# Three-Dimensional Image Analysis and Training Method of Action Characteristics of Sanda Whip Leg Technique Based on Wavelet Transform

Authors: Lei Song
Journal: Advances in Multimedia
 (2022)

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## Abstract

The whip leg technique is an indispensable offensive action for high-level Sanda athletes in the competition. In order to improve the effective guidance of the action of Wushu Sanda whip leg, based on wavelet transform, the three-dimensional image analysis of Sanda whip leg technical action characteristics, to explore the movement speed of each link of the attacking leg, the contraction form, and force sequence of major muscles or muscle groups and put forward correct and reasonable movement techniques, is expected to provide theoretical basis and reference for coaches and athletes in the training of Sanda whip leg movement. Based on this, this paper attempts to use the three-dimensional image analysis system and surface electromyography acquisition system from the perspective of wavelet transform to collect the speed of the attacking leg movement and the parameters related to muscle discharge and to quantitatively analyze and evaluate its movements. The sequence of activities of the whip leg strike is hip joint-knee joint-hip joint-knee joint-ankle joint. It is suggested to strictly follow the principle of link movement in practice, and the completion of the whole movement should be relaxed and natural.


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## Body

## 1. Introduction

In the offensive action of Sanda, the “whip leg” is one of the most important means of scoring [1]. It is widely used in competitions and has great power. Hitting the opponent can not only directly score points but also ingeniously inflict heavy damage on the opponent, causing it to be “forced to count the seconds,” and even directly gain an advantage [2]. Relevant data statistics show that in each game’s offensive actions (excluding other defensive counterattack tactics), the use rate of the whip leg is about 30% [3]. It can be seen that whether an athlete can complete a high-quality whipping action in a game directly affects the outcome of the game [4]. According to the technical statistics of the 216 men’s games in the 2010 National Sanda Championships, the use of whip legs accounted for 78.25% of all leg techniques and 39.51% of the entire Sanda technique [5]. The use rate of leg techniques was significantly higher than that of any other movements. But the analysis found that the score rate and usage rate are not proportional. It shows that there are still problems that need to be improved and improved in the teaching and training of whipping [6].Sanda whip leg is one of the most powerful leg techniques. It not only has the characteristics of flexion and extension leg technique but also has the function of sweeping and turning leg technique. It has the characteristics of large attack force and fast recovery speed. The kicking of whip leg is to turn the body, twist the waist, and turn the hip with the support leg as the axis, and the hip drives the thigh. The thigh drives the calf, and the corresponding links are accelerated in turn with the transmission of power. Finally, when the instep reaches the maximum speed, it bounces and kicks at the target. This rotational force generation method “uses the inertial motion of the large mass part generated by the imbalance to generate force consciously.” In addition, the power generated by twisting the waist and turning the hip can greatly exert the potential of the human body and produce an ideal attack effect. The three-dimensional image of Sanda whip leg is a kind of signal, and time and frequency are the two basic physical quantities to describe and analyze the signal [7]. As one of the methods in the field of digital signal analysis and processing, the time-frequency joint analysis method can reflect the trend of signal frequency components changing with time and overcome the shortcomings of Fourier transform in nonstationary signal processing [8]. The joint analysis of signal characteristics from two aspects in the frequency domain can analyze the signal more comprehensively and has become an indispensable mathematical tool in modern signal analysis [9]. The wavelet transform can continuously adjust the time width and bandwidth of the analysis with the transformation of the frequency [10]. With the continuous increase of the frequency, the corresponding time width decreases and the bandwidth increases, which is in line with the expectation of high- and low-frequency signal analysis [11]. However, since the time width and bandwidth are only a qualitative description, the wavelet transform cannot quantitatively analyze the analysis results but can only display the overall change trend of the analysis signal and can display the change effect of the signal from the time-frequency domain. Effectively reflect the overall characteristics of the signal [12]. When performing time-frequency analysis on the signal through wavelet transform, the whole picture of the signal can be analyzed, and the effective or interesting time-frequency interval of the signal can be obtained. Using the digital down-conversion (DDC) technique, the frequency band of interest can be effectively moved to the low frequency and reduce the data redundancy by decimation filtering and filter out the signal outside the frequency band of interest, which changes the relationship between the signal frequency and the sampling rate after down-conversion. The time width and bandwidth have been changed, and the details of the signal in a specific frequency band can be analyzed, so the wavelet transform can effectively analyze the trend of the signal change [13].


## 2. State of the Art

Sanda, as an important part of Chinese martial arts, has been piloted since 1979. In recent years, with the standardization of Wushu work and the introduction of new rules for Wushu Sanda, “standards” and “norms” have become signs of the maturity of Sanda movement [14]. Although it is still suffering from the controversy of “loss of traditional characteristics” and unbalanced development of technical structure,” the pace of its rapid development has become an indisputable fact [15]. At present, the three technical structures of punching, kicking, and throwing have developed in a balanced manner. It has become the main theme of the development of the project [16]. Since the leg technique has become the main scoring method in the game, it has played a key role in the outcome of the game [17], especially the whip leg technique which is characterized by a small range of motion, strong suddenness, wide striking range, strong kicking power [18], easy to attack and difficult to defend, wide striking parts, good cohesion when combined with other techniques, strong movement coherence, etc. The high technical movements and the key technical movements determine the outcome of the game. However, in the competition, athletes of different sports levels have different performances such as the use of the leg whipping technique and the scoring rate. The sport level not only affects the application effect of the leg whipping technique, but also, it has become the main factor that induces the risk of acute sports injury to the lower extremity joints [19]. Some studies have shown that the start-up time of Wuying-level Sanda athletes is faster than that of first-level athletes [20]. The biological laws of the athlete are better than those of the general population, and the isokinetic muscle strength and stability of the bilateral lower extremity joints of the athlete-level athletes are significantly better than those of the first-level athletes.Through the scale transform and translation transform of the basic wavelet, the wavelet transform can realize the positioning function of frequency and time. With the increase of frequency, the time resolution can be improved and the frequency domain resolution can be reduced. On the contrary, as the frequency continues to decrease the time resolution, the frequency domain resolution decreases and the frequency domain resolution increases, which can automatically adapt to the requirements of time-frequency analysis.As a powerful signal analysis algorithm, wavelet transform is widely used and has a wide range of practical significance, mainly including many disciplines in the field of mathematics, signal analysis and image processing, quantum mechanics and theoretical physics, military electronic countermeasures, and weapon intelligence. STFT, WVD, and wavelet transform all provide strong theoretical support for time-frequency joint analysis and lay the foundation for hardware implementation of time-frequency analysis function.


## 3. Research Methods

### 3.1. Time-Frequency Analysis of Wavelet Transform

Wavelet can track time and frequency information. It can “look close” to short-time pulses or “look far” to detect long-time slow waves. There are two functions that play a very important role in wavelet analysis, i.e., scale function and wavelet function. These two functions generate a set of function families that can be used to decompose and reconstruct signals. The time-frequency analysis method can process and analyze the signal from the time-frequency dimension at the same time, avoiding the limitations of pure time-domain or frequency analysis. The emergence of the time-frequency analysis method solves the problem that Fourier transform can only analyze the signal from the frequency domain, and provides a new method for the field of signal analysis. STFT and wavelet transform are two typical time-frequency analysis methods, which are also implemented in the acquisition system. These two methods have their own advantages and disadvantages. Different time-frequency analysis methods can be selected under different requirements. This paper mainly introduces the time-frequency realization based on wavelet transform, and the content of STFT is only briefly introduced. The definition formula of STFT is as follows:(1)STFTxt,Ω=∫xτg∗τ−te−jΩτdτ=<xτ,gτ−tejΩτ>.Among them,xτ is the analysis signal, and gτ is the window function. The basic idea of the STFT algorithm is to use the local characteristics of the window function gτ; taking a rectangular window as an example, multiply the signal to be analyzed by the window function to achieve local interception of the signal, and use the Fourier transform to obtain the corresponding current timet, spectrum of the segment signal. In order to obtain a complete time-frequency relationship, by changing the center position t of the window function through constant translation, that is, changing the time center of the window function analysis, the corresponding frequency spectrum at different times can be determined, thus forming the relationship between timetand frequencyΩ, time-frequency relationship diagram.Wavelet transform is widely used in digital signal processing and has important applications in filtering, denoising, compression, time-frequency analysis, and so on. The definition of wavelet transform is(2)WTxa,b=1a∫xtψ∗t−badt=∫xtψa,b∗tdt=<xt,ψa,bt>.Among them,xt is the analysis signal, Ψt is the basic wavelet function, and Ψa,btis the wavelet basis function, which is obtained by translating and scaling the basic wavelet function Ψt. Its frequency domain expression is
(3)WTxa,b=a2π∫−∞+∞XΩΨ∗aΩejΩbdΩ.The “wavelet” in the wavelet transform indicates that the wavelet functionΨt has volatility. With the change of time, the waveform exhibits the form of oscillation, and the waveform is attenuated as a whole, and it is a band-limited signal in the time domain; its support range is limited. At the same time, the wavelet function behaves as a band-pass filter in the frequency domain; it only allows the signal within the passband to pass and suppresses the frequency components of the signal outside the passband, and its frequency domain support range is also limited (Figure 1). Such a wavelet function Ψt is called basic wavelet or mother wavelet, which has limited support in both time and frequency domains, and realizes the function of simultaneous localization in time and frequency domains. The mother wavelet Ψt is stretched and shifted, and its expression is
(4)ψa,bt=1aψt−ba.Figure 1
Approximate extraction diagram of frequency domain approximate extraction algorithm.It can be seen from formula (2) that not only t is a continuous variable, but also a and b are continuous variables, so the above formula is called continuous wavelet transform (CWT). Let the Fourier transform of Ψt be ΨΩ. According to the properties of the Fourier transform, the wavelet basis function, the Fourier transform ofΨa,btis
(5)ψa,bt=1aψt−ba,FTΨa,bΩ=aΨaΩe−jΩb.The frequency domain expression of wavelet transform is(6)WTxa,b=a2π∫−∞+∞XΩΨ∗aΩejΩbdΩ=a2π<XΩ,Ψa,bΩ>.In the time-domain and frequency domain definitions of wavelet transform (1), a, b, and t are all continuous variables, but when implemented on a computer, the operation of continuous variables cannot be realized, so the continuous variables need to be discrete and converted into a form that can be calculated by a computer. If the scale factor a is discretized as a=2j, j∈Z, the wavelet realized by this discretization is called binary wavelet [19]. The scale factor jump of binary wavelet is too large, and it is too rough to realize time-frequency analysis, so it is still necessary to use continuous wavelet transform to realize the function of time-frequency analysis. According to the time-domain definition of wavelet transform, let
(7)ht=ψ∗−ta.Then, there are(8)hb−t=ψ∗t‐ba.Then, the time-domain definition of wavelet transform can be transformed into(9)WTxa,b=1a∫xtψ∗t−badt=1a∫xthb−tdt=1axb∗hb.According to formula (9), the integral expression can be transformed into the convolution expression commonly used in digital signal processing. At the same time, the continuous wavelet transform time-domain expression is discretized; let
(10)WTxa,b=1a∫xtψ∗t−badt=∑k1a∫kk+1xtψ∗t−badt.Since the continuous variablet is in the interval k~k+1, xt=xk, the above formula can be rewritten as
(11)WTxa,b=1a∫xtψ∗t−badt=∑k1axk∫kk+1ψ∗t−badt=∑k1axk∫−∞k+1ψ∗t−badt−∫−∞k+1ψ∗t−badt.In the same way, the frequency domain expression of wavelet transform is discretized, and the expression is as follows:(12)WTxa,k=a2π∑m=−M/2M/2X2πMmΨ∗2πMamej2π/Mkm,m=0,1,⋯,M−1.At different scales, the relationship between the center frequencyfa of the corresponding wavelet basis function and the center frequency fc of the basic wavelet Ψt is
(13)fa=fca.The sampling rate of the analyzed signalxn is fs, and the pseudofrequency feq of the analyzed signal under the corresponding scale a is
(14)feq=fs⋅fa=fs⋅f0a.Thus, there is a relationship between scale and pseudofrequency as(15)a=fs⋅f0feq.


### 3.2. Visual Image Recognition of Wushu Sanda Whip Leg Action

Set the empirical scale function of Wushu Sanda whip leg action, and use the gradient descent method to segment the region of Wushu Sanda whip leg action image, so that the sparse feature values of the visual image of Wushu Sanda whip leg action meet the conditions. According to the sparse prior representation result, the empirical scale function and the empirical wavelet function are established to calculate the segmentation function of the visual image of Wushu Sanda whip leg action. Template matching of visual images of Wushu Sanda whip leg action is based on approximate sparse representation. Combined with the three-dimensional translation matrix feature decomposition method to perform feature segmentation and edge contour feature detection of the visual image of Wushu Sanda whip leg movement, construct at least four sets of two-dimensional images for visual reconstruction of Wushu Sanda whip leg movement, and calculate the visual image of Wushu Sanda whip leg movement. For the local prior pixel set, using the morphological knowledge to carry out the visual decomposition of Wushu Sanda whip leg movement, establish a visual feature analysis and adaptive feature extraction model of Wushu Sanda whip leg movement, and realize the Wushu Sanda whip leg movement visual feature extraction results according to the results of Wushu Sanda whip leg movement and Sanda whip leg action visual image recognition.


## 3.1. Time-Frequency Analysis of Wavelet Transform

Wavelet can track time and frequency information. It can “look close” to short-time pulses or “look far” to detect long-time slow waves. There are two functions that play a very important role in wavelet analysis, i.e., scale function and wavelet function. These two functions generate a set of function families that can be used to decompose and reconstruct signals. The time-frequency analysis method can process and analyze the signal from the time-frequency dimension at the same time, avoiding the limitations of pure time-domain or frequency analysis. The emergence of the time-frequency analysis method solves the problem that Fourier transform can only analyze the signal from the frequency domain, and provides a new method for the field of signal analysis. STFT and wavelet transform are two typical time-frequency analysis methods, which are also implemented in the acquisition system. These two methods have their own advantages and disadvantages. Different time-frequency analysis methods can be selected under different requirements. This paper mainly introduces the time-frequency realization based on wavelet transform, and the content of STFT is only briefly introduced. The definition formula of STFT is as follows:(1)STFTxt,Ω=∫xτg∗τ−te−jΩτdτ=<xτ,gτ−tejΩτ>.Among them,xτ is the analysis signal, and gτ is the window function. The basic idea of the STFT algorithm is to use the local characteristics of the window function gτ; taking a rectangular window as an example, multiply the signal to be analyzed by the window function to achieve local interception of the signal, and use the Fourier transform to obtain the corresponding current timet, spectrum of the segment signal. In order to obtain a complete time-frequency relationship, by changing the center position t of the window function through constant translation, that is, changing the time center of the window function analysis, the corresponding frequency spectrum at different times can be determined, thus forming the relationship between timetand frequencyΩ, time-frequency relationship diagram.Wavelet transform is widely used in digital signal processing and has important applications in filtering, denoising, compression, time-frequency analysis, and so on. The definition of wavelet transform is(2)WTxa,b=1a∫xtψ∗t−badt=∫xtψa,b∗tdt=<xt,ψa,bt>.Among them,xt is the analysis signal, Ψt is the basic wavelet function, and Ψa,btis the wavelet basis function, which is obtained by translating and scaling the basic wavelet function Ψt. Its frequency domain expression is
(3)WTxa,b=a2π∫−∞+∞XΩΨ∗aΩejΩbdΩ.The “wavelet” in the wavelet transform indicates that the wavelet functionΨt has volatility. With the change of time, the waveform exhibits the form of oscillation, and the waveform is attenuated as a whole, and it is a band-limited signal in the time domain; its support range is limited. At the same time, the wavelet function behaves as a band-pass filter in the frequency domain; it only allows the signal within the passband to pass and suppresses the frequency components of the signal outside the passband, and its frequency domain support range is also limited (Figure 1). Such a wavelet function Ψt is called basic wavelet or mother wavelet, which has limited support in both time and frequency domains, and realizes the function of simultaneous localization in time and frequency domains. The mother wavelet Ψt is stretched and shifted, and its expression is
(4)ψa,bt=1aψt−ba.Figure 1
Approximate extraction diagram of frequency domain approximate extraction algorithm.It can be seen from formula (2) that not only t is a continuous variable, but also a and b are continuous variables, so the above formula is called continuous wavelet transform (CWT). Let the Fourier transform of Ψt be ΨΩ. According to the properties of the Fourier transform, the wavelet basis function, the Fourier transform ofΨa,btis
(5)ψa,bt=1aψt−ba,FTΨa,bΩ=aΨaΩe−jΩb.The frequency domain expression of wavelet transform is(6)WTxa,b=a2π∫−∞+∞XΩΨ∗aΩejΩbdΩ=a2π<XΩ,Ψa,bΩ>.In the time-domain and frequency domain definitions of wavelet transform (1), a, b, and t are all continuous variables, but when implemented on a computer, the operation of continuous variables cannot be realized, so the continuous variables need to be discrete and converted into a form that can be calculated by a computer. If the scale factor a is discretized as a=2j, j∈Z, the wavelet realized by this discretization is called binary wavelet [19]. The scale factor jump of binary wavelet is too large, and it is too rough to realize time-frequency analysis, so it is still necessary to use continuous wavelet transform to realize the function of time-frequency analysis. According to the time-domain definition of wavelet transform, let
(7)ht=ψ∗−ta.Then, there are(8)hb−t=ψ∗t‐ba.Then, the time-domain definition of wavelet transform can be transformed into(9)WTxa,b=1a∫xtψ∗t−badt=1a∫xthb−tdt=1axb∗hb.According to formula (9), the integral expression can be transformed into the convolution expression commonly used in digital signal processing. At the same time, the continuous wavelet transform time-domain expression is discretized; let
(10)WTxa,b=1a∫xtψ∗t−badt=∑k1a∫kk+1xtψ∗t−badt.Since the continuous variablet is in the interval k~k+1, xt=xk, the above formula can be rewritten as
(11)WTxa,b=1a∫xtψ∗t−badt=∑k1axk∫kk+1ψ∗t−badt=∑k1axk∫−∞k+1ψ∗t−badt−∫−∞k+1ψ∗t−badt.In the same way, the frequency domain expression of wavelet transform is discretized, and the expression is as follows:(12)WTxa,k=a2π∑m=−M/2M/2X2πMmΨ∗2πMamej2π/Mkm,m=0,1,⋯,M−1.At different scales, the relationship between the center frequencyfa of the corresponding wavelet basis function and the center frequency fc of the basic wavelet Ψt is
(13)fa=fca.The sampling rate of the analyzed signalxn is fs, and the pseudofrequency feq of the analyzed signal under the corresponding scale a is
(14)feq=fs⋅fa=fs⋅f0a.Thus, there is a relationship between scale and pseudofrequency as(15)a=fs⋅f0feq.


## 3.2. Visual Image Recognition of Wushu Sanda Whip Leg Action

Set the empirical scale function of Wushu Sanda whip leg action, and use the gradient descent method to segment the region of Wushu Sanda whip leg action image, so that the sparse feature values of the visual image of Wushu Sanda whip leg action meet the conditions. According to the sparse prior representation result, the empirical scale function and the empirical wavelet function are established to calculate the segmentation function of the visual image of Wushu Sanda whip leg action. Template matching of visual images of Wushu Sanda whip leg action is based on approximate sparse representation. Combined with the three-dimensional translation matrix feature decomposition method to perform feature segmentation and edge contour feature detection of the visual image of Wushu Sanda whip leg movement, construct at least four sets of two-dimensional images for visual reconstruction of Wushu Sanda whip leg movement, and calculate the visual image of Wushu Sanda whip leg movement. For the local prior pixel set, using the morphological knowledge to carry out the visual decomposition of Wushu Sanda whip leg movement, establish a visual feature analysis and adaptive feature extraction model of Wushu Sanda whip leg movement, and realize the Wushu Sanda whip leg movement visual feature extraction results according to the results of Wushu Sanda whip leg movement and Sanda whip leg action visual image recognition.


## 4. Results and Analysis

### 4.1. Time-Frequency Domain Wavelet Spectral Refinement

For the basic wavelet expressed in the time domain, after the basic wavelet function can be discretized, the result in the frequency domain can be calculated by using the DFT operation. The time-domain waveform is shown in Figure2.Figure 2
The scaling of the basic wavelet and the influence of parametersa and b on the time-frequency domain.Starting from the band-pass nature of the wavelet function spectrum, most of the DFT results are zero, and only the value of the band-pass part has practical significance. First, select the threshold value of the band-pass part, which determines the frequency range of the band-pass part of the wavelet transform. The larger the value is, the smaller the range of the band-pass part is selected, and the lower the calculation accuracy is. After a large number of reliable experiments, it is found that the threshold value is selected as 1% of the absolute value of the maximum wavelet spectrum, which can ensure that the information of the wavelet band-pass part is preserved, and the accuracy of the wavelet transform result is better. Figure3 shows the spectrum of the complex Morlet wavelet (both bandwidth and center frequency are 3), in which the curve represents the spectrum obtained by FFT operation on the time-domain sampled signal, and the two points represent the selection under the condition that the threshold is 1%.Figure 3
Wavelet basis function FFT and band-pass limit diagram.According to the above steps, the band-pass part of the spectrum of the complex Morlet wavelet is refined, and the bandwidth factor and the center frequency factor are both 3, as shown in Figure4, which is the time-domain expression wavelet spectrum refinement diagram, in which the hollow circle is the result of the wavelet basis function FFT operation, the hexagonal star points are the left and right boundaries of the wavelet band pass corresponding to the threshold, and the curve is after the refinement. It can be seen from the figure that the refined spectrum is smoother and its frequency resolution is better. For the frequency domain wavelet, since its frequency domain expression is known, the frequency domain expression can be directly discretized, and then, according to the selected threshold, the left and right boundaries of the frequency domain band-pass part of the wavelet are selected, which are consistent with the time domain. The method is the same; only the part on the positive half-axis of the frequency is judged for the band-pass part; after the frequency boundary of the band-pass part is obtained, the part within the boundary is refined by the target number of N points, so as to obtain the band-pass part. As the basic theory of analyzing and involving digital control system, discrete system theory develops rapidly. In the performance analysis of high-order systems, it is difficult to apply the time-domain analysis method. The frequency domain analysis method is mainly applicable to linear time-varying systems. It is a practical engineering method for analyzing and designing control systems and is widely used. As shown in Figure 5, it is a complex Morlet wavelet (both bandwidth factor and center frequency factor are 3), in which the hollow circle represents the discretization of the frequency domain expression. In the obtained spectrogram, the hexagonal star points represent the two boundary values of the band-pass part selected under the condition that the threshold is 1%, the curve is the dense discretization result under the target number of points in the band-pass range, and (a) is the spectrum refinement and overview, and (b) is a detailed view of the spectral refinement.Figure 4
Refinement of time-domain wavelet spectrum by CZT algorithm.
(a)(b)Figure 5
Wavelet band-pass partial spectrogram with frequency domain expression.
(a)(b)


### 4.2. The Characteristics of Kinematics and EMG Synchronization in T1 (Preparation End) and T2 Stage (Knee Bending and Leg Raising)

According to the above parameter settings, select sample data. The data used in the experiment comes from Baidu Gallery, and there are a total of 10,000 visual pictures of some Wushu Sanda whip leg movements. The height and weight of the Sanda athletes were measured and numbered. Then, the fixed sandbags equipped with the sensor of the event group fight test instrument were whipped in place for three times. Compare the visual images of Sanda whip leg action to delete the unqualified images, select 1,000 images as the training set for this experiment, and set the image format in the database to400∗400. 1000 images were randomly divided into 5 groups of test data. In the T1 (preliminary end) stage, the knee angle of the attacking leg is 144±140, keeping the right knee flexed at a small angle, which is beneficial for the athlete to put the strong leg behind and move the footsteps quickly to give the opponent a powerful blow. In the T2 stage (bend the knee and raise the leg), after the right leg is kicked off the ground, the body is slightly tilted, the right leg is raised to the front, the knee tip is facing the front, the thigh and the trunk are about 90°, the calf is naturally drooping, and the ankle joint is naturally relaxed, and at the end of this phase, your knees are at your chest height. In the T2 stage, the hip joint velocity was 2.75±0.54 m/s, the knee joint velocity was 6.12±1.42 m/s, and the ankle joint velocity was 6.93±1.56 m/s. The hip angle was 41±90, the knee angle was 67±190, and the ankle angle was 122±110.Indicating that the completion of the knee-bend and leg-raise action mainly involves these muscles. The contribution of the muscles to the action can be seen from the size of the iEMG,rectusossae>bicepsfemoris>sartorius>gastrocnemius>tensorfascialata. Combined with the analysis of the working methods of the corresponding muscles, the knee flexion and leg raising stage is mainly the attacking leg bending and raising (near fixation), and the iliopsoas, rectus femoris, sartorius, tensor fascia lata, and pubis muscles rapidly contract to flex. Hip (thigh flexion) movement; active force of the biceps femoris, gastrocnemius, semitendinosus, semimembranosus, and gracilis to flex the knee (calf flexion). The action shows the characteristics of accelerated contraction, rapid braking, and one-step action. Muscle contraction shows the characteristics of active knee flexion and fast muscle contraction. The rapid completion and braking of the knee-bending and leg-raising action are directly related to the degree of relaxation of the calf and ankle joints. According to the analysis, the calf sags naturally, the ankle joint is relaxed, and the knee joint angle can be quickly reduced when the knee is flexed, which is conducive to the rapid completion of the action. The rapid reduction of the knee joint angle reduces the radius of rotation of the attacking leg, the moment of inertia becomes smaller, the difficulty of rotation is reduced, and the rotation is completed quickly.


### 4.3. The Characteristics of Kinematics and EMG Synchronization in T3 Stage (Hip and Buckling)

Stage T3 (hip and knee) is completed on the basis of bending the knee and raising the leg; the attacking leg hip joint is internally rotated; the knee joint is turned to the left side (internal buckle), the lower leg is folded and parallel to the ground, and the instep is aligned with the attacking direction. At T3, the hip joint velocity was1.56±0.37 m/s, the knee joint velocity was 5.17±1.23 m/s, and the ankle joint velocity was 7.22±1.11 m/s. The hip angle was 51±10°, the knee angle was 95±15°, and the ankle angle was 139±19°.In the T3 stage, the contraction and discharge of the muscles of the attacking leg are mainly manifested in the tensor fascia lata (TFL), and its iEMG changes greatly. It shows that the action of raising the hip and buckling the knee is mainly completed by attacking the tensor fascia lata of the leg, and other muscles have an auxiliary role. The working method of the muscles corresponding to the action is mainly to straighten the hip and buckle the knee (near fixation). From the technical point of view of the movement, straightening the hips makes the knees buckle down, buckles the knees as a brake during the swing, and buckles the knees bringing a series of favorable changes. According to the principle of kinetic energy transmission, thigh braking enables energy to be transmitted from the thigh to the calf, and the mass of the calf is much lighter than that of the thigh, and the corresponding speed will increase, thereby increasing the whipping speed of the calf. In addition, the buckled knee changes the direction of the calf, increasing the effect of the horizontal strike.


### 4.4. Characteristics of Kinematics and EMG Synchronization in T4 (Strike Contact Sandbag) and T5 Stages (Return)

After the explosion, the knee is extended and the ankle is actively flexed to hit the target quickly and powerfully. In motion, when the end of the link chain is expected to generate maximum speed and force, the movement of the limb is often expressed from the proximal link to the distal loop.The segments are accelerated and braked in turn, and the speed of each segment is shown to increase sequentially from the proximal end to the distal end. The whipping action is mainly to get the maximum speed in the end link. The explanation of the sequential principle of joint activity in the general textbook “Sports Biomechanics” of the National Academy of Physical Education is as follows: the joints with large cross-sectional areas of muscles around the joints are called large joints, and vice versa. The large joints exert force first to overcome the inertia of the links and limbs and facilitate the initiation of the joints and limbs; the secondary joints exert force to facilitate the acceleration of the links and limbs in one step; the small joints exert force last to facilitate the control of the direction and range of motion. Therefore, the whip leg must strictly follow this law; otherwise, the range, speed, and strength of the movement will be limited, resulting in a decrease in the quality of the movement or failure. From this, it is not difficult for us to conclude that the order of activities of the whip leg strike is hip joint-knee joint-hip joint-knee joint-ankle joint. At T4, the hip joint velocity was1.12±0.24 m/s, the knee joint velocity was 1.26±0.31 m/s, and the ankle joint velocity was 7.13±2.21 m/s. The hip angle was 75±6°, the knee angle was 130±11°, and the ankle angle was 135±14°.During the T4 (strike contact with sandbag) stage, the changes in the integral EMG values of the vastus lateralis (VL), vastus medialis (VM), rectus femoris (RF), and gastrocnemius (GC) muscles of the attacking leg were very obvious, especially the role of the quadriceps which shows that the quality of the striking action is mainly closely related to the quadriceps. EMG changes combined with action analysis, the quadriceps femoris contraction completes the knee extension action (near fixation), the calf triceps contraction completes the ankle joint foot flexion action, and the knee is actively and quickly buckled before the whiplash to obtain a higher right knee acceleration. That is to say, the movement of the calf is based on the noninertial reference frame of the thigh; that is, the calf is rotated forward around the thigh axis by the moment of its center of mass under the action of the inertial force from the front and upper direction of the thigh on the knee joint, thereby forming a hitting action. During the whole whipping process, bend the hips, raise the knees, turn the body to straighten the waist, buckle the knees, and drive the calves to whip the inside, front, and top. The speed and strength of the movement are closely related to the contraction speed of the agonist muscle and the relaxation degree of the antagonist muscle. Active contraction of the agonist muscle accelerates the movement, while the antagonist muscle acts as a hindrance. The ability to relax muscles can reduce the negative confrontation between muscles and improve the speed of movement. When the active muscle group is contracted hard, the antagonistic muscle group is relaxed in a timely manner, which can reduce the resistance of the antagonistic muscle group and increase the contraction speed and strength of the active muscle group, and the movement becomes faster, and the strike is more powerful. In the T5 stage, the athlete should quickly move the center of gravity forward; the right leg (attacking leg) should fall forward, master the balance of the body after the attack, and prepare for the next defensive action or the next offensive action. When restoring the posture, the knee joint angle is152±7°. Therefore, in the restoration phase, the athlete should keep the included angle of the two knees at about 150° and keep the two knees in a slightly flexed state, which is conducive to the athlete’s quick start and rapid entry into the T1 stage.


### 4.5. Displacement and Velocity Characteristics during Action Period

The movement displacement of the attacking foot is measured in Figure6. The comparison found that the movement displacement of the 2 groups was in the same direction at all time periods, but there were differences in magnitude. The excellent group had a leftward displacement of 0.46±0.19 m during the hitting period and a backward displacement of 0.45±0.08 m during the recovery period, which was larger than that of the ordinary group. The upward displacement of the normal group (1.22±0.10 m) in the recovery period was larger than that of the excellent group, and there was a statistically significant difference. Figure 6 shows the t-test diagram of the applied displacement.Figure 6
t-test plot of action displacement.The action time of the attack was measured (Figure7). The comparison found that the action time of the 2 groups was different in all periods. The action time of the excellent group was 0.32±0.05 s relatively short in the start-up period, and there was a statistically significant difference.Figure 7
t-test plot of action time.


## 4.1. Time-Frequency Domain Wavelet Spectral Refinement

For the basic wavelet expressed in the time domain, after the basic wavelet function can be discretized, the result in the frequency domain can be calculated by using the DFT operation. The time-domain waveform is shown in Figure2.Figure 2
The scaling of the basic wavelet and the influence of parametersa and b on the time-frequency domain.Starting from the band-pass nature of the wavelet function spectrum, most of the DFT results are zero, and only the value of the band-pass part has practical significance. First, select the threshold value of the band-pass part, which determines the frequency range of the band-pass part of the wavelet transform. The larger the value is, the smaller the range of the band-pass part is selected, and the lower the calculation accuracy is. After a large number of reliable experiments, it is found that the threshold value is selected as 1% of the absolute value of the maximum wavelet spectrum, which can ensure that the information of the wavelet band-pass part is preserved, and the accuracy of the wavelet transform result is better. Figure3 shows the spectrum of the complex Morlet wavelet (both bandwidth and center frequency are 3), in which the curve represents the spectrum obtained by FFT operation on the time-domain sampled signal, and the two points represent the selection under the condition that the threshold is 1%.Figure 3
Wavelet basis function FFT and band-pass limit diagram.According to the above steps, the band-pass part of the spectrum of the complex Morlet wavelet is refined, and the bandwidth factor and the center frequency factor are both 3, as shown in Figure4, which is the time-domain expression wavelet spectrum refinement diagram, in which the hollow circle is the result of the wavelet basis function FFT operation, the hexagonal star points are the left and right boundaries of the wavelet band pass corresponding to the threshold, and the curve is after the refinement. It can be seen from the figure that the refined spectrum is smoother and its frequency resolution is better. For the frequency domain wavelet, since its frequency domain expression is known, the frequency domain expression can be directly discretized, and then, according to the selected threshold, the left and right boundaries of the frequency domain band-pass part of the wavelet are selected, which are consistent with the time domain. The method is the same; only the part on the positive half-axis of the frequency is judged for the band-pass part; after the frequency boundary of the band-pass part is obtained, the part within the boundary is refined by the target number of N points, so as to obtain the band-pass part. As the basic theory of analyzing and involving digital control system, discrete system theory develops rapidly. In the performance analysis of high-order systems, it is difficult to apply the time-domain analysis method. The frequency domain analysis method is mainly applicable to linear time-varying systems. It is a practical engineering method for analyzing and designing control systems and is widely used. As shown in Figure 5, it is a complex Morlet wavelet (both bandwidth factor and center frequency factor are 3), in which the hollow circle represents the discretization of the frequency domain expression. In the obtained spectrogram, the hexagonal star points represent the two boundary values of the band-pass part selected under the condition that the threshold is 1%, the curve is the dense discretization result under the target number of points in the band-pass range, and (a) is the spectrum refinement and overview, and (b) is a detailed view of the spectral refinement.Figure 4
Refinement of time-domain wavelet spectrum by CZT algorithm.
(a)(b)Figure 5
Wavelet band-pass partial spectrogram with frequency domain expression.
(a)(b)


## 4.2. The Characteristics of Kinematics and EMG Synchronization in T1 (Preparation End) and T2 Stage (Knee Bending and Leg Raising)

According to the above parameter settings, select sample data. The data used in the experiment comes from Baidu Gallery, and there are a total of 10,000 visual pictures of some Wushu Sanda whip leg movements. The height and weight of the Sanda athletes were measured and numbered. Then, the fixed sandbags equipped with the sensor of the event group fight test instrument were whipped in place for three times. Compare the visual images of Sanda whip leg action to delete the unqualified images, select 1,000 images as the training set for this experiment, and set the image format in the database to400∗400. 1000 images were randomly divided into 5 groups of test data. In the T1 (preliminary end) stage, the knee angle of the attacking leg is 144±140, keeping the right knee flexed at a small angle, which is beneficial for the athlete to put the strong leg behind and move the footsteps quickly to give the opponent a powerful blow. In the T2 stage (bend the knee and raise the leg), after the right leg is kicked off the ground, the body is slightly tilted, the right leg is raised to the front, the knee tip is facing the front, the thigh and the trunk are about 90°, the calf is naturally drooping, and the ankle joint is naturally relaxed, and at the end of this phase, your knees are at your chest height. In the T2 stage, the hip joint velocity was 2.75±0.54 m/s, the knee joint velocity was 6.12±1.42 m/s, and the ankle joint velocity was 6.93±1.56 m/s. The hip angle was 41±90, the knee angle was 67±190, and the ankle angle was 122±110.Indicating that the completion of the knee-bend and leg-raise action mainly involves these muscles. The contribution of the muscles to the action can be seen from the size of the iEMG,rectusossae>bicepsfemoris>sartorius>gastrocnemius>tensorfascialata. Combined with the analysis of the working methods of the corresponding muscles, the knee flexion and leg raising stage is mainly the attacking leg bending and raising (near fixation), and the iliopsoas, rectus femoris, sartorius, tensor fascia lata, and pubis muscles rapidly contract to flex. Hip (thigh flexion) movement; active force of the biceps femoris, gastrocnemius, semitendinosus, semimembranosus, and gracilis to flex the knee (calf flexion). The action shows the characteristics of accelerated contraction, rapid braking, and one-step action. Muscle contraction shows the characteristics of active knee flexion and fast muscle contraction. The rapid completion and braking of the knee-bending and leg-raising action are directly related to the degree of relaxation of the calf and ankle joints. According to the analysis, the calf sags naturally, the ankle joint is relaxed, and the knee joint angle can be quickly reduced when the knee is flexed, which is conducive to the rapid completion of the action. The rapid reduction of the knee joint angle reduces the radius of rotation of the attacking leg, the moment of inertia becomes smaller, the difficulty of rotation is reduced, and the rotation is completed quickly.


## 4.3. The Characteristics of Kinematics and EMG Synchronization in T3 Stage (Hip and Buckling)

Stage T3 (hip and knee) is completed on the basis of bending the knee and raising the leg; the attacking leg hip joint is internally rotated; the knee joint is turned to the left side (internal buckle), the lower leg is folded and parallel to the ground, and the instep is aligned with the attacking direction. At T3, the hip joint velocity was1.56±0.37 m/s, the knee joint velocity was 5.17±1.23 m/s, and the ankle joint velocity was 7.22±1.11 m/s. The hip angle was 51±10°, the knee angle was 95±15°, and the ankle angle was 139±19°.In the T3 stage, the contraction and discharge of the muscles of the attacking leg are mainly manifested in the tensor fascia lata (TFL), and its iEMG changes greatly. It shows that the action of raising the hip and buckling the knee is mainly completed by attacking the tensor fascia lata of the leg, and other muscles have an auxiliary role. The working method of the muscles corresponding to the action is mainly to straighten the hip and buckle the knee (near fixation). From the technical point of view of the movement, straightening the hips makes the knees buckle down, buckles the knees as a brake during the swing, and buckles the knees bringing a series of favorable changes. According to the principle of kinetic energy transmission, thigh braking enables energy to be transmitted from the thigh to the calf, and the mass of the calf is much lighter than that of the thigh, and the corresponding speed will increase, thereby increasing the whipping speed of the calf. In addition, the buckled knee changes the direction of the calf, increasing the effect of the horizontal strike.


## 4.4. Characteristics of Kinematics and EMG Synchronization in T4 (Strike Contact Sandbag) and T5 Stages (Return)

After the explosion, the knee is extended and the ankle is actively flexed to hit the target quickly and powerfully. In motion, when the end of the link chain is expected to generate maximum speed and force, the movement of the limb is often expressed from the proximal link to the distal loop.The segments are accelerated and braked in turn, and the speed of each segment is shown to increase sequentially from the proximal end to the distal end. The whipping action is mainly to get the maximum speed in the end link. The explanation of the sequential principle of joint activity in the general textbook “Sports Biomechanics” of the National Academy of Physical Education is as follows: the joints with large cross-sectional areas of muscles around the joints are called large joints, and vice versa. The large joints exert force first to overcome the inertia of the links and limbs and facilitate the initiation of the joints and limbs; the secondary joints exert force to facilitate the acceleration of the links and limbs in one step; the small joints exert force last to facilitate the control of the direction and range of motion. Therefore, the whip leg must strictly follow this law; otherwise, the range, speed, and strength of the movement will be limited, resulting in a decrease in the quality of the movement or failure. From this, it is not difficult for us to conclude that the order of activities of the whip leg strike is hip joint-knee joint-hip joint-knee joint-ankle joint. At T4, the hip joint velocity was1.12±0.24 m/s, the knee joint velocity was 1.26±0.31 m/s, and the ankle joint velocity was 7.13±2.21 m/s. The hip angle was 75±6°, the knee angle was 130±11°, and the ankle angle was 135±14°.During the T4 (strike contact with sandbag) stage, the changes in the integral EMG values of the vastus lateralis (VL), vastus medialis (VM), rectus femoris (RF), and gastrocnemius (GC) muscles of the attacking leg were very obvious, especially the role of the quadriceps which shows that the quality of the striking action is mainly closely related to the quadriceps. EMG changes combined with action analysis, the quadriceps femoris contraction completes the knee extension action (near fixation), the calf triceps contraction completes the ankle joint foot flexion action, and the knee is actively and quickly buckled before the whiplash to obtain a higher right knee acceleration. That is to say, the movement of the calf is based on the noninertial reference frame of the thigh; that is, the calf is rotated forward around the thigh axis by the moment of its center of mass under the action of the inertial force from the front and upper direction of the thigh on the knee joint, thereby forming a hitting action. During the whole whipping process, bend the hips, raise the knees, turn the body to straighten the waist, buckle the knees, and drive the calves to whip the inside, front, and top. The speed and strength of the movement are closely related to the contraction speed of the agonist muscle and the relaxation degree of the antagonist muscle. Active contraction of the agonist muscle accelerates the movement, while the antagonist muscle acts as a hindrance. The ability to relax muscles can reduce the negative confrontation between muscles and improve the speed of movement. When the active muscle group is contracted hard, the antagonistic muscle group is relaxed in a timely manner, which can reduce the resistance of the antagonistic muscle group and increase the contraction speed and strength of the active muscle group, and the movement becomes faster, and the strike is more powerful. In the T5 stage, the athlete should quickly move the center of gravity forward; the right leg (attacking leg) should fall forward, master the balance of the body after the attack, and prepare for the next defensive action or the next offensive action. When restoring the posture, the knee joint angle is152±7°. Therefore, in the restoration phase, the athlete should keep the included angle of the two knees at about 150° and keep the two knees in a slightly flexed state, which is conducive to the athlete’s quick start and rapid entry into the T1 stage.


## 4.5. Displacement and Velocity Characteristics during Action Period

The movement displacement of the attacking foot is measured in Figure6. The comparison found that the movement displacement of the 2 groups was in the same direction at all time periods, but there were differences in magnitude. The excellent group had a leftward displacement of 0.46±0.19 m during the hitting period and a backward displacement of 0.45±0.08 m during the recovery period, which was larger than that of the ordinary group. The upward displacement of the normal group (1.22±0.10 m) in the recovery period was larger than that of the excellent group, and there was a statistically significant difference. Figure 6 shows the t-test diagram of the applied displacement.Figure 6
t-test plot of action displacement.The action time of the attack was measured (Figure7). The comparison found that the action time of the 2 groups was different in all periods. The action time of the excellent group was 0.32±0.05 s relatively short in the start-up period, and there was a statistically significant difference.Figure 7
t-test plot of action time.


## 5. Conclusion

The conclusions of this paper are as follows: in the preparation stage, the knee joint angle of the attacking leg is about 140°, which is conducive to rapid movement. Bend your knees, lift your legs, straighten your hips, bend your knees, and hit the ball at three stages of speed, 135° change. In the return phase, the knee joint angle is about 150° and slightly bent. The angle of each joint in each stage should be kept as much as possible in order to achieve better results in fast motion training. In the knee flexion and leg lifting stage, rectus abdominis, sartorius, tensor fascia lata, biceps, and gastrocnemius participate in the contraction, and the EMG contribution isrectus>femoralhead>sartorius>gastrocnemius>latissimusmembranetensor. The stage of straightening the hips and flexing the knees is mainly completed by the tensor fascia lata. In the striking stage, there are mainly the iEMG of the lateral femoris, medial femoris, rectus femoris, and gastrocnemius, especially the quadriceps femoris. Fast motion exercises should mainly develop these muscles and pay attention to the sequence of their use. In the process of whip leg movement, a reasonable compensatory movement is formed through the adjustment of the body center of gravity to maintain the stability of the body. It can not only improve the quality of action completion but also help to maintain the consistency of each action link in the whip leg movement. The moving distance of the body center of gravity in the attack direction reflects the depth of the attack. The internal rotation of the heel of the supporting leg and the stretching of the link are two of the important factors to adjust the striking distance of the whip leg.



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*Source: 1004568-2022-09-24.xml*