)m×k；
Second, for different intrusion types YiAnd the obtained characteristic parameter data is calculated according to the following ratio of 6: 2: 2, proportionally classifying the classifier into a training set, a verification set and a test set, wherein the training set is used for training a classifier model and calculating optimal parameter values, the verification set is used for cross-verifying the classification performance of the classifier so as to select a proper classifier, and the test set is used for finally verifying whether the determined classifier can meet the expected requirement and testing the classification effect of the classifier;
and finally, training a classifier according to a dichotomy and an SMO algorithm:
intrusion event type YiDividing the Chinese character into two categories by taking a dichotomy as a standard;
selecting Support Vector Machine (SVM) by adjusting kernel function
Mapping feature dimensions to higher dimensions, where xiPerforming feature extraction, feature conversion and data compression on the original data to obtain k-dimensional vectors
aiThe feature vector of the ith group of data is processed by a decision function
Classifying two types of patterns, wherein
Segmenting a hyperplane for the classifier;
dividing the intrusion type Y according to the dichotomyiSequentially dividing the support vector machine into two types, and designing a plurality of Support Vector Machines (SVM);
during trainingAnd extracting a training set: x is the number of1、x2…xiCorresponding to the target value y1、y2…yi(yiE { -1,1}) for the case of linear inseparability, a relaxation factor epsilon is introducediNot less than 0; the constraint condition of the original problem is
The objective function is:
the original problem is converted into a dual problem by applying a convex optimization theory and a Lagrange dual function method, namely:
selecting two multipliers for optimization, setting the rest multipliers as constants, and setting the objective function as a convex function; iteratively updating and calculating alpha according to KKT conditions and dual problem constraint conditionsiRepeating the above steps to obtain all optimized multipliers alpha*；
Obtain the optimal solution alpha*Then, w can be obtained*,b*
The system decision function is
Wherein the Gaussian kernel function is defined as
Feature vectorxiMapping to an infinite dimension;
and adjusting sigma, cross-verifying each support vector machine SVM, and selecting a proper support vector machine SVM to store into a system database.
Based on the above, the categories of preselected features include: sample signal energy
Maximum signal strength maxθ|f[θ]Average intensity of disturbance
Wavelet transformation time-frequency diagram characteristics and signal variance
Signal number ratio exceeding average intensity
Wherein sgn (x) is a step function
The invention provides a distributed optical fiber vibration sensor system in a second aspect, which comprises a distributed optical fiber vibration sensor, a feature extraction module and a mode classification module; after a coherent detection method is adopted for detecting the distributed optical fiber vibration sensor to obtain a vibration signal f [ theta ] to be classified at a vibration point, the vibration signal f [ theta ] is subjected to a pattern recognition method by the feature extraction module to obtain intrusion event feature parameter data, the feature parameter data are sent to the pattern classification module, and then the intrusion event is classified by a classifier trained by the pattern recognition method in a database of the pattern classification module, so that the intelligent pattern recognition of the distributed optical fiber vibration sensor is realized.
Based on the above, the distributed optical fiber vibration sensor includes a single-mode optical fiber, an optical fiber circulator, a laser, an optical fiber coupler, an acousto-optic modulator, an erbium-doped optical fiber amplifier, a photodetector and a coherent demodulation module; the laser generates two continuous narrow linewidth optical signals through the optical fiber coupler, the light beam I is used as local reference light, the light beam II is converted into pulse light with PRF of 20kHz after passing through the acousto-optic modulator AOM, then narrow linewidth pulse detection optical signals with 200MHz frequency shift are generated through the erbium-doped fiber amplifier EDFA, and finally the detection light is injected into the single mode fiber through the fiber circulator; the detection light generates coherent Rayleigh backward scattering light in the optical fiber, namely signal light carrying outside invasion disturbance information; the signal light and the local reference light generate interference light through a mixer, and then the interference light signal is converted into an electric signal through a photoelectric detector and is output in a baseband signal form; and then, collecting coherent light signals to be demodulated through an A/D converter, and obtaining vibration signals f [ theta ] to be classified at vibration points after orthogonal frequency mixing, low-pass filtering and zero-crossing rate detection.
Compared with the prior art, the invention has prominent substantive characteristics and remarkable progress, in particular: the method is based on coherent detection of optical time domain reflection distributed optical fiber sensors to collect corresponding intrusion signals, provides an intrusion signal identification and classification method, and can realize positioning, identification and alarm of intrusion vibration signals by combining signal demodulation, feature extraction, dimension reduction and high-order mapping support vector machine methods. And obtaining intrusion event characteristic parameters by extracting the vibration signal characteristics. After receiving the characteristic parameters, the mode classification module classifies the intrusion events in real time by calling a trained Support Vector Machine (SVM) in the database and displays the intrusion events through terminal output equipment. The system realizes the distributed monitoring and identification of the perimeter security protection of the sensor optical fiber laying area, and is used for meeting the requirements of real-time monitoring, safety guarantee, dynamic intrusion identification and the like of the perimeter area.
Detailed Description
The invention provides a distributed optical fiber vibration sensor system and a mode identification method thereof, wherein the system comprises a distributed optical fiber vibration sensor, a feature extraction module and a mode classification module; after a coherent detection method is adopted for detecting the distributed optical fiber vibration sensor to obtain a vibration signal f [ theta ] to be classified at a vibration point, the characteristic extraction module is used for carrying out characteristic extraction on the vibration signal f [ theta ] to obtain intrusion event characteristic parameter data, the characteristic parameter data are sent to the pattern classification module, and then the trained classifier in a database of the pattern classification module is called to classify the intrusion event, so that the intelligent pattern recognition of the distributed optical fiber vibration sensor is realized.
The system of the invention adopts a coherent detection method to demodulate signals to obtain vibration signals f [ theta ] to be classified at vibration points. Specifically, the distributed optical fiber vibration sensor comprises a single-mode optical fiber, an optical fiber circulator, a laser, an optical fiber coupler, an acoustic-optical modulator, an erbium-doped optical fiber amplifier, a photoelectric detector and a coherent demodulation module; the laser generates two continuous narrow linewidth optical signals through the optical fiber coupler, the light beam I is used as local reference light, the light beam II is converted into pulse light with PRF of 20kHz after passing through the acousto-optic modulator AOM, then narrow linewidth pulse detection optical signals with 200MHz frequency shift are generated through the erbium-doped fiber amplifier EDFA, and finally the detection light is injected into the single mode fiber through the fiber circulator; the detection light generates coherent Rayleigh backward scattering light in the optical fiber, namely signal light carrying outside invasion disturbance information; the signal light and the local reference light generate interference light through a mixer, and then the interference light signal is converted into an electric signal through a photoelectric detector and is output in a baseband signal form; and then, collecting coherent light signals to be demodulated through an A/D converter, and obtaining vibration signals f [ theta ] to be classified at vibration points after orthogonal frequency mixing, low-pass filtering and zero-crossing rate detection.
The pattern recognition method of the present invention is used to design a classifier:
(1) selecting a sample, and extracting the characteristics of the vibration signal f [ theta ] to be classified at the acquired vibration point to obtain the characteristic parameter data of the intrusion event:
according to different intrusion event types YiEach sample having at least 100 groups, each Mi(i ═ 1,2,3, … …).
(2) Primary screening, completing sample cleaning: preselected feature ai＝ai1，ai2…ainWherein a isiFor the characteristic vector of the ith group of data, according to the preselected characteristic a ═ a for different intrusion scenes Yi1，a2…anCollecting the characteristics of sample signals at abnormal vibration point of optical fiber sensor
Group (M/i. ltoreq. M)i(i is 1,2,3, … …)), obtaining m groups of characteristic vectors A of the sample signals at the abnormal vibration point of the optical fiber sensor1；
Averaging according to each column to obtain A2Calculating the covariance matrix A2 TA2Characteristic value λ of1、λ2…λi(i ≦ n) and corresponding normalized feature vector ξ1、ξ2…ξiWherein λ isjIs A2In xij(j ∈ (1, …, i)) the sum of variances after directional projection;
will be lambdajSorting from big to small, selecting the first k lambadas1、λ2…λk(k ≦ i) represents the sum of data variances corresponding to the principal direction of the feature, and the corresponding feature vector ξ1、ξ2…ξkComposition characteristic a ═ a1，a2…anζ ═ ξ (ξ) of the conversion matrix1、ξ2…ξk)n×kCompleting affine transformation of all the characteristic vectors in the main direction to obtain characteristic parameters A3＝(A1ζ)m×k；
In this step, lambda isjArranging from large to small, selecting the first k as main features, enabling the corresponding feature vector to be the main direction with the largest projection rear square difference, performing matrix multiplication operation on the original data and the feature vector to realize feature value radial transformation, mapping sample points in the non-main value direction to the main value direction to realize small sample feature extraction and simultaneously complete denoising, and compressing data to convert the original matrix into an m multiplied by k matrix (k is less than or equal to n).
(3) For different intrusion types YiAnd the obtained characteristic parameter data is calculated according to the following ratio of 6: 2: 2, classifying the parameters into a training set, a verification set and a test set in proportion, wherein the training set is used for training a classifier model and calculating optimal parametersThe verification set is used for cross-verifying the classification performance of the classifiers so as to select a proper classifier, and the test set is used for finally verifying whether the determined classifier can meet the expected requirement and testing the classification effect of the classifier; dividing the intrusion types into different categories according to the sequence of permutation and combination to prepare for subsequent cross validation and SVM selection;
(4) according to dichotomy and intrusion type YiClassifying data, selecting a Support Vector Machine (SVM) as a classifier, selecting a Gaussian kernel as a kernel function of the SVM, adjusting model parameters, and training different types of SVM according to an SMO algorithm, specifically:
intrusion event type YiDividing the Chinese character into two categories by taking a dichotomy as a standard;
selecting Support Vector Machine (SVM) by adjusting kernel function
Mapping feature dimensions to higher dimensions, where xiPerforming feature extraction, feature conversion and data compression on the original data to obtain k-dimensional vectors
aiThe feature vector of the ith group of data is processed by a decision function
Classifying two types of patterns, wherein
Segmenting a hyperplane for the classifier;
dividing the intrusion type Y according to the dichotomyiSequentially dividing the support vector machine into two types, and designing a plurality of Support Vector Machines (SVM);
during training, extracting a training set: x is the number of1、x2…xiCorresponding to the target value y1、y2…yi(yiE { -1,1}) for the case of linear inseparability, a relaxation factor epsilon is introducediNot less than 0; the constraint condition of the original problem is
The objective function is:
the original problem is converted into a dual problem by applying a convex optimization theory and a Lagrange dual function method, namely:
selecting two multipliers for optimization, setting the rest multipliers as constants, and setting the objective function as a convex function; iteratively updating and calculating alpha according to KKT conditions and dual problem constraint conditionsiRepeating the above steps to obtain all optimized multipliers alpha*；
Obtain the optimal solution alpha*Then, w can be obtained*,b*
The system decision function is
Wherein the Gaussian kernel function is defined as
The feature vector xiMapping to an infinite dimension;
(5) and adjusting sigma, cross-verifying each support vector machine SVM, and selecting a proper support vector machine SVM to store into a system database. The classification accuracy can be effectively improved by using the Gaussian kernel function, but the overfitting problem is accompanied, cross verification is needed between the accuracy and the fitting degree for improving the classification effect of the support vector machine SVM, the sigma is adjusted, and a reasonable sample is selected for classification and a proper SVM is selected to be stored in a system database.
To improve the recognition rate, the categories of the preselected features include, according to experimental experience: sample signal energy
Reflecting the total energy of the signal and the maximum intensity max of the signalθ|f[θ]I reflects the maximum vibration amplitude and the disturbance average intensity of the signal
Reflecting signal average vibration amplitude, wavelet transformation time-frequency diagram characteristic reflection signal frequency characteristic and signal variance
Signal number ratio reflecting the intensity of signal energy change and exceeding average intensity
Reflecting the intensity of the vibration change of the signal, wherein sgn (x) is a step function
The process of using the system of the invention to carry out the pattern recognition aiming at the optical fiber invasion event comprises the following steps:
the photoelectric detector converts the received coherent light signal into an electric signal, and then the electric signal is demodulated into an intrusion signal f [ k ] by an anti-mixing filter, an A/D sampling and coherent demodulation module]Calculating the signal energy of the signal
Maximum signal strength maxk|f[k]Average intensity of disturbance
Wavelet transformation time-frequency diagram characteristics and signal variance
Signal number ratio exceeding average intensity
And (3) waiting for the characteristic quantity to form a characteristic vector X, completing characteristic conversion X zeta, classifying a newly-entered mode by using the newly-converted characteristic through a trained SVM, and realizing dynamic intelligent mode recognition of the distributed optical fiber sensor and transmitting the dynamic intelligent mode recognition to output equipment for assisting decision making.
If the system generates misjudgment, a misjudgment sample or an unknown sample is collected and stored in a database for model updating, and the system is updated and upgraded periodically according to the collected sample so as to improve the accuracy.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and all the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (3)
1. A mode identification method of a distributed optical fiber vibration sensor system is characterized in that firstly, the vibration signals f [ theta ] to be classified at the collected vibration points are subjected to feature extraction to obtain intrusion event feature parameter data:
according to different intrusion event types YiEach sample having at least 100 groups, each Mi(i 1,2, 3.. said.);
preselected feature ai＝ai1，ai2...ainWherein a isiFor feature vectors of the ith set of data, pinsFor different invasion scenes YiAccording to a preselected characteristic a ═ a1，a2...anCollecting the characteristics of sample signals at abnormal vibration point of optical fiber sensor
Group (M/i. ltoreq. M)i(i ═ 1,2, 3.. once.)) to obtain m groups of characteristic vectors A of the sample signals at the abnormal vibration points of the optical fiber sensor1；
Averaging according to each column to obtain A2Calculating the covariance matrix A2 TA2Characteristic value λ of1、λ2…λi(i ≦ n) and corresponding normalized feature vector ξ1、ξ2…ξiWherein λ isjIs A2In xij(j ∈ (1, …, i)) the sum of variances after directional projection;
will be lambdajSorting from big to small, selecting the first k lambadas1、λ2…λk(k ≦ i) represents the sum of data variances corresponding to the principal direction of the feature, and the corresponding feature vector ξ1、ξ2…ξkComposition characteristic a ═ a1，a2...anζ ═ ξ (ξ) of the conversion matrix1、ξ2…ξk)n×kCompleting affine transformation of all the characteristic vectors in the main direction to obtain characteristic parameters A3＝(A1ζ)m×k；
Second, for different intrusion types YiClassifying the obtained characteristic parameter data into a training set, a verification set and a test set according to the ratio of 6: 2, wherein the training set is used for training a classifier model and calculating an optimal parameter value, the verification set is used for cross-verifying the classification performance of the classifier so as to select a proper classifier, and the test set is used for finally verifying whether the determined classifier can meet the expected requirement and testing the classification effect of the classifier;
and finally, training a classifier according to a dichotomy and an SMO algorithm:
intrusion event type YiDividing the Chinese character into two categories by taking a dichotomy as a standard;
selecting Support Vector Machine (SVM) by adjusting kernel function
Mapping feature dimensions to higher dimensions, where xiPerforming feature extraction, feature conversion and data compression on the original data to obtain k-dimensional vectors
aiThe feature vector of the ith group of data is processed by a decision function
Classifying two types of patterns, wherein
Segmenting a hyperplane for the classifier;
dividing the intrusion type Y according to the dichotomyiSequentially dividing the support vector machine into two types, and designing a plurality of Support Vector Machines (SVM);
during training, extracting a training set: x is the number of1、x2…xiCorresponding to the target value y1、y2…yi(yiE { -1,1}) for the case of linear inseparability, a relaxation factor epsilon is introducediNot less than 0; the constraint condition of the original problem is
The objective function is:
the original problem is converted into a dual problem by applying a convex optimization theory and a Lagrange dual function method, namely:
selecting two multipliers for optimization, setting the rest multipliers as constants, and setting the objective function as a convex function; iteratively updating and calculating alpha according to KKT conditions and dual problem constraint conditionsiRepeating the above steps to obtain all optimized multipliers alpha*；
Obtain the optimal solution alpha*Then, w can be obtained*，b*
The system decision function is
Wherein the Gaussian kernel function is defined as
The feature vector xiMapping to an infinite dimension;
adjusting sigma, cross-verifying each support vector machine SVM, selecting a proper support vector machine SVM and storing the proper support vector machine SVM in a system database;
the categories of preselected features include: sample signal energy
Maximum signal strength maxθ|f[θ]Average intensity of disturbance
Wavelet transformation time-frequency diagram characteristics and signal variance
Signal number ratio exceeding average intensity
Wherein sgn (x) is a step function
2. A distributed optical fiber vibration sensor system comprises a distributed optical fiber vibration sensor, and is characterized in that: the system also comprises a feature extraction module and a mode classification module;
after a coherent detection method is adopted for detecting a distributed optical fiber vibration sensor to obtain a vibration signal f [ theta ] to be classified at a vibration point, the characteristic extraction module carries out the mode recognition method in claim 1 on the vibration signal f [ theta ] to obtain intrusion event characteristic parameter data, the characteristic parameter data are sent to the mode classification module, and then the intrusion event is classified by calling a classifier trained by the mode recognition method in claim 1 in a database of the mode classification module, so that the intelligent mode recognition of the distributed optical fiber sensor is realized.
3. A distributed fibre optic vibration sensor system according to claim 2, wherein: the distributed optical fiber vibration sensor comprises a single-mode optical fiber, an optical fiber circulator, a laser, an optical fiber coupler, an acousto-optic modulator, an erbium-doped optical fiber amplifier, a photoelectric detector and a coherent demodulation module;
the laser generates two continuous narrow linewidth optical signals through the optical fiber coupler, the light beam I is used as local reference light, the light beam II is converted into pulse light with PRF of 20kHz after passing through the acousto-optic modulator AOM, then narrow linewidth pulse detection optical signals with 200MHz frequency shift are generated through the erbium-doped fiber amplifier EDFA, and finally the detection light is injected into the single mode fiber through the fiber circulator; the detection light generates coherent Rayleigh backward scattering light in the optical fiber, namely signal light carrying outside invasion disturbance information;
the signal light and the local reference light generate interference light through a mixer, and then the interference light signal is converted into an electric signal through a photoelectric detector and is output in a baseband signal form; and then, collecting coherent light signals to be demodulated through an A/D converter, and obtaining vibration signals f [ theta ] to be classified at vibration points after orthogonal frequency mixing, low-pass filtering and zero-crossing rate detection.
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