Computer-Visualized Sound Parameter Analysis Method and Its Application in Vocal Music Teaching

Abstract

In order to improve the quality of vocal music teaching, this paper applies the computer visualization sound parameter analysis method to vocal music teaching and discusses the scheme of parametric coding. Moreover, this paper adopts the transient signal detection mechanism to divide the signal. For frames that have detected a shock signal, frequency-domain parametric differential predictive coding can be used like temporal noise shaping (TNS) techniques. In addition, based on the short-term periodicity and short-term stationarity of speech signals, an analytical synthesis model based on harmonic decomposition is proposed. Through the simulation data analysis, it can be seen that the computer visualization sound parameter analysis method proposed in this paper has a very good application effect in vocal music teaching and can improve the quality of vocal music teaching.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Vocal music teaching is not intuitive teaching; it is perceptual. Moreover, the correct singing method is mainly obtained by training, and the training must be carried out within a limited class time, which requires the teacher’s teaching language expression to be refined and accurate. Teachers need refined and accurate language expression and should be able to grasp the main contradictions in teaching, reflect the focus of teaching, solve problems in voice, prescribe the right medicine, and make complex theories simple and clear. It is common to hear such teaching prompts: sink the breath, drop the jaw, lift the laughing muscle, lower the larynx, stick to the pharyngeal wall, and so forth [1]. However, these overly specialized teaching languages often make students at a loss in the learning process. In addition, teachers often give special lectures on a certain issue in the classroom, mask the content of the explanation, or talk about vocal music theory in general. This kind of teaching phenomenon overemphasizes teachers’ self-experience and ignores students’ own cognitive ability, which often makes students feel baffled, boundless, confused, and at a loss [2]. Moreover, the expression of vocal music teaching language should be logical and should be based on lively and easy-to-understand teaching language. Refined and accurate teaching language comes from the teacher's own objective and keen hearing and also from the teacher’s own subjective teaching experience. It is the basic skill of teaching and the key to vocal music teaching. In vocal music teaching, teachers should constantly expand their knowledge and enrich and develop their own teaching language and can achieve the teaching effect of turning complexity into simplicity, abstraction into concreteness, and vagueness into vividness [3].

Vocal music teaching should follow the logical system of the subject and should make academic norms for the teaching courses. On the basis of fully understanding of the teaching, according to the step-by-step teaching objectives, the clear teaching content is formulated. Let students develop their own initiative under the premise of systematically mastering basic knowledge and basic skills [4]. In the actual teaching process, it is necessary to take into account individual differences and indeed to promote the fullest development of individuals. The middle-level education in vocal music teaching is based on acknowledging the differences in teaching objects and acknowledging the differences in the professional level of students at all levels, especially acknowledging that there are differences in teaching requirements and teaching progress in the same grade concept, which is also a prominent feature of vocal music teaching that is different from other areas of teaching [5]. Fully activate and mobilize the initiative and enthusiasm of students in their own development and be good at guiding students to use their own abilities and will to carry out creative learning [6]. The basic training of students cannot be neglected, and blind advancement and unscrupulous growth are avoided. It must be based on the systematic nature of vocal music teaching, pay attention to the logical organization of vocal music teaching materials, reflect the value of vocal music training, and pay attention to the internal connection between stages [7]. Vocal music teaching must follow the laws of educational practice, grasp the principles of vocal music teaching, formulate clear teaching guidelines and professional specifications based on the objective and practical conditions of vocal music teaching, and form a scientific and reasonable standardized system [8]. Vocal music teaching should pay attention to the principle of doing what is within one’s capacity and progressing step by step and insist on conducting professional training and theoretical teaching steadily. At the same time, it is necessary to make the teaching of students go in front of the development of students. In vocal music teaching, it is necessary to insist on the assessment principle that students are graded from low to high; scientific and effective teaching steps and reasonable teaching progress can make teaching achieve the expected teaching effect [9]. At the same time, the concept of seeking truth from facts and hierarchical education cannot be ignored. This makes it more difficult to formulate teaching standards. For a long time, people have thought that the standard of art itself is a relatively comparative thing, and there is no absolutely unified standard [10]. Especially in vocal music art, it is impossible to measure right and wrong with specific standards. There is still a perception that the benevolent sees the benevolence and the wise sees the wisdom. Therefore, the long-standing artistic standards have been formulated relatively broadly and vaguely. Although, in teaching, we can have a unified understanding of the standards of voice conditions, accurate intonation, beautiful timbre, deep breathing, clear articulation, and everyone’s feeling and receptive ability to music, because of differences in the quality and aesthetics of teachers, the standards will vary from person to person [11]. The hierarchical education of vocal music teaching makes the teaching have more clear progress standards and specifications and forms a system that can guide students to learn step by step. Moreover, such teaching objectives are clearer and more pertinent, and the determination of relevant teaching content, the selection of teaching methods, and the organization of teaching activities are more meaningful [12].

Learning vocal music begins with the imitation of sound. Personalization is an important feature of vocal music teaching. Such techniques are easy to imitate but not easy to describe. Although the theory of a discipline requires logical and normative language expressions, as an individual imitation process, it can rely on another set of auxiliary languages [13]. In fact, in the process of vocal music teaching, there has always been a set of body language, and each vocal music teacher has a set of habitual gestures, which are the teacher’s popular expression of singing methods. Most of the students will experience and remember these sign language actions in unconscious imitation [14]. For example, when the teacher asks to open the inner mouth and lower the position of the larynx, along with the elaboration of these concepts and themes, the teacher will use the suggestive language “yawn,” “sigh down,” “suck and sing,” and so forth and attach corresponding mouth movements and gestures. These habitual mouth shapes, gestures, or body language has the function of intuitive prompting, guidance, and emphasis. Although these habitual gestures cannot exist independently, they render a singing state in an auxiliary way and are an indispensable teaching method [15]. I am accustomed to transforming a set of words into a set of pictures. Traditional vocal music teaching cannot transform familiar words into pictures, but the development of modern science and technology has provided new conditions for today’s teaching activities. TV video brings visual images into teaching activities [16]. When students watch the opera video, the pursuit of sound quality is no longer a set of illusory language descriptions. A real timbre is displayed in a visual form, and students often even associate an imaginary sound with a specific physical movement of a famous singer. This powerful episodic memory effect is not possessed by any traditional written language and oral language. It directly points to the human heart and enables vocal imitation to enter the same level as instrumental imitation. This is the material condition that vocal music teaching can make full use of in the modern language environment [17]. The progress of art history, of course, can be guided by the interpretation of language produced by theoretical changes, and the rapid development of science and technology has provided a new medium of expression for language expression. Many ancient arts that lack systematic language expression have more room to show that their semantics have not been fully exhausted than disciplines that have a set of traditional expression terms and thus limit their scope of thinking [18].

This paper uses the computer visualization sound parameter analysis method to study the effect of vocal music teaching and constructs an intelligent vocal music teaching system to improve the quality of vocal music teaching.

2. Computer Visualized Sound Parameter Analysis Method

2.1. Perceptual Domain Audio Theory

As shown in Figure 1, the encoder generally divides the audio signal into approximately stationary frames of 20–50 ms, and then the time-frequency analysis module parses out the spectrum of each frame. The role of mental model analysis is to obtain some information from time-frequency analysis. For example, it obtains the allowable quantization error of each frequency band according to the masking effect in the frequency domain and determines the time-domain and frequency-domain resolution requirements according to the stationarity of the signal, and so on.

[figure(s) omitted; refer to PDF]

In this paper, the limit of “transparent” encoding is determined from the receptive field theory, and a simplified algorithm for specific implementation is given. Before that, this paper introduces a concept of sound pressure, which is defined as$$\begin{array}{}\text{(1)}& L_{SPL}=20Lo{g}_{10}\frac{p}{p_0}dB.\end{array}$$

SPL is the abbreviation of Sound Pressure Level, that is, sound pressure; p is the pressure generated by the sound source excitation, and Pascal is the unit; $p_0$ is the reference pressure, which is $20\mu Pa$. The sound pressure range that the human ear can perceive ranges from almost imperceptible subtle sounds to tingling, about 0 to 150 dB.

The absolute hearing threshold refers to the minimum sound pressure of a single frequency audio information that the human ear can perceive in a noise-free environment. By definition, this threshold varies with frequency. The absolute hearing threshold is approximated as$$\begin{array}{}\text{(2)}& T_{\text{quiet}}f=3.64{\frac{f}{1000}}^{-0.8}-6.5e^{-0.6{f/1000-3.3}^2}+{10}^{-3}{\frac{f}{1000}}^{4}dB.\end{array}$$

In order to facilitate the analysis, considering the exponential characteristics of the human ear’s sensitivity to frequency, the following concept is proposed to redistribute the 20 Hz to 20 kHz that the human ear can perceive into Bark units:$$\begin{array}{}\text{(3)}& zf=13\arctan 0.00076f+3.5\arctan {\frac{f}{7500}}^2\text{Bark}.\end{array}$$

A notable consequence of this classification is that the low-frequency region has a higher-frequency-domain resolution but a narrower bandwidth, while the high-frequency region has a wider band and lower-frequency-domain resolution. This paper proposes a modification to the nonlinear expression in formula (3) and obtains the expression method of the easy inverse function:$$\begin{array}{}\text{(4)}& \begin{array}{c}zf=7{\sinh }^{-1}\frac{f}{650},\\ fz=650\sinh \frac{z}{7}.\end{array}\end{array}$$

The masking between frequency bands is different from the above-mentioned three types of masking effects in that it acts between different frequency bands, rather than being limited to a single frequency band. This predictable masking effect of a certain frequency band on adjacent frequency bands is often represented by a class of convolution functions between frequency bands in perceptual domain analysis:$$\begin{array}{}\text{(5)}& S{F}_{dB}x=15.81+7.5x+0.474-17.5\sqrt{1+{x+0.474}^2}dB.\end{array}$$

Since it is a convolution between frequency bands, the unit of x is Bark, and the unit of SF is dB.

The general masking threshold calculation sequence is to first convolve the energy of each frequency band and then divide it into musical and noise components according to the special design of the audio in each frequency band and calculate the thresholds of noise masking musical tone and musical tone masking noise.$$\begin{array}{}\text{(6)}& \begin{array}{c}T{H}_N=E_T-14.5-B,\\ T{H}_T=E_N-K.\end{array}\end{array}$$

In the above formula, $T{H}_N$ and $T{H}_T$ represent the thresholds of tone masking noise and noise masking tone, respectively, $E_N$ and $E_T$ are the energy of noise and tone, and B represents the frequency band number. Now, the amplitude of the signal is reduced in the time domain; that is, a gain value is extracted to correctly restore the original signal at the decoding end. Because the energy of the burst signal is reduced, the original nonstationary audio frame is more approximately stationary, and then it is used as a stationary signal for time-frequency analysis to obtain parameters for encoding, as shown in Figure 2 for details.

[figure(s) omitted; refer to PDF]

For detected frames with impulsive signals, differential predictive coding of frequency domain parameters similar to Temporal Noise Shaping (TNS) techniques can be used. The principle of this de-“pre-echo” algorithm is shown in Figure 3.

[figure(s) omitted; refer to PDF]

The number of bits required for encoding is$$\begin{array}{}\text{(7)}& PE={\displaystyle \sum _{i=1}^{25}{\displaystyle \sum _{m=b{l}_i}^{bh}{\log }_{2}2n\mathrm{int}\frac{\mathrm{Re}\omega }{\sqrt{6T_i/k_i}}+1+{\log }_{2}2n\mathrm{int}\frac{\mathrm{Im}\omega }{\sqrt{6T_i/k_i}}+1}}.\end{array}$$

In the above formula, k_i represents the number of frequency parameters in this frequency band, and n int is the rounding operator.

Doing frequency-domain analysis FFT is well understood. The reason for normalization is that if the absolute silence 0 dB at 4 kHz is used for representation. The harmonic energy that can be represented by the largest 16-bit PCM can be calculated as$$\begin{array}{}\text{(8)}& 20\times {\log }_{10}\frac{2^{16}}{2^0}=20\times 15\times {\log }_{10}2=90.3090dB.\end{array}$$

However, if PCM is 8 bits, it is only about 45 dB. The so-called normalization means that if the encoder is to be suitable for PCM of any number of bits, the following processing must be done:$$\begin{array}{}\text{(9)}& xn=\frac{sn}{N{2}^{b-1}}.\end{array}$$

In the above formula, N is the window length of the FFT, b is the number of bits of the PCM, which is assumed to be 16 here, and s(n) is the source signal obtained by sampling. The maximum energy in the frequency domain of x(n) is 0 dB, which is the sequence we will do frequency-domain analysis and processing. Then, a 512-point FFT was done with a 1/16 crossed Hanning window. It is defined as follows:$$\begin{array}{c}\text{(10)}& Pk=PN+20{\log }_{10}{\displaystyle \sum _{n=0}^{N-1}\omega nxn{e}^{-j\frac{2\pi kn}{N}}},0\le k\le \frac{N}{2},\begin{array}{c}PN+90.302dB\\ \omega n=\frac{1}{2}1-\cos \frac{2\pi n}{N}.\end{array}.\end{array}$$

Such normalization and the choice of parameter PN make P(k) obtained by the audio signal after FFT limited to 0–90 dB. Then, the job is to simply distinguish the musical tones from the noise components. If the maximum value in the spectrum is more than 7 dB greater than the frequency energy in a given range nearby, it is regarded as the signal part of the musical sound; otherwise, it is noise. In mathematical language, it is$$\begin{array}{}\text{(11)}& S_{\text{Tonal}}=Pk|Pk>Pk+1,Pk>Pk+{\Delta }_k+7dB.\end{array}$$

The masking source of a musical tone is regarded as the energy superposition of 3 adjacent frequency-domain parameter values:$$\begin{array}{}\text{(12)}& P_{\text{Tonal}}k=10{\log }_{10}{\displaystyle \sum _{j=-1}^1{10}^{0.1Pk+j}}.\end{array}$$

The remaining part other than ${\mathrm{\Delta }}_k$ defined in formula (12) is regarded as a masking source of noise, and its energy is combined as$$\begin{array}{}\text{(13)}& P_{\text{Noise}}\overline{k}=10{\log }_{10}{\sum }_j{10}^{0.1Pj}dB,\forall Pj\notin P_{\text{Tonal}}k,k\pm 1,k\pm {\Delta }_k.\end{array}$$

$\overline{k}$ is the geometric mean of all j. Considering the exponential sensitivity of the human ear to frequency, the geometric mean is equivalent to the arithmetic mean of the indices.

After classifying and merging the masking sources, the next thing to consider is the convolution in the frequency domain, that is, the mutual masking between frequency bands. The equivalent mathematical expressions are given here, and the necessary frequency-domain linear to frequency band (Bark units) conversions have been made.$$\begin{array}{}\text{(14)}& \begin{array}{c}{T}_{\text{Tomal}}i,j=P_{\text{Tonal}}j-0.275zj+SFi,j-6.025dB,\\ T_{\text{Noise}}i,j=P_{\text{Noise}}j-0.175zj+SFi,j-2.025dB.\end{array}\end{array}$$

In the above formula, P_Tonal,Noise represents the energy of the masking source obtained in the above steps, the function z(j) is the frequency band that converts the linear frequency-domain parameter j to the Bark unit, and SF is the convolution between the frequency bands. $T_{\text{Tonal,Noise}}i,j$ represents the masking threshold generated by masking source j for position i in the frequency domain. It can be seen that the calculation formulas of the masking thresholds of musical and noise are different due to their different properties.

In this regard, on the basis of all the obtained $T_{\text{Tonal,Noise}}i,j$, the global masking threshold can be obtained:$$\begin{array}{}\text{(15)}& T_{\text{global}}i=10{\log }_{10}{10}^{0.1T_{q}i}+{\displaystyle \sum _{l=1}^L{10}^{0.1T_{\text{Tonal}}i,l}}+{\displaystyle \sum _{m=1}^M{10}^{0.1T_{\text{Noise}}i,m}}dB.\end{array}$$

2.2. Bit Allocation, Quantization, and Huffman Coding

The purpose of the bit allocation module is to use the global masking threshold obtained above to obtain a signal masking ratio, namely, SMR (Signal to Mask Ratio). Furthermore, it determines how many bits are required for quantization according to the formula NMR(m) = SMR − SNR(m) (dB). Among them, m represents the bits; NMR refers to the noise masking ratio, SNR refers to the signal-to-noise ratio, and the unit is dB. A demonstration of the NMR(m) = SMR − SNR(m) (dB) relationship is shown in Figure 4.

[figure(s) omitted; refer to PDF]

The task of the “Rate/Distortion Control” module shown in Figure 5 is to allocate all bit rates to the currently encoded audio frame, and the distortion generated by the quantized frequency domain parameters meets the encoding requirements in terms of sound quality.

[figure(s) omitted; refer to PDF]

2.3. Research on Parametric Audio Coding

Based on the short-term periodicity and short-term stationarity of speech signals, an analytical synthesis model based on harmonic decomposition is proposed. The block diagram of parametric audio coding of ASAC is given as a prototype of parametric waveform hybrid coding, as shown in Figure 6.

[figure(s) omitted; refer to PDF]

A common modeling of speech is to treat speech as the output of an excitation passing through a time-varying filter, where the excitation is expressed as$$\begin{array}{}\text{(16)}& et=\mathrm{Re}{\displaystyle \sum _{l=1}^{Lt}{a}_{l}t{e}^{j{\displaystyle \int {\omega }_l\sigma d\sigma +{\varphi }_l}}}.\end{array}$$

That is, it is a linear combination of some harmonics of different amplitude, frequency, and phase. The speech signal s(t) is represented by the following convolution:$$\begin{array}{}\text{(17)}& st={\displaystyle {\int }_0^{t}ht-\tau ;tet\text{d}\tau }.\end{array}$$

If the description of the time-varying filter in the frequency domain is $H\omega ;t=M\omega ;t\exp j\mathrm{\Phi }\omega ;t$, then the speech signal passing through the filter can be described as$$\begin{array}{}\text{(18)}& st={\displaystyle \sum _{l=1}^{Lt}{a}_{l}tM{\omega }_{l}t;t\exp j{\displaystyle {\int }_0^t{\omega }_l\sigma \text{d}\sigma +\mathrm{\Phi }{\omega }_{l}t;t+{\varphi }_l}}.\end{array}$$

By merging, $\begin{array}{c}{A}_{l}t=a_{l}tM{\omega }_{l}t;t\\ {\psi }_{l}t={\displaystyle {\int }_0^t{\omega }_l\sigma \text{d}\sigma }+\mathrm{\Phi }{\omega }_{l}t;t+{\varphi }_l\end{array}$and the above formula is simplified to$$\begin{array}{}\text{(19)}& st={\displaystyle \sum _{l=1}^{Lt}{A}_{l}t\exp j{\psi }_{l}t}.\end{array}$$

After adding some assumptions about the short-term stability of the signal to this expression, that is, the part ${\psi }_{l}t$ in the linearized formula (20), ${\psi }_{l}t={\omega }_{l}t+{\mathrm{\Phi }}_l+{\varphi }_l$ is obtained, and the sampled audio signal is written as$$\begin{array}{}\text{(20)}& \widehat{s}t={\displaystyle \sum _{l=1}^{L_k}{\gamma }_l^k\exp jn{\omega }_l^k}.\end{array}$$

In the above formula, ${\gamma }_l^k=A_l^k\exp j{\theta }_l^k$ integrates the information of magnitude and phase. In the sense of Least Mean Squared (LMS) error, an attempt is made to extract a set of $A_l^k,{\theta }_l^k,{\omega }_l^k$ to minimize the ${\epsilon }^k={\sum }_n{yn-\widehat{s}n}^2$ objective function. The result of the calculation is that the optimal $A_l^k,{\theta }_l^k,{\omega }_l^k$ estimate is the coefficient obtained from the DFT analysis.

2.4. Two Block Diagrams of Parametric Coding STN and an Overview of HILN

The harmonic + impact + noise model reasonably divides the signal into 3 distinct parts when coded. This paper analyzes whether the impact of the residual signal can be masked according to the mental model, to adjust the time-frequency resolution of the harmonic analysis, until the harmonic analysis cycle is terminated, and output the harmonic parameters and the frequency band energy encoding parameters of the noise part, as shown in Figure 7.

[figure(s) omitted; refer to PDF]

According to the signal segmentation method in Figure 7 and the analysis/synthesis loop of ASAC, another algorithm block diagram of STN can be constructed. Using the time-frequency-domain division of the three signal parts like Levine, the upper frequency limit is limited in the harmonic extraction loop, and the residual signal is energy envelope encoded. The final output is the encoding of a “shock” frame + the harmonic parameters of the stationary frame + the noise envelope, as shown in Figure 8. The model of the parametric audio hybrid encoder selected in this paper is shown in Figure 9.

[figure(s) omitted; refer to PDF]

2.5. Recursive Selection of Frequency Domain Coefficients

The quantitative mathematical formula is$$\begin{array}{}\text{(21)}& P_i\Delta L_{dB}=1-{10}^{-0.2K\times \Delta L_{dB}}.\end{array}$$

A set of methods for recognizing probabilities of differences in receptive fields are established. The first is to evenly set some reference points on the Bark units to define the global difference recognition probability:$$\begin{array}{}\text{(22)}& P=1-{\displaystyle \prod _{i\in D}1-P_i}=1-{10}^{-0.2K{\displaystyle \sum _{i\in D}\Delta L_{dB}^i}}.\end{array}$$

In order to minimize the recognition probability, that is, to achieve a sound quality effect that is “transparent” to the human ear, we only need to examine the ${\displaystyle \sum _{i\in D}\mathrm{\Delta }{L}_{dB}^i}$ function. This ${\displaystyle \sum _{i\in D}\mathrm{\Delta }{L}_{dB}^i}$ function is further simplified. Considering that there are a total of D reference points in the frequency domain and that the convolution excitation of the source signal must be greater than the convolution excitation generated by the comprehensive reconstruction of any set of frequency-domain parameters selected (in energy dB), the recursion ${\epsilon }_k={\displaystyle \sum _{i\in D}Ei-X_{k}i}>0$ is minimized. Greedy recursion is to choose $A_l^k,{\theta }_l^k,{\omega }_l^k$ so that each recursion of ${\epsilon }_k$ is reduced at the current maximum speed, which can be expressed mathematically as$$\begin{array}{}\text{(23)}& A_l^k,{\theta }_l^k,{\omega }_l^k=\arg \max {\epsilon }_{k-1}-{\epsilon }_k.\end{array}$$

Figure 10 shows the block diagram of minimizing ${\epsilon }_k={\displaystyle \sum _{i\in D}Ei-X_{k}i}dB>0$ in the prototype. Therefore, the selected icD is the set of frequency parameters of argmin${}^{\ast }$, which is equivalent to the set of parameters for maximizing ${\epsilon }_{k-1}-{\epsilon }_k$ in (23), but the writing method is different.

[figure(s) omitted; refer to PDF]

2.6. Shock Detection Algorithm

Impulsive signals in the time domain are a challenge to the performance of all transform encoders because they do not meet the stationary harmonic assumption and are different from simple noise. The general impact detection steps are shown in Figure 11.

[figure(s) omitted; refer to PDF]

From simple reasoning, the impulse signal is a burst of energy accumulation in the time domain, and we can guess an obvious downsampling algorithm: low-frequency filtering.$$\begin{array}{}\text{(24)}& En=\frac{1}{N}{\displaystyle \sum _{m=-N/2}^{N/2-1}xn+m\omega m}.\end{array}$$

The window function acts as a low-pass filter, which is effective for the detection of shock signals in a silent background, and uses energy instead of the absolute value; $En=1/N{\displaystyle {\sum }_{m=-N/2}^{N/2-1}{xn+m}^2\omega m}$. If the fluctuation of energy can characterize the change of the shock signal, then obviously $\text{d}\log E/\text{d}t=\text{d}E/\text{d}t/E$ is more effective, because it is a relative energy difference rather than an absolute energy difference, which is closer to the recognition ability of the human ear. Although it is a simple improvement, it greatly contributes to the accurate detection of shocks.

We assume that $X_{k}n={\displaystyle {\sum }_{m=-N/2}^{N/2-1}xnh+m\omega m}{e}^{-2/\pi mk/N}$ represents the coefficients of the k STFTs of the nth segment. Obviously, the length of h should be chosen to mask all “preechoes” even with shock. This is followed by the weighting of the spectrum X_k(n) to obtain$$\begin{array}{}\text{(25)}& En=\frac{1}{N}{\displaystyle \sum _{m=-N/2}^{N/2-1}{W}_k{X_{k}n}^2}.\end{array}$$

In the above formula, W_k is the weight. Generally speaking, the music energy of the signal is concentrated in the bass part, and the reason for the sharp change between short frames in the high-frequency part is the shock. Therefore, the detection function here should be amplified; that is, an increasing function similar to W_k is adopted. It is worth noting that $W_k=k$ is equivalent to taking the first derivative of the energy. Then, we make a difference on the set of $En,n\in D$, and if there is $En-En+1>E_{threshold}$, it is considered that there is a shock here. Masri regards formula (26) as a spectral vector and defines the following to measure the energy change between short frames:$$\begin{array}{}\text{(26)}& SDn={\displaystyle \sum _{m=-N/2}^{N/2-1}{H{X}_{k}n-X_{k}n-1}^2}.\end{array}$$

If H(x) = (x + |x|)/2, then the detector so defined is only sensitive to the shock of rising energy but not to the “negative shock” of sudden energy drop. The function defined to be continuous with $2\pi$ loop is ${\phi }_{k}n=\arg X_{k}n$. In the assumption of stationary signal, the kth component in adjacent short frames n and n + 1 frames is continuous, which can be linearly interpolated as$$\begin{array}{}\text{(27)}& f_{k}n=\frac{{\phi }_{k}n-{\phi }_{k}n-1}{2\pi h}{f}_s.\end{array}$$

Equivalently, it can also be considered that the first-order difference of ${\phi }_{k}n$ to n is constant in a short time; namely,$$\begin{array}{}\text{(28)}& {\phi }_{k}n-{\phi }_{k}n-1\approx {\phi }_{k}n-1-{\phi }_{k}n-2.\end{array}$$

In other words, the second-order backward difference is zero: $\mathrm{\Delta }{\phi }_{k}n={\phi }_{k}n-2{\phi }_{k}n-1+{\phi }_{k}n-2\approx 0$. Therefore, it is obviously only necessary to count the magnitude of the second-order difference as defined above, which is to measure the impact component. Bello gives a simple measure definition called absolute phase offset:$$\begin{array}{}\text{(29)}& {\xi }_{phase}n=\frac{1}{N}{\displaystyle \sum _{k=1}^N\Delta {\phi }_{k}n}.\end{array}$$

2.7. Concatenation of Interframe Parameters

$A_j^l,{\theta }_j^l,{\omega }_j^l,j\in D^l$ is the frequency parameter set of frame I, $\forall j\in D^l$. We examine the existence of $l\in D^{l+1},A_j^l-A_i^{l+1}<Am{p}_{threthold}j,{\omega }_j^l-{\omega }_i^{l+1}<Fre{q}_{threthold}j$, where the two thresholds change with frequency; in particular, $Fre{q}_{threthold}j$, which can be rewritten as$$\begin{array}{}\text{(30)}& z{\omega }_j^l-z{\omega }_i^{l+1}<\mathrm{0.25.}\end{array}$$

Since the audio signal is regarded as the superposition of short-term stable harmonics in the modeling of STN, the amplitude, phase, and frequency of each harmonic in a frame are regarded as constants. If it is simply reconstructed, it is as follows:$$\begin{array}{}\text{(31)}& \widehat{s}m+IH={\displaystyle \sum _{k=1}^K{A}_k^l\cos {\omega }_{k}m+{\varphi }_k},0\le m\le H,\end{array}$$

H represents the length of the frame, which should be the same length as the analysis frame. The consequence of no interpolation is a discontinuity in the sound due to abrupt changes in harmonic parameters from frame to frame.$$\begin{array}{}\text{(32)}& {\widehat{A}}_k^{l}m=A_k^l+\frac{A_k^{l+1}-A_k^l}{H}m.0\le m\le H.\end{array}$$

Then, we interpolate the frequency and phase. It is a little more complicated because the two are correlated and the frequency is the derivative of the phase. The first is to understand the concept of a phase; that is, $\theta m=m\omega +\phi$. Then, it is obvious that the so-called continuous function means that all parameter groups ${\omega }_k^l,A_k^l,{\varphi }_k^l$ are equal at the junction of frame and frame, and the first-order derivative is the frequency value of each frame. Therefore, it is used as a coefficient problem to solve the following 3rd-degree polynomial:$$\begin{array}{}\text{(33)}& {\theta }_{l}m=\gamma +km+\alpha m^2+\delta m^3.\end{array}$$

The following is satisfied:$$\begin{array}{}\text{(34)}& \begin{array}{c}{\theta }_{l}0={\varphi }_l,\\ {\theta }_{l}H={\varphi }_{l+1},\\ {\theta }_{l}0={\omega }_l,\\ {\theta }_{l}H={\omega }_{l+1}.\end{array}\end{array}$$

However, the solution is not unique, and $\theta m;M,M\in Z$. Robert McAULAY gave a very reasonable constraint; that is, the change of the $\theta m$ function is minimized in the frame interval $fM={\displaystyle {\int }_0^H{\theta m;M}^2\text{d}m}$. The final result is$$\begin{array}{}\text{(35)}& {\theta }_{l}m={\varphi }_l+{\omega }_{l}m+\alpha M^{\ast }{m}^2+\beta M^{\ast }{m}^3.\end{array}$$

From the above formula,$$\begin{array}{}\text{(36)}& \begin{array}{c}\begin{array}{c}\alpha M\\ \beta M\end{array}=\begin{array}{cc}\frac{3}{H^2}& -\frac{1}{H}\\ -\frac{1}{H}& \frac{1}{H}\end{array}\begin{array}{c}{\varphi }_{l+1}-{\varphi }_l-{\omega }_{l}H+2\pi M\\ {\omega }_{l+1}-{\omega }_l\end{array},\\ M^{\ast }=\mathrm{int}\frac{1}{2\pi }{\varphi }_l+{\omega }_{l}H-{\phi }_{l+1}+{\omega }_{l+1}-{\omega }_l\frac{H}{2}.\end{array}\end{array}$$

At this point, the reconstructed audio signal of each frame after interpolation can be completely written:$$\begin{array}{}\text{(37)}& \widehat{s}m+IH={\displaystyle \sum _{k=1}^K{A}_k^{l}m\cos {\theta }_k^{l}m},1\le m\le H.\end{array}$$

3. Computer-Visualized Sound Parameter Analysis Method and Its Application in Vocal Music Teaching

The method proposed in this paper is applied to the vocal music teaching, and the vocal music teaching parameters are identified by the computer visual sound parameter analysis method, and the vocal music characteristic research is carried out to improve the vocal music teaching effect. Moreover, this paper uses Matlab to construct a computer visual sound parameter analysis model to obtain a vocal music teaching model and uses simulation experiments to verify the vocal music feature recognition and vocal music teaching effect of this model. The results shown in Table 1 and Figure 12 are obtained.

Table 1

The analysis method of computer visualization sound parameters and its application effect in vocal music teaching.

No.	Feature recognition	Teaching effect	No.	Feature recognition	Teaching effect
1	89.01	84.60	13	91.67	82.15
2	89.45	82.47	14	89.51	88.01
3	88.28	83.42	15	88.52	81.09
4	91.89	87.75	16	91.73	84.95
5	89.38	87.33	17	92.98	86.08
6	88.15	84.83	18	89.92	86.75
7	88.53	87.28	19	92.14	82.44
8	88.18	84.83	20	91.29	84.77
9	88.34	88.09	21	92.93	85.28
10	88.59	83.01	22	90.60	81.63
11	91.19	82.98	23	90.63	83.11
12	88.77	83.77	24	92.60	82.36

[figure(s) omitted; refer to PDF]

It can be seen from the above research that the computer visualization sound parameter analysis method proposed in this paper has a very good application effect in vocal music teaching and can improve the quality of vocal music teaching.

4. Conclusion

Vocal music teaching contains the systematicity that all the teaching links are connected with each other and cannot be separated. However, from the perspective of long-term teaching experience, more attention should be paid to the problem of those talents who have been buried due to educational philosophy. In this way, the sound teaching and education of vocal music will have a good incentive mechanism and a reasonable restriction mechanism. Therefore, starting from the teaching practice, constantly discovering and excavating students’ creativity and constantly cultivating and improving students’ creativity are the foundation of teaching. This paper studies the effect of vocal music teaching combined with the computer visualization sound parameter analysis method and constructs an intelligent vocal music teaching system. Through the simulation data analysis, it can be seen that the computer visualization sound parameter analysis method proposed in this paper and its application in vocal music teaching are very good and can improve the quality of vocal music teaching.

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