TW382116B - A computer synthesized plunk string instrument device and method of the same - Google Patents

Abstract

A plunk string instrument technique which uses a steel string measurement device to detect the vibration of real strings and employs the measuring result as learning data of scattering recurrent network. Such scattering recurrent network is used as the solid model of the string and output the synthesized parameters after sufficient learning. The generated synthesized parameters can create exactly the original sound after mixing and amplifying. The computer music synthesizing technique can generate different audio string effects according to different kinds of plunking waveform and sampling positions just as a virtual plunk stringed instrument.

Description

Printed by the Central Standards Bureau of the Ministry of Economic Affairs and Consumer Cooperatives A7 B7 V. Description of the invention (5 — 1 Field of invention and background A. Field of the invention The present invention relates to a device and method for computer musicians to print music, especially to a device Apparatus and method for generating simulated string sounds according to various plucked waveforms and combined parameters. Β _ Background of the Invention Due to the rapid development of multimedia and virtual reality applications, realistic music and electronics The method of music synthesis is even more urgent. In recent years, related to the technology of music synthesis, in recent years, the analysis of the physical sounds and sounds of musical instruments has been used as data for music synthesis to replace the pure electronic sound effects. Two sacrifice. Eight levels into two categories. Frequency modulation method (FM) and wave table method —able), the basic structure of the modulation method is composed of two-level sinusoidal 〇SCillator, the former name In order to modulate the oscillator (modulating oscilIator), its oscillation frequency is called the modulation frequency (频率 frequency). The output of this stage and the carrier frequency The frequency input of the carrier oscillator (carrier osciiiator), so that you can get a rich waveform at the output of the carrier oscillator. Since the frequency modulation method only uses a sine oscillator to generate sound, its advantage is that the operation is easy, but this is also exactly The disadvantage is that it cannot fully simulate the sound of real musical instruments, so this method is only applied to the previous generation of sound cards or low-cost electronic toys. Even now there are still many researchers who use various methods to find parameters that perform better. However, due to the limitations of the FM method itself, it is difficult to apply the Chinese National Standard (CNS) A4 specification (210X297 mm) to the paper size of the FM method itself (please read the precautions on the back before filling this page)

Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs Λ7 --------------- 'V. Description of Invention (乂) ~~~ There is a major breakthrough in the structure. A new generation of sound cards or synthesizers has turned to the wave table method in order to obtain sounds closer to real musical instruments. The wave table method first records and saves the sounds played by various real musical instruments. When synthesizing the sound, the original stored sounds are processed according to the looping, keyshift, and subsequent stages After processing such as postfiltering, etc., it is transmitted to the output terminal ', which is the synthesized signal. Since the original signal of the wavetable method is obtained from actual recording, it is more realistic in terms of tone color than FM. However, the sounds synthesized by the wave table method all process pre-recorded sounds, so it is impossible to simulate the dynamics of transient attacks on the instrument. In addition, any sound needs to be pre-recorded for audio storage, so the required memory space is quite large. More importantly, the wavetable method cannot generate new waveforms other than pre-recorded messages by itself, and it cannot generate new timbre according to the playing situation. This is a bottleneck that conventional synthetic music can hardly break through. In recent years, research has attempted to simulate the physical characteristics of physical musical instruments with digital waveguide chirpers (Dig &H; al Waveguide Filter). For example, the patent “Digital Signal Procesising_ Using Waveguide Networks” (US Patent No. 4,984,276) filed by smith, Julius 0. 1991 has set an important milestone. Later, many physical models of musical instruments were based on digital waveguide filters and wave filters. The digital waveguide ferrule uses a two-way delay-line to simulate the transmission of conductive waves during string vibration. Among them, more than 3 paper sizes are applicable to Chinese National Standard (CNS) A4 specifications (21〇297297 feet) --J --- 丨-(Please read the precautions on the back before filling this page) ”丁,-'°. 01. l · · Printed by the Consumer Cooperatives of the Central Bureau of Quasi-Economic Bureau of the Ministry of Economic Affairs Λ 7 Β7 V. Description of the Invention (Evening) The scattering junction method is applied to correspond to the uneven reflection phenomenon of the string medium. Such as' Smith, Julius 0. The 1993 patent "Digital Signal Processing Using Closed Waveguide Networks j (U.S. Patent No. 5,212,334) is an extension of the waveguide filter to a nonlinear decentralized rendezvous method. Smith, Julius 0. A patent

"Multidimensional Digital Waveguide Signal Synthesis System and Method" (U.S. Patent No. 5,448,01 0) is an application of a multi-dimensional decentralized rendezvous method. Although the edge-conduction filter can more realistically simulate the dynamics of plucked string vibrations, it lacks a systematic method to determine the internal number required to simulate different strings. Therefore, when designing a digital waveguide filter, it is often necessary to find parameters by trial and error. Moreover, the signal measured by the microphone must be used to generate a raw input waveform with a random number function. This is very different from the actual cutting of a plucked string. 5-2 Purpose and Summary of the Invention The main purpose of the present invention is to propose a split and method of electronic music synthesis, which can be based on the waveform of plucked strings input by the player and the synthetic parameters of the distributed recurrent neural network. Produces original sounds that approximate the real instrument being simulated. Another object of the present invention is to propose a virtual plucked musical instrument device and method, which use a decentralized recursive neural network to simulate the physics of a real plucked musical instrument. _ _ 4 paper ruler > Specifications (210X297 公 楚) ~~ ------ (Please read the precautions on the back before filling this page)

Description of the invention (+) Economics Deng Central Bureau of Standards Bureau printed the characteristics of the employees' consumer cooperatives, and used interpolation, function, and synthesis of musical instrument sounds. Waveform fingering to dynamically pick strings. Another object of the present invention is to synthesize the required parameters of the strings, and to obtain a simulation of the set-type neural network to generate α. After entering the player's plucking style, 'synthetic sounds produce different synth sounds. Oh, another object of the present invention is phasic,-^ 's on the edge-a method of synthesizing timbre, which can be used to simulate the vibration of a string in a neural-like network and obtain information in multiple different neurons. A. "The study of the network to obtain the learning parameters, and then according to the algorithm cubic-method proposed by the present invention, and to the synthesis parameters, so that the synthesized color is closer to the real piano sound. In order to achieve the above purpose, the present invention of Shi 10, proposes a set of physical models combining musical instruments

A computer music synthesizing device and method for neural network-like learning rules & φ u L Baiji rule. In the present invention, a scattered recurrent network (Scattering Recurrent Network, SRN) is used to solve the problem that the physical model parameters of the musical instrument cannot be obtained efficiently. It also uses the non-linear characteristics of neural-like networks to make SRNs more flexible in practical applications through the selection of activation functions. In addition, the present invention also uses a set of steel string measurement systems, uses its electromagnetic sensors to measure the vibration of the physical strings, and uses the actual measurement data of the string vibrations as the training data for SRN, and Make the neural network-like sounds of real instruments. In addition, the present invention also uses interpolation method and function method. The paper size is applicable to China National Standard (CNS) A4 specification (210X297). (Please read the precautions on the back before filling this page}

Order five. Description of the invention (left Λ7 B7 Printed by the Consumer Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs and slope fingering to simulate the actual plucking action as the original input waveform, so the synthesized sound is closer to the real plucking instrument Sound. 3 Brief description of the diagram, '/ picture ~ is the structure diagram of the known neurons. Figure 2A ~ 2C are schematic diagrams of the common common actuation functions. Figure 2A is a conventional forward-looking neural network. Figure 2B shows the basic structure of a conventional feedback-like neural network. Figure 4 is a schematic diagram of a distributed rendezvous model of the reflection phenomenon caused by uneven acoustic impedance coefficients of the present invention. Figure 5 is the present invention Schematic diagram of the string simulation network SRN. _Figure six heart six C is a schematic diagram of the basic structure of the neurons included in the SRN of the present invention, where Figure six A represents the position node '囷 six B represents a separate node' Fig. 7 is a schematic diagram of the steel string measuring device of the present invention. Fig. 8 is a light flow diagram of the string vibration measurement of the present invention and the obtained data processing flow. 'Fig. 9A is a double neuron full connection Schematic diagram of the completed RNN. Fig. 9B is a sound diagram of a network architecture of an approximately forward type obtained by extending the RNN of Fig. 9a along time and extending and expanding the network structure. The network structure diagram of the approximate forward pass type obtained by expanding the SRN through the material sequence. Figure 11 is a flowchart of the SRN parameter learning of the present invention. V Figure 12 is a structural diagram of the entire music synthesis system of the present invention. Figures 13A to 13E are schematic diagrams of the initial waveforms of the m S RN of the present invention. The paper size: Chinese National Standards (CNS). Read the notes on the back first and fill in the purchase. I. ir -9. B7 Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs 5. Description of the invention (Figure 14 is a schematic diagram of the SRN synthesis model of the present invention.

Figs. 15A to 15D show the results obtained by applying the SRN of the present invention to cello A ', measuring point one and measuring point four. The figures 16 and 7 A to D are the output results of each sampling position of the SRN of the present invention. Sample Figure 17 shows the STFT analysis of each measurement point in Figure 15. Figure 18 shows STFt analysis of each measurement point in Figure 16. 5-4 Detailed description of the present invention The present invention will first introduce the basic concepts of neural-like networks, such as a ^ ", 'Ό, so that the review members can understand the basic principles of the SRN applied by the present invention. Familiar with the operating principles of neural-like networks, you can omit the description of ^ Wang Pu Er. Basically, a neural-like network is composed of many basic units' including neurons (NeurorOll and the tendon that connects each neuron ( Synapse) 12, 13 are shown in Figure 1. A neuron u can be divided into two parts: round-in (1 邛 plus) 12 and output (0 such as 1) plus 13: its input 12 receives neighboring neurons Or the external stimulus sends the signal through weighting of the tendon through weighting, and the output terminal 13 sends the signal to other neurons or as a system output. The receiving terminal 2 will receive the signal after receiving the turn-in signal. After two levels of processing, the signal is sent out. In general, the first stage 14 is to accumulate all the round-in signals as the net-input signal of the subsequent stage, such as formula (1) This paper standard is applicable to the national standard of Yin (CNS) A4 specifications (2 0X297 mm) (Please read Notes Eris and then fill in the back of this page)

V. Description of the invention (7) Λ 7 Β7 Printed by the Consumer Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs. net, = -Θ, (1) where A: represents the neuron, + threshold wz, y. represents ~ the weighting of the input connected to the neuron ί /: represents the net of the neuron, Net-input. The role of the subsequent stage 15 is to pass the net input signal through the activation function to become the output of the neuron. The general actuation function is shown in Figure 1A as a step functión, Figure 2B as a bipolar ramp function, and Figure 2C as a bipolar sigmoid function. The architecture of the network can be divided into two categories: feed forward and feedback networks, as shown in Figures 3a and 3b. In the forward network, as shown in FIG. 3A, the neurons are arranged in layers to form an input layer 31, a hidden layer 32, and an output layer 33. The input layer 31 receives an external stimulus signal from the network (excitation) 34 ′ The output layer 33 sends out a round-robin signal of the network 35 ^ No matter how many layers there are between the input 31 and the round-out layer 33, it is called a hidden layer 32. Because its transfer method only receives the output of the previous layer as input, the layer-by-layer transfer is called the forward type. In the feedback network, as shown in Figure 3B, the output signal 36 can be returned as the first 8 paper sizes applicable to the national standard (CNS) M specifications (21 〇χ297 mm) ------- (Please read the notes on the back before filling in this page) —CD Pack -----— ^ Order ^ _----- ^-Λ7 B7 V. Description of the Invention (Y-plane or same-layer neurons Input, even if only a ^ connected in the network is called a feedback network. In addition, if its transmission path forms a closed loop, it is called a recurrent netwrk. In order to be able to build a suitable piano The stringer model must make the vibration model of the device model close to the physical characteristics of the desired simulated musical instrument. As far as the analysis of the dynamics of the strings in the acoustics is' assuming the strings are homogeneous —), no energy The ideal state of lossless, volumeless and flexible, then the wave equation of string vibration conduction is as follows: Ky " = sy (2) (3) (Please read the precautions on the back before filling in this Page) --------— κι— 装 — -r-order-Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs The solution of the above wave equation with different boundary conditions can be regarded as the sum of two waves with the same velocity left and right. The second general solution is as follows: = yr {t-X / cj + yi (t + x / cj (4) where C = ^ represents the transverse wave velocity, and the outer (ί-χ / c) and + represent the transmitted waves transmitted to the right and to the left, respectively. If the vibration of the string is taken into account, Friction effects such as friction force, end point consumption, etc., must further consider the energy consumption of the paper scale system w (----- ©-A V. Invention Description (y). We can use the following The resistance force is proportional to the vibration force of the string to approximate the above-mentioned friction effect. Assuming the resistance constant is defined as w, the resistance can be expressed as 咿 and added to equation (2), so the wave equation is changed to:

Kyn = uy + sy (5) and the solution of the above formula can be deduced to get the following results and BU-M + coffee% BU / c) (彳 After sampling, we can further obtain discrete-time to Conducive to the implementation on digital systems. Assume that the sampling period at a sampling position 'time is r, because the wave velocity is. Therefore, the sampling interval on the string is: y (xm, in) = e < u / 2 ^ J \ (tn _ ^ w / cj + e (un £ XXm / c) yi ^ + Xm / c ^

-(ulle) mT (please read the note on the back I to fill out this page) Printed by the Central Consumers ’Bureau of the Ministry of Economic Affairs ^ ritn ^ m) + 9l {tn, xm) ⑺ Which ί„ = «· Γ, = w .cr. Competitive push_ Go further—define the Passive Loss Constant as w -uTIle 10 This paper size applies the Chinese National Standard (CNS> VI 4 Specification (ΤΓοX 297 ^ · ^ ..I.) -------- * Order L ----- ο ------ J--I --- Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs Λ7 B7 V. Description of the invention (丨 o) yOn ^ m)-^ lOn ^ m) = fr (, n ~ + fl (nl · m) (S) \ On real instruments, the ends of the string are usually fixed, so the amplitude of the endpoints is always maintained. 'Zero' assuming the string length £, add the above limit to equation (8), and G can be obtained at any time: I " less (^, 〇) = 〇 = 外 (&, 〇) + about (/ „, 〇 ) \ y (tn, L) = 0 = φΓ (ίη, 1) + φι (ίη, Σ) ⑼ According to equation (9) 'At the left and right endpoints, the right and left propagation waves can be expressed as \ < Plitn, L > ~ (pr {tn, D (10) If the same is caused by the unevenness of the string material, unit density, etc. — the sound of the conduction path Different impedance (Acoustic Impedance), the reflection phenomenon will occur at the intersection. At this time, it is necessary to further consider the determination of the amount of passing waves and reflection waves. The intersection point is It is called the scattering junction. Assume that on a vibrating string, there is a junction point (juncti〇n) whose acoustic impedances (Acoustic Impedanc e) at the left and right ends are Zl and z2 respectively as shown in the figure and right The transmitted waves incident to the left are β 4 1 and W 42 respectively. The amplitude of this junction 43 can be expressed as yJ (11) s /. 11 This paper size applies the Chinese National Standard (CNS) A4 specification (210X297 cm) (Please read the notes on the back before filling this page) -----n I I-- I I. _— ^ --- In 1— n ΙΊ nn ------ n Central Bureau of Standards, Ministry of Economic Affairs Printed by the employee consumer cooperative Λ 7 _______ B7 _____ 5. The description of the invention (丨 丨) is simplified for the symbol '"Α) will be omitted hereafter, and the departure waves from left to right (departure waves) are 1 45 and # 44, can be calculated according to the following formula, // = yJ -ψΐ U2 = 〆, the model above 2 (12) is The ideal way to a proposed string vibration 'but the truth may be more complex. In order to be able to effectively approximate a TempOral Dynamic System 'and conform to the dynamic equation of string vibration described above, we use a feedback-type neural network with a closed loop' called Recurrent Neurai Network (RNN for short) is used as the basic structure of a musical instrument model. Based on the dynamic characteristics of string vibration obtained above, combined with the RNN network learning rules, we propose a new string simulation network: a decentralized recurrent neural network (the following _SRN), as shown in Figure 5. Utilizing this, the present invention successfully solves the problem that the parameters of the conventional stomach and stomach solid model cannot be taken effectively. According to formulas W and ⑴), SRN contains two important types of parameters: the energy leakage constant U and the reflection coefficient γ. The important feature of this network is that we consider both the energy loss of the string vibration and the step-by-step processing of the non-uniformity of the medium around the string. When the wave conduction generates reflection, its passing wave and reflected wave The problem of determining the amount of paper: this structure 12 paper standards t National Financial Standards (CNS) A4 specifications (2 丨 G x 297 public splash) (Please read the precautions on the back before filling this page) 7 ---- --- Γ ----- ^ --HE} -equipment --- ψ--Γ Order. Λ7 Λ7 Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs ---_______ B7 V. Description of the Invention (丨 >) ~ —-For the simulation of string vibration, it is quite complete. This—the upper half of the new Recurrent Neural Network (RNN) represents a guided wave to the right and the lower half represents a conducted wave to the left. And the neurons in this network can be divided into three types according to formulas (11) and (12): the vibrations at the sampling position on the upper late chord. We call them displacement nodes, and It has the characteristics of decentralized intersection, that is, the media on either side of any sampling position is not consistent. P represents a conductive wave flowing into ^ in the left-right direction, which is called an arrival node, and / represents an outgoing conductive wave, which is called a departure node. The basic structure of each neuron is shown in Figure 6. 'The pre-stage of each neuron is an accumulating action and the latter stage is an activating function. Figure 6A represents a position node. There are two input terminals 6 1, 62 to receive signals from two preceding-stage incident nodes, and two output terminals 63, which are expected to send signals to two separate nodes at the subsequent stage. Figure 6B represents separate nodes. There are two input terminals 65, 66 to receive the signals from the previous-stage incident node and the position node, and one output terminal 67 to send signals to the subsequent-stage incident node; the figure represents the incident node, and one input 68 receives the signal from the previous-stage separated node. Each output terminal 69'70 sends a signal to the subsequent stage separation node and location node. Assuming that α (·) represents the actuation function, according to Figure 5 and Figure 6, the incident nodes at the upper and lower halves at time ί + 1 can be calculated by the following formulas: • * Ψΐ, ί-Ι ^ + 1 ) = = α [Μ > υ_χ // ιΜ (〇) < Pi, i + l (t +1) = a [netfM (t)] = a [wi > i + l fi > i + i (t) ] (13 > / 13 This paper size applies to Chinese National Standard (CNS) A4 specification (210X297 mm) ~ -------. I 1'Bull-up --------- ^ Ir (Please idle first Read the notes on the back and fill in this page again} --------- A7 B7 V. Invention description) And the instantaneous amplitude of each sampling position at r + l can be expressed as follows: a [netf (t + l)] , i = 2, ..., Nl 〇, i = l or i = N (⑷ where netf (r +1) = η ^ · φ ^ _λ {ΐ + 1) + riJ + l φ ^ + \ (ί +1) (15) At the same time, the left and right departure waves (departure waves) can be calculated from the following formulas' / + 1) = a [net {+ lJ (t +1) ] = a [yi (t + 1)-φί > ί + ι (ί +1)] + 1) = ainetf ^ t +1)] = a [y. ^ + 1). φ .._ χ {ί + 1}] (16) And the learning of neural network is to obtain proper training data first, so we designed a steel string Ν seven measuring apparatus shown in FIG. This measuring device includes several electromagnetic sensors 71 of electric guitars, and is placed in parallel with each sampling point 73 along the strings 72 to be measured to synchronize the vibration state of each point at each sampling instant as an output target. (Desired 〇utput). The two ends of the string 72 are fixed ends 77. (Please read the notes on the back before filling this page)

-AW Printed by the Consumer Cooperative of the Central Standards Bureau of the Ministry of Economics The working principle of the electromagnetic inductor 71 is to use the principle that the magnetic flux of the induction coil is changed by the vibration of the steel string 72 to generate an electronic wheel output signal. Each group of inductors 71 is composed of six electromagnetic coils, while a typical electric guitar has two to three inductors. The steel string measurement system we designed currently has six sensors, and the number of sensors can be increased or decreased according to the needs of the experiment. In addition, we have designed a special slide kit (not shown) for the sensor 71 to make it feel ____14 This paper size applies to Chinese national standards (mm)-~ -----_ Central Bureau of Standards, Ministry of Economic Affairs Employee consumer cooperative seal Λ7 -------- ~ __B7 V. Description of the invention (丨 y) Should cry 7 1 * · ,. . You can move on the slide rail to change the sampling position. During the measurement, the six measuring devices 71 on the system sample synchronously, and these measured values pass through the amplifier 74, analog / digital converter (A / d) The converter 75 is finally sent to the real-time audio storage device 76 (Audio Engine, Spectral Co., U, S_A ·). The sampling frequency used is 32 kHz, and the quantization level (Quantization level) is 16 bits.

After the stored data is post-processed, it can be used for SRN training and testing, as shown in Figure 8. In step 8 丨, 'first obtain the measured data through the steel string measuring device', and then in step bismuth, store the data in the real-time audio storage setting as the SRN learning data. In step p, the Sony / Phihp digital interface (soon / philip Digitai, S / P DIF) technology is applied to convert the data into digitization. Then in step & 4, the digitized data can be directly transferred to a personal computer for processing. Finally, in step 85, the digitized data is used as the training vector of the SRN. For the learning of the SRN model, the present invention adopts "BaCk-Propagati〇n Thr〇Ugh" Time (BPTT) to learn the parameters of the network. Since SRN is too complicated to explain its relationship with BPTT, only a simpler RNN is used to illustrate it. Figure ... Nine a is a fully-connected RNN with two neurons. Many RNN learning methods have been proposed, and these methods all define a cost function (c〇st functi〇n), and then take the gradient of this cost function ( gradient), adjust along its negative direction | plus 15 on the nerve key This standard applies to the Chinese National Standard (CNS) A4% grid " 7 ^ 0X297 Gongchu) '-: ~ (Please read the precautions on the back before (Fill in this page) -L —-- ·· ---- Private --- >-* 1Τ ------- Γ1Γ. —; 5. Description of the invention (丨 left) A7 B7 weights (weights ). Its + BPTT will advance an RNN along time and expand the network structure ’to obtain a network structure of approximately feed forward type.阍 Show 偁 Take Figure 9A as an example. Assuming that its initial value is divided into 1 (〇) and _ at time 0, and this network transmits in a synchronous manner, then at time 1, the value of each neuron is as follows: i yx (1) = a (wx 1 · (0) + w12 · y2 (〇)) Wl) = α〇22.} 2 (〇) + you 21 • Nai) (17) and so on 'in time, + 1 _ 'The value of each neuron can be calculated from the following formula: | ^ (i +1) = a (wn · ^ (t) + Wn. Y2 (/)) [> * 2 (t + Y) = a (w22 -y2 (t) + yl (/)) (18) Figure 9B is the network structure of its approximate forward type. In this way, the standard Back Propagation Method can be used to update the parameters of the network, because each layer of the structure represents the sampling instant in time. law. (Please read the notes on the back before filling in this page. J The Consumer Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs printed the same reasoning. “In terms of the SRN online learning process, the measured data is used.” It expands into a network structure similar to the predecessor. As shown in Figure 10, the parameters of SRN are automatically learned through BPTT. In Figure 10, each transient state is called the time layer 1 0 1 'and each A timing layer is composed of three subsidiary layers, which are composed of displacement nodes 104, arrival nodes 105, and departure nodes 103. It is true that this paper standard applies Chinese national standards (CNS) M specifications (210'〆297mm t) --r L ---: ----------------------------- r. -M-- I in n 1 II-ΑΊ Β7 V. Description of the invention (In terms of situation, we can only measure the vibration-like edges of a few sampling positions simultaneously '' Therefore, these position nodes with actual measurement data are called observable nodes (Visible n〇des)! 〇2; other nodes are called hidden (Hldden nodes-). Assuming that it represents the measured amplitude at the time ί of the first measurement position and represents the set of observable nodes, the error signals at any time? Can be defined as follows: 丨0, otherwise (19) where (0 represents the actual output of the i-th position node in the SRN at time t on the same day τ error function (error functj〇n) can be defined as follows: (〇 = 1/2 XeJ (t) ieA (t) (20) False S and i. represent the initial time 'and G represents the final time, then we can get the total cost function I- Lt-I— —II-.1 —.1 mf I t Γ '(Please read the precautions on the back before filling this page), -t Printed by the Consumers' Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs —

Et〇ta \ t〇A)-^ Ε (ί) 广 = 广 〇 + 1 (21) The purpose of online learning is to minimize the total cost function (T〇tai Cost Functi〇n), which means SRN The actual output will approximate the measured data. In order to achieve this goal by adjusting the energy leakage constant and the reflection coefficient of the medium, these parameters are changed along the negative direction of the gradient of the total cost function. The result is derived, where the energy leakage constant corresponds to The amount of change is as follows: 17 This paper size applies to China National Standard (CNS) A4 (210X297 mm) i. Description of the invention

Aw, Μ) / + 1, / Λ7 B7 ^ Σ ^ + υ (〇ι ~ ί0 + \ • 7 3Et〇tal {t, A) One ... taste coffee A) _ ^ < u (rl) (221 / d ^ i

iU y __v'q, 'w. Two ^ -u 4ΐι 3ietlu (tl) dwt asks 0 + 1 and the adjustment variable for the medium reflection coefficient is as follows:, al (M) if ^ Et〇tal (t〇A) dnetl { t), β ,, -ι r = / 〇 + i dnet ^ it) times, M ^ ί = ί〇 + 1 (23), _ Sui-'(,., 〇 +--(/., 〇 such as彳 ⑺ 1, v + 1__7 ~ " 3 · —η B, ^, aty (t \ Λ.) /, / + 1 ί: ί0 + 1 /, / + 1-^ ------- i-" " Install-- (Read the precautions on the back before filling in this page) v ^ fiO-PijAO ask 0 + 1 where 7 represents the learning constant 'It should not be too large to avoid shock But cannot converge, in addition, the amplitude center (0 can be obtained: ΐτ -----.—— printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs ^ etf (/) SE {t) [3iet {_u (t) | 3Ε , 0 (α1Μ) ^, (0 ⑽ 水 ⑴ ^ iei / ^ Ο) 永 ⑺ 3iet {+ ii (t) dyt {t) άιεί ^ ί) K VΑ (ί) «(0), t = tx (^ -(0 + ^ 1, / (0 + Sf + Ui (t)) * af (net fit)), tQ < t < tx 18 This paper size applies to China National Standard (CNS) Α4 specification (210 × 297 mm) 5 Description of the invention (θ Λ7 B7 df ㈣ = ^ < l (〇 ^ Vn bu) dnetf (t) δηβίφ Ταu) w) (，) = 3lu {t +1) · wt_u · a'inetf ^ ,. (?)) ', Eight) ^ ut) ^ < u (/) = ^, (^ 1)-^^^^, , (0), + 1'Λ) (25) 3E ， 〇ta \ t0, tx) Snetf + l4 (tY), dE, ota \ t0, t,) dnetyM (t) se ^ un ^ .fr 3ietf + l (t) φΜ ί (t) ~~ ^ ΤηΤΓ ·. — (26) m ,, A, " ,, v "; +1 () d (Pi + u (0; dnetf + x; (i -1) (26): (¾ ⑴.W (〇) .Ω («< 々__ cut, + ιΛ l) ^ -u (0 ^ Elo, al (t0, tx) 3ictf_Xi (J — 1) (Please read the notes on the back before filling this page) Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs—, mud ('〇,' i). ^ G ^ -i (^) 3Et0talft t \ / ^ fj, ^ ,-((0 d (Pi-u (0 ~~ d ^ P ^ 7K ~) • One (2J £ Γ /, μμ) Φ,, (rV rket9 (tn ^-so repeated learning, internal iteration The number of teas until the actual output of the SRN 'and the measured data are close enough to / meet our requirements. Figure ¥-is the flowchart of the entire SRN parameter learning. In step 111, the measurement data (refer to Figure 7 and Figure 8) are digitized by S / p DIF technology +, DIF, and then can be stored as PCM format data, that is, steps 1 ι, 2., ,,, & as the training vector for SRN. Step H3, first select a string-speed gate q υ in the measured waveform as the initial position of the sampling position node in the SRN waveform characteristics when the amplitude of the wheel position compared to other sampling positions is the highest point, and the plum position is at The measurement data after this time point is used as the rotation-out. After obtaining the initial value of the sampling position node, use: 19 Wood Paper Standard National Standard for Financial Countries (CNsT ^ iiTlT ^ · ^ public splash • l · -11 ^ } —Install ---..--- order ----------- hj —— printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs Λ7 ---____ B7 V. Description of the invention ((y) —— The initial values of the nodes in other positions, so the initial waveform of the SRN string model is generated. This is step lY4. Then start the SRN sound synthesis module h22 and record the signal obtained by the synthesis at each time. When the time reaches The previously set length uses formula (21) to calculate the overall cost function, which is step ιN [5. Then it is determined whether the total cost function has fallen to a preset learning threshold value (threSholl), step 116. If If yes, the learning process is completed, step 117. Otherwise, then 22) (23) (24) to update the network parameters, this is step 118, and step 丨 14 is performed. Repeat the learning until the total cost function reaches the preset learning threshold (thresh〇ld), and then learn The obtained parameter δ has been recorded, and the learning process is completed. When the learning process is completed, the obtained synthesis parameter record is stored, indicating that a virtual string is obtained. Therefore, in the sound synthesis stage, it is like playing- Real strings-giving a "flicking" motion, can make a virtual plucked instrument vibrate to generate sound. Figure 12 shows the architecture diagram of the entire music synthesis system. This system contains #group wave production Zhu Generator 121, the generated waveform and the SRN sound synthesis module 122 < J according to the number of strings required for the actual instrument, the SRN sound synthesis module 122 in each combination represents the string part 'and the waveform generator i21 generates The waveforms represent various different playing methods and positions. SRN $ Sound Synthesis Module 122 can output synthesis parameters learned from multiple neurons, and through the mixing and sound device 123, multiple The tone played by the strings together. The synthesized tone signal rotated by the mixing device 123 is a digital signal, which must be converted to an analog mixed signal through a digital / analog conversion stomach 124. Then, it is passed through the speaker m to expand the analog mixed signal. 20 This paper size applies to China National Standard (CNS) Α4 specification (210X297 mm) ------- Ti--pack-(Please read the precautions on the back before filling this page}

'1T • I — · 8 · A7 B7 Support and drawing point method V. Invention description (> 0 will be broadcast afterwards. To simulate the way a player plays, he knows the machine, and the last one month uses interpolation Method 'function method and tracing point method to simulate the waveform of plucked strings. Figure 夂 锸 π — ~ twelve £ shows waveforms corresponding to various playing methods. Figure 10, LA simulation uses fingernails to pluck the middle of the strings. Figure 12 Figures B and 13C represent the positions of the strings on the right and left sides of the strings. Figure 13D simulates the situation where π 亍 钿 is a finger plucked string. Figure 13E represents the strings struck. Actions, such as piano, use the hammer to hit the strings to make sounds. Different sounds and timbre can be generated according to different waveforms. This is exactly the same situation as real musical instruments, and it is also unique to the present invention. The way the waveform is generated There are roughly three types: interpolation method and function, which are described below. (^) / The interpolation method gives the amplitude of each important point, and uses the interpolation method to find the amplitude of the remaining points. , C is generated by this method. The left and right endpoints are set to 0 and the Set the degree to 1 'Calculate the slope between the toggle point and the left and right ends, respectively', and the middle points are obtained by multiplying the distance from the endpoint to the slope to obtain its amplitude. X /) Function method 21 China National Standard (CNS) A4 specification (210X 297 mm) (Please read the precautions on the back before filling out this page). Install ---, --- order, ----, economy, the staff of the Central Standards Bureau Printed by the Consumer Cooperative V. Description of the Invention (> ^) A7 B7 uses various mathematical functions to get the waveform we want. Figure 13 is the waveform obtained by using the Gaussian function. (C) Tracing point method \ For two special ones that cannot be directly represented by mathematical functions, we can use the tracing point method to 'draw a graph and then measure the relative position height according to the needs of each position node' to obtain its The desired starting state waveform. As shown in Figure XIIIE. After the initial waveform of the SRN's vibration is determined, the SRN sound synthesis model starts to operate, and its operation steps are shown in the kitchen. Its operation mode is divided into two steps: (i) the initial phase and (ii) the vibration wave transmission phase. ⑴Initialization-Install! * ί a (please read the notes on the back before filling in this hundred c-ordering printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economy First, in step 141, suppose that the initial waveform we decided is as follows: 1 一) 〇′ζ · Ι '..., ^ ν] (28) Then in step 142,' inject it into the SRN as the value of the location node at time f = 〇 (29) 22 This paper scale applies the Chinese National Standard (CNS) A4 specification ( 2 丨 0X297 mm) Printed by the Central Standards Bureau of the Ministry of Economic Affairs, Machining and Consumer Cooperatives A7 ------------ B7 V. Invention Description (yV) ~

And in step 143, the position node signal corresponding to the desired output position is sent to the output terminal, assuming that 〇 represents a set of target output positions | J out (〇 = ^. (0, Vy ;. eO ( 30) Next, 'In step 144, these values are evenly distributed to the left and right separation nodes (departure nodes): 4⑼⑼. The initial phase is completed. (Ii) The vibration wave transmission phase (Wave prOpagati 〇n) With the values of the position node and the separated node, we can use equation (1 3) to find the value of the incident node when Γ = 1, which is step 145. Then, in step 146, use equation (14) ( 15) to find the signal of the position node at this time. Then, in step 47, the target output position signal is sent to the output terminal by using formula (30). Finally, in step 148, the formula (16) is used to obtain Leave the value of the node. In this way, a cycle action is completed, and repeated operations based on this action can obtain the round signal of the SRN synthesis model at each time. Because we can vibrate the nodes at different positions of each string, For different needs, synchronous sampling, Really approaching the actual performance effect. This effect cannot be countered by the traditional 0% method. Moreover, neural network learning can obtain system parameters that are not easy to find in the physical model of the instrument. Finally, the output signal of the synthetic model is adjusted by the mixer. Sampling volume ratio and one's national standard (CNs ") ~~~~~ -______ (Please read the notes on the back before filling this page)

， 1T —----- Five Λ7 B7 Du printed by the Central Standards Bureau of the Ministry of Economic Affairs and Consumer Cooperation Du printed 'Invention Note (; ^ >) After digital / analog conversion, it can be sent to the amplifier and speakers to get realistic playing music . Simulation results: «15 and Figure 16 are the vibration waveforms obtained by synchronously measuring the four measurement points of the cello A string using the steel string measurement system. We use the first two samples to sample seven training vectors as SRN training vectors. In the SRN model, there are a total of 100 position nodes' and the left and right ends are fixed ends. The learning constant is 100,000.001. After 10,000 times of learning and fixing the obtained network parameters, voice synthesis can be performed. In the synthesis phase, we plucked the learned SRN model and recorded the vibration state of each sampling point during the 10,000 sampling time, as shown in Figure 15 and Figure 16. We found that, with the exception of the first point, the other points were quite close to the measured waveform. If you want to make the synthesis result closer or make the first point approach the measurement result like the other points, you only need to lengthen the training vector and the number of learnings to meet the requirements, and even extend the synthesis time. Because human ears are more sensitive to time-frequency responses than pure time domain signals, it is necessary to perform Short-Time Fourier Transforms (STFT) analysis. Figure 17 shows the STTTS of the signals measured at each measurement point, and Figure 18 shows the STFTs of the output signals corresponding to the sampling positions of the SRN. All the analyzed signals are first processed by Hamming Windowing. And the resolution of the signal in the frequency domain (frequency domain), we adopt a 24 & paper size applicable to the Chinese national standard (Oyang) 8 4 specifications (210 '乂 297 mm (please read the precautions on the back first) (Fill in this page again) Cultivation-© 'n VJ --5 ----

AA Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs _B: ___ V. Invention Description (<) Fast Fourier Transform (FFT) of points, where the first 1024 points are the sampling block and the last 3072 points are the complement Zero point (zero padding). The overlapping size of two adjacent blocks is 896 points. Analyzing these four graphs', we can find that the output of each sampling point of the SRN is very close to the measurement signal in time [0, 5000], and in time [5000, 1 0000], near the endpoint The performance of the sampling points is relatively poor, and the performance of the middle points is still quite good. If the synthesis effect needs to be improved, then the learning vector and training times are increased, and the performance of sampling points near the endpoints can be greatly improved. In summary, the present invention utilizes the S RN model to effectively improve the conventional problem of electronic synthesizing music. The multi-point measurement system is used to obtain enough real musical instrument vibration data as training data for the SRN model. Such a systematic model construction and parameter selection procedure are far beyond the reach of FM. After full learning of the SRN, the parameters are fixed, and a virtual musical instrument is constructed. When using S RN to synthesize music, it is only necessary to give a virtual playing such as' hammering or plucking, etc., that is, to give the initial waveform 'to trigger SRN vibration' to obtain a synthesized signal. Therefore, compared with the wavetable method, the amount of memory required is greatly reduced. Since the sound synthesis method of the present invention is generated by simulating the vibration mode of a real musical instrument, it can progressively present the dynamics of transient attacks. In addition, for the SRN, you only need to input the relative initial waveform to show different effects. In view of the above characteristics, the present invention does show that the SRN has excellent performance far beyond that of the conventional frequency modulation method and the wave table method. The above is only the preferred embodiment of the present invention, and it has reached a wide range of ___25 This paper size is applicable to the Chinese ϋΓ standard (CNS) A4 ^ — (21〇χ297, ϋ ~ ρ-- (please listen first Read the notes on the back and fill in this page again] Ding _ -'s .f Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs A7 B7 V. Description of the invention (/) Practical effects, all changes in accordance with the scope of the patent application for this invention And modifications are still covered by the patent of this invention. (Please read the precautions on the back before filling out this page) Binding-Staple. 9. 26 This paper size applies to China National Standard (CNS) A4 (210X297 mm) )

Claims (1)

Apply for patent Fan Yuan, 1._ A plucked musical instrument device using computer music synthesis, comprising: a plurality of waveform generating devices printed by the staff consumer cooperative of the Central Bureau of Standards of the Ministry of Economic Affairs, for receiving measurement data of a string vibration, and Output a starting waveform; a plurality of distributed recurrent neural network learning modules for receiving string vibration measurement values, and output learning parameters based on the starting waveform; a plurality of SRN sound synthesis modules, using Based on the learning parameters, synthesizing the parameters obtained through the rotation learning; a mixing device for rotating the digital mixing signals according to the synthesis parameters rotated by the plurality of SRN sound synthesizing modules; and a digital / analog conversion device To input the digital mixing signal 'and to rotate the analog mixing signal "2. The device as described in the item of the scope of patent application, wherein the number of the srn sound synthesizing module is equal to that of the simulated musical instrument Number of strings. 32. The device described in item 丨 of the scope of patent application further includes a speaker device for receiving the aforementioned analog mixed signal and outputting the amplified analog mixed signal. 4. The device as described in item i of the patent application range, wherein the plurality of waveform generating devices include: an interpolation calculation module, which uses interpolation to obtain the amplitude of each point; f Please read the notes on the back if you want to fill in this page.) Order. ·· A8 B8 C8 D8 Among them, the function method calculation module applies for the patent scope and the trace point method calculation module, using the trace point pattern θ to serve the initial waveform · And a function method calculation module, using mathematical functions to pay the initial waveform. According to the device described in the fourth scope of the patent application, A φ Xi is 4 ^ '. The interpolation method to calculate the chess set is to obtain the amplitude of each point in the following way:, Read the amplitude of the sampling point;. Set left and right The endpoint is 0 and the height of the toggle point is i; calculate the slope between the toggle point and the left and right endpoints; calculate the distance difference between each intermediate point and the endpoint; and multiply the distance difference by the slope To get the middle of each;. Point amplitude. \ 6 · The device set as described in item 4 of the scope of patent application is to obtain the initial waveform in the following ways: Input a parameter of a mathematical function; and output the waveform of the mathematical function. 7_ The device according to item 4 of the scope of patent application, wherein the tracing point method calculation module obtains the initial waveform in the following ways: input a drawn plucking pattern; according to the needs of each position node of the plucking pattern , Measure the relative position height of the position node; and turn out one of the initial state waveforms obtained from the measurement result. _8. The device described in item 1 of the scope of patent application, wherein the distributed recurrent neural network learning module obtains the learning parameters in the following ways: 27 If the paper scale is applicable, please read the meaning on the back. (Please fill in this page again for details)-Order 11. ^ ψ! Printed by A8 B8 Γ—S8-________ D8 points, application ^ ------ (a) Set a learning Threshold value; (b) Read the above initial waveform; (c) Perform the update of the white feather dry white parameters of the distributed recurrent neural network, and generate—learning parameters; (d) Execute according to the learning parameters' The above-mentioned overall cost function of the starting waveform is calculated and a calculation result is generated; (e) When the calculation result is less than or equal to the learning threshold, stopping the learning of the starting waveform and outputting the learned parameters; and C0 When the calculation result is greater than the learning critical value, the learning parameter value of the decentralized recursive neural network is updated, and returns to (C). \ 9 / The device according to item 8 of the scope of patent application, wherein the learning parameters include * energy leakage constant and medium reflection coefficient. } 0. The device as described in item 1 of the scope of the patent application, wherein the plurality of SRN sound synthesis modules obtain synthesis parameters in the following manner: (a) Initialize the position nodes and Departure node; (b) Obtain the value of the incident node at the first time according to the fp point 's Hai departure point at that position and an incident node calculation formula; (c) Calculate according to the instantaneous amplitude at the first time Obtain the value of the position node within this time; (d) Calculate the value of the departure node based on the left and right departure waves during that time; and use the Chinese I standard for this paper scale ( CNS) 8 4 specifications (210x297 mm) " --- (Please read the precautions on the back before filling this page) Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs Perform the steps (a) to (e) to synthesize the parameters. Device, where the plurality of SRN sound synthesizing modules are based on D, +. + I, ^ You initialize the position nodes and departure nodes of the distributed recurrent neural network in the following manner: a state with zero time, Calculate the value of an initial waveform; calculate the aggregate value of a target output position based on the value of the edge initial waveform; and evenly distribute the aggregate value of the target round-out position to the separation nodes passing in the left and right directions. The device described in item 10 of the scope of patent application, wherein the calculation method of the incident node is: (+ 1) = α [ηεί? ._ γ (ί)] = a [wi} i ^ i / i; i_i (〇 ] + + 1) = a [netf. + L (t)} = a [wiji + i 1.3. The device as described in item 10 of the scope of patent application, wherein the instantaneous amplitude is calculated as: \ a [ne t ^ (ί + 1) 1 > I = ^ ^ /-(^ + 1) = I 〇i = 1 or i = N, where netf {t + 1) = rM_! · (ί + 1} + ^ / + 1 'φ ^ ί + λ {ί + l), Ία ---- (Please read the notes on the back ^ before filling in this j, ΈΤ_ θι. 29 This paper size applies to Chinese National Standard (CNS) A4 Specifications (2 Sichuan > < 297 Gonglu A8 B8 C8 D8 Ministry of Economic Affairs t Central Government led the staff consumer cooperation) Printing the patent application scope t / device as described in item i 0 of the patent application scope, where And the departure wave to the right is calculated as: fi + U (i + 1) = a {netf + li (t +1)] = a [yi (t + 1)-φί ί + γ {ί + 1 }] / ΐ-Ι, ϊΟ + 1) = alnetf ^^ t +1)] = a [yj (t + 1)-+1)] 1-5. —A method of plucked string instruments for computer music synthesis, including: Generate a starting wave based on the waveform of a plucked string ; According to the initial state waveform, initialize an incident node, a position node, and a departure node of a distributed recurrent neural network; perform an update of the learning parameters of the distributed recurrent neural network according to the initial state waveform; And generate a learning parameter; perform calculation of the overall cost function of the decentralized recursive neural network based on the learning parameter ', and generate a calculation result; adjust the change of the energy leakage constant according to the calculation result of the overall cost function Variables and the media reflection coefficient; when the calculation result of the overall cost function drops to a learning threshold, the learning parameters are recorded; and the synthesized parameters are obtained according to the learning parameters. K6. The method as described in item 15 of the scope of patent application, wherein the step of initializing the position node and the departure node of the decentralized recursive neural network includes a step of: calculating a start with a state of zero time The value of the waveform; 30 papers? China National Standards (CNS --_ ί1Θ 裳 ------ Order—— C Read the notes on the back before filling in this page) Shard · Scope of Patent Application According to the value of the starting waveform, ° the set value of the target output position; and the 隼 厶 Α ^ v set 0 value of the target round-out position is evenly distributed to the left and right separation nodes. 17. The method according to item 15 of the scope of patent application further comprises: when the calculation result of the above-mentioned overall cost function has not reached the above-mentioned learning threshold, readjusting the above-mentioned incident node, position node, and leaving node. The amount of change in the leakage constant and the adjustment variable of the medium's reflection coefficient. IΉ asks for the method described in item 15 of the patent scope, wherein the above incident nodes are obtained according to the following mathematical equations: ~-卞 +1) = ♦ ⑽⑽ 十 ~ -⑴] (…) = 小 吒 +1 吒Bu, Chuan. //// + 1⑴] 〇R The method described in item 15 of the patent scope, wherein the above position node is obtained according to the following mathematical equation: yi {t + 1) = ^ alnetf ( t + 1)]? / = 2,... ^-1 〇, i = 1 or i: =: n one of them ^ ~ ί ί --- IT · ~~ .—. I -___, (Please First read the notes on the back and then fill out this page) ό —---- neU y ^ + 1) " Γυ ~ \ · φυ-ΐ (ί ^ -1) + riJ + l. ^. / + 1 ( / + 1) Cancel 20. The method described in item 15 of the scope of patent application, wherein the separation node is obtained according to the following mathematical formula:. · 31 scope of patent application + 1) = a [netf + li (t + Dl ^ a (y ^ + 1)-9iJ + l (t + 1)] + 1) = a (net {_X i (t + 1) 3 ^ + 1 )-+ 1)] 2 1 · The method described in item 15 of the scope of patent application, wherein the cost function is obtained according to the following mathematical formula: τ- > total / v E (? 〇Jl) = Σ5⑴, where E (t) is the error function t = t0 +1 2 2 _As described in the scope of patent application No. 21, the change amount of the energy leakage constant is adjusted according to the following formula: AW • V dw ί + Ι, ί / + 1,] = " ίχ, (ί) ./+ 1 ,, (卜 〇 ^^ 0 + 1 J ^ 〇tal (^ $ ^ t〇t〇 (^ 〇 ^ ι ) ^ 7etf (t -1) --.------_ • —Order ---- b-»© 1 Please read the note on the back before completing this ^ 〇 Chinese Ministry of Economic Standards Printed by the Bureau ’s Consumer Cooperatives ^ = ^ 0 + 1 23 · The method described in item 21 of the scope of the patent application, where the medium reflection coefficient is adjusted according to the following formula: 32 Paper standards ) Congxiu (21Qx297 public envy) Printed by the Consumers' Cooperative of the Sixth Central Bureau of Standards, Ministry of Economic Affairs Patent application scope △ Wide ,,, Office M-1 < = », + 1 e tUSl.) T & net ^ 77 \ ---- r " —A…, /,, (f) = I ⑴ Ιμ-ΛΟ V ~ n &, 〇, al (tn, t,) dr. η i 史 · 史 ， 川 ⑴ ο shirt 'as described in the scope of the patent application No. 21 method to calculate the vibration I t method, including -step following ^ ω =-^ Μΐ ohetj ^ t ) =-(^^ + £! ^ 〇ι〇 ^^ total. ^. (0 ^ ietfu (t) ~ ^ x ^ + '^ rr ^ ^ ϋίίί ^). Ϋ J ^)-a \ netm, two ⑺Correction) ^, (0 + s ^ (t) + ^ /, (0) -a \ netf (t) X t〇 、 丨 < /, 25. A plucked instrument method using computer music synthesis includes the following steps According to the interpolation method, the tracing method or the function method, a plurality of initial waveforms of plucked strings are generated; according to the initial waveforms, the incident nodes, the position nodes, and the departure nodes of a plurality of distributed recurrent neural networks are initialized; • Perform the calculation of the overall cost function of the plurality of decentralized and recursive neural networks based on the plurality of initial state waveforms; calculate the nose based on the overall cost function '. 33 papers with a 5-week integral energy leakage constant Standards: National Standards (CNS) A4 (210X297 mm) (Please read back first Please note this page before filling in this page) Order n! I _ ^ WT— · The incident node is the variable of the patent scope change and the media reflection coefficient printed by the Consumer Cooperative of the Central Standards Bureau of the Ministry of Economic Affairs; when the overall cost function is The calculation result drops to a learning threshold, and the learning parameters are recorded. According to the learning parameters, the synthesis parameters of the plurality of starting waveforms are obtained. According to the synthesis parameters of the plurality of starting waveforms, digital mixing signals are rotated out. The digital mixed signal is an analog mixed signal; and amplifying processing of the analog mixed signal is performed. 2.6 • The method described in item 25 of the scope of patent application, which is obtained according to the following mathematical equations: Ψΐ, Ψΐ-ΐΟ + 1) = alnetf ^^ t)] = + 1) = a [netfl + 1 ( t)) = Ω [^ /) ί + 1. 27. The method described in item 25 of the scope of patent application, where the position node is obtained according to the following mathematical equation ... a [netf (ί + 1)] 5 〇, 2, Ν -I or i-'where yt (t + 1) = -like + i) =' /-I1 ('+ U + +1) N 28. As described in item 25 of the scope of patent application The method of the 'separation section' is based on the following mathematical equations: Point system 34 This paper size applies the Chinese National Standard (CNS) A4 specification (210X297 mm) Scope of patent application 2.9. Obtained from the following mathematical equations as described in item 25 of the scope of patent application: The function is E total 〇0, '1) = 5⑴, where E (t) is the error function 30. The method described in item μ of the range, in which the change amount of the rate 1 is adjusted according to the following formula: Energy leakage abnormality; --L ----- f Jing first read the precautions on the back, and then fill out this j-order Aw ι + Ι, ζ i + 1, z ί = 5ί〇 + 1 Aw Printed by the Consumer Cooperatives of the Central Bureau of Standards of the Ministry of Economic Affairs, M, I t (-, _ 1 >, ^? 〇 + 1 ^ eiM, / (il) ~ 5 ^ T ~ '1¾ ^ 2. ^ (0-/:-1, (^ 1) f = i〇 + lo 31 · As the method described in the scope of the application for the patent No. 29, Gan yin among the above materials The radiation coefficient is adjusted according to the following formula: 1 Application scope A8 B8 C8 D8 A dE, 0, a, · dnet ^ (t) Ί dnet ^ t) " =? 7 艺 < V⑴ 屮 m-ι⑴ / = / 〇 +! DE, o, al { t0, tx) Δ ',, + ι = -Jr Uri, i \\ = π Σ p p m + i (') δΕ l0, a, (tn, t,) dnet ^ t) 'dr,! λ .λ = / 〇 +! 32. The method as described in item 29 of the scope of patent application, further comprising a step of calculating the amplitude by the following formula: '^ (0 dEtota \ UA) dnetyt (ί), just 涿. ， 0 ^ 0 + 一 细 iud 水 ⑺ 细 ίυ (〇 水 ⑺ 细 ， ⑺ (Xt) · a '(nett = t ^ Ue ^ + S ^ XO + Sf ^ -a'inetJit)), h < t < t, __ ___—) / L _ i nn Bi ^^ i If ^ fct ~ T \ Jy〆nn ^^ 1 h 1.-广; — (Please read the notes on the back before filling this page) Order economy Printed by the Consumer Standards Cooperative of the Ministry of Standards of the People's Republic of China 3 3 The method described in item 25 of the scope of patent application, where the interpolation method includes the steps: Read the amplitude of the sampling point '' Set the left and right endpoints to 0 and the toggle point. The height is 1; the slope between the toggle point and the left and right endpoints is calculated; the distance difference between each intermediate point and the endpoint is calculated; and the distance difference is multiplied by the slope to obtain the amplitude of the intermediate points. 36 This paper size applies to China National Standard (CNS) A4 (210X297 mm) Printed by the Consumer Cooperatives of the Central Bureau of Standards of the Ministry of Economic Affairs A8 B8 1 C8 D8 6. Scope of patent application} 4. As described in item 25 of the scope of patent application The method, wherein the function method includes the steps of: specifying a mathematical function; inputting parameters of the mathematical function; and outputting a waveform of the mathematical function. S / .. The method described in item 25 of the scope of the patent application, wherein the calculation of the trace point method includes the steps: 'draw a plucked pattern; and measure the relative position height of the position node according to each position node. Obtain a starting state waveform. 3..6. The method according to item 25 of the scope of the patent application, wherein the learning parameters include: energy leakage constant and medium reflection coefficient. (Please read the notes on the back before filling this page) This paper uses Chinese National Standard (CNS) A4 (210X297 mm)