Direct digital frequency synthesizer based on rbf neural network with stage-by-stage optimization
By using a phased optimized RBF neural network, the problems of DDS output signal accuracy and hardware resource consumption were solved, achieving an efficient frequency synthesis scheme and improving the performance and adaptability of DDS.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF POSTS & TELECOMM
- Filing Date
- 2023-10-09
- Publication Date
- 2026-07-28
AI Technical Summary
While improving the accuracy of the output signal, existing DDS technology increases hardware resource consumption. The BP neural network algorithm suffers from slow convergence speed, weak nonlinear fitting ability, and easy trapping in local extrema.
A phased optimization RBF neural network is adopted, including coarse and fine adjustment stages. The K-means++ algorithm is used to select the center value of the hidden layer nodes, and the L-BFGS-B algorithm is combined to adjust the center value, thereby optimizing the training process of the RBF neural network. The network is constructed using a DDS structure consisting of a phase accumulator, an RBF neural network module, a digital-to-analog converter, and a low-pass filter.
It improves the accuracy of the DDS output signal and the flexibility of frequency adjustment, reduces the consumption of hardware resources, and enhances the performance and scalability of DDS.
Smart Images
Figure CN117200707B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of direct digital frequency synthesizer technology, and in particular to a direct digital frequency synthesizer based on a staged optimized RBF neural network. Background Technology
[0002] A Direct Digital Synthesizer (DDS) is a programmable device that uses digital signal processing technology to generate high-precision, high-stability signals. DDS offers advantages such as high frequency resolution, fast frequency switching speed, good phase continuity, and strong anti-interference capabilities, and is widely used in communication systems, radar systems, and testing instruments. A DDS mainly consists of four components: a phase accumulator, a read-only memory (ROM) lookup table, a digital-to-analog (D / A) converter, and a low-pass filter. Due to ROM capacity limitations, traditional DDS technology requires phase truncation, leading to phase truncation errors and increased spectral spurious signals. To reduce or eliminate truncation spurious signals, researchers have proposed a sine wave generator design based on backpropagation neural network (BP neural network) technology. Specifically, this design replaces the ROM lookup table with a BP neural network, overcoming the impact of truncation errors in traditional DDS sine wave generators. However, the BP neural network algorithm has some specific problems that affect its performance, hardware capabilities, and accuracy. Specifically, the BP neural network algorithm has a slow convergence speed, which affects hardware performance. Furthermore, the BP neural network algorithm has a weak ability to fit nonlinear functions, resulting in insufficient accuracy of the output signal. Finally, the BP neural network is prone to getting trapped in local optima during weight adjustment, which can cause the algorithm to become stuck in local optima and lead to network training failure.
[0003] In summary, how to improve the accuracy of DDS output signals without increasing hardware resource consumption is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0004] This invention provides a direct digital frequency synthesizer based on a staged optimized RBF neural network to solve the problem of improving the accuracy of DDS output signals without increasing hardware resource consumption.
[0005] To achieve the above objectives, the present invention provides a direct digital frequency synthesizer based on a staged optimized RBF neural network, comprising:
[0006] A phase accumulator is used to generate a phase signal;
[0007] The RBF neural network module is used to convert phase signals into amplitude signals;
[0008] A digital-to-analog converter is used to convert digital amplitude information into low-frequency sawtooth signals;
[0009] A low-pass filter is used to suppress high-frequency noise in sawtooth wave signals from digital-to-analog converters, converting the sawtooth wave signals into smooth analog signals.
[0010] The RBF neural network module includes a hidden layer and an output layer. The hidden layer contains multiple nodes, each with a corresponding radial basis function. For each input phase information, each hidden layer node can map it to a corresponding feature value. The output layer is connected to the nodes of the hidden layer through weights. After multiplying the feature value of each node with its corresponding weight, the values obtained by multiplying all nodes are summed to obtain an amplitude value corresponding to the phase information.
[0011] As a further improvement of the present invention, the phase accumulator includes a full adder and an accumulation register, wherein the full adder is used to sum the input frequency word with the accumulation result of the previous cycle to obtain a new accumulation result, and the accumulation register is used to store the output value of the full adder in each clock cycle and provide the accumulation input value for the full adder in the next cycle.
[0012] As a further improvement of the present invention, the radial basis function is an inverse square function, specifically in the form of: Where x represents the input phase information, c represents the center of the node, and R represents the width of the radial basis function.
[0013] As a further improvement of the present invention, the training process of the RBF neural network module includes two optimization stages: coarse tuning and fine tuning.
[0014] As a further improvement of the present invention, the coarse adjustment stage includes: selecting the center value of the hidden layer nodes using the K-means++ clustering algorithm, calculating the width of the radial basis function based on the center value, initializing the hidden layer weights in a random manner, and then updating these weights using a pseudo-inverse algorithm.
[0015] As a further improvement of the present invention, the fine-tuning stage includes: adjusting the optimal center value of the coarse-tuning stage using the Limited-memory Broyden–Fletcher–Goldfarb–Shanno with Box constraints (L-BFGS-B algorithm) until the output error meets the requirements.
[0016] As a further improvement of the present invention, the adjustment range of the L-BFGS-B algorithm is ±1 of the center value of the coarse adjustment stage.
[0017] As a further improvement of the present invention, the digital-to-analog converter receives the digital amplitude signal output by the RBF neural network module, and after undergoing an internal D / A conversion process, converts the digital amplitude signal into a corresponding analog low-frequency sawtooth wave signal, and transmits it to the low-pass filter.
[0018] As a further improvement of the present invention, the low-pass filter is used to receive the analog low-frequency sawtooth wave signal output by the digital-to-analog converter. Through the design characteristics of the low-pass filter, the high-frequency noise components in the analog low-frequency sawtooth wave signal are suppressed, thereby outputting a smooth analog signal.
[0019] Beneficial effects:
[0020] 1. This invention provides a novel frequency synthesis technology. By introducing and optimizing the RBF neural network, it provides a new, more efficient and flexible frequency synthesis scheme, which has stronger scalability and adaptability when dealing with complex and nonlinear frequency synthesis tasks.
[0021] 2. Due to the improved training efficiency and accuracy of RBF neural networks, the performance of direct digital frequency synthesizers has been significantly optimized. Specifically, the output sine wave shape is closer to the ideal sine wave, the frequency accuracy is higher, and the frequency adjustment is more flexible and faster. Attached Figure Description
[0022] Figure 1 This is a diagram of the direct digital frequency synthesizer architecture in this invention;
[0023] Figure 2 This is a flowchart of the phased optimization RBF neural network algorithm in this invention;
[0024] Figure 3 This is a diagram of the RBF neural network structure in this invention;
[0025] Figure 4 This is a training diagram of the BP neural network in this invention;
[0026] Figure 5 This is the prediction graph of the BP neural network in this invention;
[0027] Figure 6 This is a training diagram of the traditional RBF neural network in this invention;
[0028] Figure 7 This is the prediction graph of the traditional RBF neural network in this invention;
[0029] Figure 8This is the training diagram of the RBF neural network using a phased optimization strategy in this invention;
[0030] Figure 9 This is the prediction graph of the RBF neural network using a phased optimization strategy in this invention;
[0031] Figure 10 This is a simulation diagram of the output of the direct digital frequency synthesizer in this invention. Detailed Implementation
[0032] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail with reference to the following specific embodiments and the accompanying drawings, but this is not intended to limit the scope of the present invention.
[0033] like Figures 1 to 10 As shown, this invention discloses a direct digital frequency synthesizer based on a staged optimized RBF neural network. The direct digital frequency synthesizer comprises a phase accumulator, an RBF neural network module, a digital-to-analog converter (DAC), and a low-pass filter. The phase accumulator generates a phase signal, the RBF neural network module converts the phase signal into a digital amplitude signal, the DAC converts the digital amplitude signal into a low-frequency sawtooth signal, and the low-pass filter suppresses high-frequency noise in the sawtooth signal from the DAC, converting the sawtooth signal into a smooth analog signal. The innovation of this invention lies in the first-time introduction of an RBF neural network into a direct digital frequency synthesizer, providing a new, more efficient, and flexible frequency synthesis scheme with greater scalability and adaptability when handling complex and nonlinear frequency synthesis tasks.
[0034] The phase accumulator consists of an N-bit full adder and an N-bit accumulator register. At the rising edge of each clock cycle, the N-bit full adder adds the phase data output from the accumulator register to the frequency control word K. The result is then input back into the accumulator register, allowing the full adder to continue adding to the frequency control word at the next rising edge of the clock cycle. In this way, the phase accumulator continuously performs linear phase accumulation on the frequency control word under the influence of the clock. The output data of the phase accumulator is the input data of the RBF neural network module, and the overflow frequency of the phase accumulator is the output signal frequency of the DDS, which can be expressed as:
[0035]
[0036] Among them, f out f is the output signal frequency of the DDS. clk Where K is the clock frequency, K is the frequency control word, and N is the number of bits in the phase accumulator. Preferably, the phase accumulator includes a 16-bit full adder and a 16-bit accumulator register for generating the phase signal.
[0037] The RBF neural network module includes an input interface, a computational core, and an output interface. The input interface receives the output signal of the phase accumulator and uses it as the input to the RBF neural network. The computational core consists of a radial basis function (RBF) calculation module and a neuron calculation module, used to process the input signal and perform the forward computation of the RBF neural network. The RBF calculation module calculates the radial basis function value between the input signal and the center value of the RBF neural network, while the neuron calculation module uses the RBF value and hidden layer weights to calculate the output value of the RBF neural network. The output interface outputs the calculated neural network output value, i.e., the digital amplitude signal, to the digital-to-analog converter. This can be represented as:
[0038]
[0039] Where, x i Let y be the i-th input value of the RBF neural network, y be the output value of the RBF neural network, N be the number of neurons in the hidden layer, and w be the output value of the RBF neural network. i Let G(x) be the weight of the i-th hidden layer neuron. i ) represents the radial basis function value of the i-th hidden layer neuron.
[0040] Preferably, the radial basis function is an inverse square function, with the following functional form:
[0041]
[0042] Where x is the input to the neural network, c is the center value of the hidden layer, and R is the width of the radial basis function, which is calculated as follows:
[0043]
[0044] Where, d max It is the maximum distance between all the center values, and k is the number of center values.
[0045] This invention proposes an efficient phased optimization strategy for the training process of RBF neural networks. The phased optimization strategy consists of two stages: coarse tuning and fine tuning. Specifically, the coarse tuning stage uses the K-means++ clustering algorithm to select the center values of the hidden layer nodes of the RBF neural network. Leveraging the characteristics of low randomness and fast clustering speed of the K-means++ algorithm, it can quickly find reasonable cluster centers. Therefore, using the K-means++ algorithm to determine the center values of the hidden layer nodes of the neural network can improve the generalization and approximation capabilities of the RBF neural network. After the coarse tuning stage, the output error is used to determine whether the requirements are met. If not, the fine tuning stage begins. In the fine tuning stage, the L-BFGS-B algorithm is used to adjust the optimal center values from the coarse tuning stage. The L-BFGS-B algorithm is an improved BFGS algorithm that uses a limited memory approach to handle multivariate function minimization problems with boundary constraints, significantly reducing storage requirements and computational load compared to the BFGS algorithm. To ensure the stability and efficiency of the adjustment process, a relatively compact search range is set for each center value as the boundary for center value adjustment. This setup is based on the idea that since the center values in the coarse-tuning stage are already quite good, a better solution can be found in the vicinity of these values without searching the entire range. This setup ensures the search efficiency of the L-BFGS-B algorithm while preventing the search process from jumping out of the reasonable range, which would lead to a decrease in the quality of the solution. This staged optimization strategy greatly improves the training efficiency and accuracy of the RBF neural network, thereby significantly enhancing the performance of the direct digital frequency synthesizer.
[0046] During the coarse adjustment phase, the K-means++ clustering algorithm is used to determine the center values of the hidden layer nodes in the RBF neural network. The K-means++ algorithm is an improved K-means clustering algorithm, and its basic steps are as follows:
[0047] (1) Randomly select a point as the first cluster center;
[0048] (2). For each point x in the dataset, calculate the shortest distance d(x) to the selected cluster center;
[0049] (3) Select a new cluster center. The probability of selection is proportional to the square of d(x).
[0050] (4) Repeat this process until k cluster centers are selected.
[0051] During the fine-tuning stage, the optimal center value from the coarse-tuning stage is adjusted using the Limited-memory Broyden–Fletcher–Goldfarb–Shanno with Boxconstraints (L-BFGS-B algorithm) until the output error meets the requirements. The L-BFGS-B algorithm is a limited-memory method used to handle multivariate function minimization problems with boundary constraints. The basic steps of the L-BFGS-B algorithm are as follows:
[0052] (1) Select an initial point and set parameters such as the number of iterations and tolerance;
[0053] (2). Calculate the initial gradient (usually the gradient of the objective function at the initial point);
[0054] (3) Calculate the approximate inverse of the Hessian matrix using the finite-memory BFGS method;
[0055] (4) Use the line search method to find the step size that satisfies the Wolfe condition;
[0056] (5) Update the current parameters using the step size and the inverse of the approximate Hessian matrix.
[0057] (6) If the maximum number of iterations is reached, or the change in the objective function value or the magnitude of the gradient is less than a preset threshold, then stop the iteration. Otherwise, return to step 2;
[0058] (7) Update the parameters while satisfying the boundary constraints.
[0059] Preferably, the process of selecting the hidden layer center value using the K-means++ algorithm is as follows:
[0060] (1). Randomly select a point from the input dataset as the first center value c1;
[0061] (2). For each data point x i Calculate the square of the shortest distance between it and the center value, denoted as d(x). i ) 2 ;
[0062]
[0063] Among them, c j The selected center value is k, and the number of center values is k.
[0064] (3). Choose a new center value, with a probability P(x) of selection. i) and d(x i ) 2 Proportional, that is:
[0065]
[0066] Where n is the number of all input data points.
[0067] (4). Repeat steps 2 and 3 until k center values are selected.
[0068] Preferably, the process of adjusting the optimal center value determined in the coarse adjustment stage using the L-BFGS-B algorithm is as follows:
[0069] (1). Set the initial point to the optimal center value of the coarse adjustment stage, that is:
[0070] x0 = c
[0071] (2). Set the number of iterations T and the tolerance δ.
[0072] (3) Calculate the initial gradient g0, which is the gradient of the objective function at the initial point:
[0073]
[0074] The objective function is in the form of:
[0075]
[0076] Where N is the number of training samples, x k It is the k-th input sample, y k This corresponds to the actual output value, h(x) k ) is an RBF neural network for x k The predicted value.
[0077] The prediction function h(x) of the RBF neural network is of the following form:
[0078]
[0079] Where M is the number of neurons in the hidden layer, ω j G is the weight of the j-th hidden layer. j (x) is the output value of the j-th hidden layer neuron.
[0080] (4) Calculate the approximate inverse of the Hessian matrix using the finite-memory BFGS method, and initialize it as the identity matrix, i.e.:
[0081] H0 = I
[0082] (5). Perform iterative steps: For each iteration step t = 0, 1, 2, ..., T-1, perform the following steps:
[0083] 5.1. Calculate the search direction using the inverse of an approximate Hessian matrix:
[0084] p t =-H t g t
[0085] 5.2. Use the line search method to find the step size α that satisfies the Wolfe condition. t .
[0086] The Wolfe condition consists of two parts: the Armijo condition (also known as the sufficient descent condition) and the curvature condition.
[0087] The Armijo condition, also known as the sufficient descent condition, requires that the new function value decreases by at least a certain amount compared to the original value. The Armijo condition can be expressed as:
[0088]
[0089] Where α is the step size, f is the objective function, x is the current point, p is the search direction, and c1 is a small positive number.
[0090] Curvature condition: This requires that the new derivative value be at least a fraction of the original derivative value. Specifically, for the same α, the curvature condition can be written as:
[0091]
[0092] Where c2 is a constant close to 1.
[0093] 5.3. Update the current parameters using the step size and search direction:
[0094] x t+1 =x t +α t p t
[0095] x t+1 This is the adjusted center value.
[0096] 5.4. Calculate the new gradient:
[0097]
[0098] 5.5. Update the inverse of the approximate Hessian matrix using the BFGS method:
[0099] H t+1 =BFGS(H t ,g t+1 -g t ,xt+1 -x t )
[0100] Where BFGS(H,s,y) represents updating the inverse of the Hessian matrix using the BFGS formula, where y = x k+1 -x k s = g k+1 -g k The formula is:
[0101]
[0102] (6) If the maximum number of iterations T is reached, or the change in the objective function value or the magnitude of the gradient is less than a preset threshold, i.e.: |f(x t+1 )-f(x t )|<δ or‖g t+1 If || < δ, then stop iterating. Otherwise, return to step 5.
[0103] (7) Update the parameters while satisfying the boundary constraints. The boundary constraints in this optimization process are:
[0104] c-1≤x t+1 ≤c+1
[0105] This boundary condition prevents overfitting during the optimization process, ensuring the stability and reliability of the optimization results. In other words, the adjustment range using the L-BFGS-B algorithm is ±1 of the center value in the coarse-tuning stage.
[0106] In this embodiment, the staged optimization strategy of the RBF neural network includes the following steps:
[0107] Step 1: Select the hidden layer node centers of the RBF neural network using the K-means++ clustering algorithm;
[0108] The specific steps of the K-means++ algorithm are as follows:
[0109] S1 randomly selects a point from the input dataset as the first center value c1;
[0110] S2 for each data point x i Calculate the square of the shortest distance between it and the center value, denoted as d(x). i ) 2 ;
[0111]
[0112] Among them, c j The selected center value is k, and the number of center values is k.
[0113] S3 chooses a new center value, with a probability P(x) of selection. i ) and d(x i ) 2 Proportional, that is:
[0114]
[0115] Where n is the number of all input data points.
[0116] S4 Repeat steps 2 and 3 until k center values are selected.
[0117] Step 2: Calculate the width of the radial basis function based on the selected hidden layer center. The radial basis function is denoted as G(x).
[0118]
[0119] Among them, c j Let R be the center value of the j-th hidden layer neuron, and R be the width of the radial basis function.
[0120] The formula for calculating the width of the radial basis function is as follows:
[0121]
[0122] Where, d max It is the maximum distance between all the center values, and k is the number of center values.
[0123] Step 3: Randomly initialize the hidden layer weights, and then use a pseudo-inverse algorithm to update the weights of the RBF neural network;
[0124] The output of the RBF neural network is:
[0125] Y = HW
[0126] Where Y is the output of the RBF neural network, H is the output of the hidden layer of the RBF neural network, and W is the weight of the hidden layer of the RBF neural network.
[0127] in, W = (w1, w1, ..., w m ) T .
[0128] Using the pseudo-inverse of H Find:
[0129]
[0130] Step 4: Determine whether the output error of the RBF neural network is less than 1e-6. If it is less than 1e-6, end the training; otherwise, proceed to the fine-tuning stage.
[0131] The magnitude of the output error of an RBF neural network is measured by an objective function, which has the following form:
[0132]
[0133] Where N is the number of training samples, x k It is the k-th input sample, y k This corresponds to the actual output value, h(x) k ) is an RBF neural network for x k The predicted value.
[0134] The prediction function h(x) of the RBF neural network is of the following form:
[0135]
[0136] Where N is the number of training samples, x k It is the k-th input sample, y k This corresponds to the actual output value, h(x) k ) is an RBF neural network for x k The predicted value.
[0137] Step 5: If the algorithm is in the fine-tuning stage, the L-BFGS-B algorithm is used to adjust the optimal center value in the coarse-tuning stage until the output error of the RBF neural network is less than 1e-6 or the maximum number of iterations of 1000 is reached.
[0138] In this way, the problems of accuracy instability and large computational resource consumption in the traditional RBF neural network training process are overcome, making the RBF neural network more suitable for direct digital frequency synthesizers, thereby improving the performance of direct digital frequency synthesizers.
[0139] The digital-to-analog converter receives a digital amplitude signal from the RBF neural network module. After an internal D / A conversion process, it converts the received digital amplitude signal into a corresponding analog low-frequency sawtooth wave signal and transmits the analog low-frequency sawtooth wave signal to a low-pass filter for processing.
[0140] The low-pass filter is used to receive analog low-frequency sawtooth wave signals from the digital-to-analog converter. Through the design characteristics of the low-pass filter, high-frequency noise components in the signal are effectively suppressed, allowing only low-frequency components to pass through, thereby outputting a smooth analog signal.
[0141] Terminology Explanation:
[0142] Direct Digital Synthesizer (DDS): A DDS is a device that uses digital signal processing technology to generate high-precision, high-stability, and programmable output signals. It is widely used in communication systems, radar systems, test instruments, and other fields. A DDS mainly consists of four major components: a phase accumulator, a ROM lookup table, a digital-to-analog (D / A) converter, and a low-pass filter.
[0143] ROM (Read-Only Memory): A read-only memory is a hardware device for storing data, characterized by the fact that the stored data can only be read and cannot be modified. In this paper, ROM refers to the part of DDS used to store pre-calculated sine waves. However, due to the capacity limitations of ROM, traditional DDS technology requires truncation of the input phase, resulting in phase truncation error.
[0144] Phase truncation error: Due to the capacity limitation of ROM, traditional DDS technology needs to truncate the input phase, and the resulting error is called phase truncation error.
[0145] Backpropagation (BP) neural networks are a type of feedforward neural network that uses the backpropagation algorithm for training. However, BP neural networks have a slow convergence speed, weak fitting ability for nonlinear functions, and are prone to getting trapped in local optima during weight adjustment.
[0146] RBF Neural Network (Radial Basis Function, RBF): RBF neural network is a special type of neural network that uses radial basis functions as activation functions. It has better performance than BP neural network for handling certain types of problems, such as function approximation and pattern recognition.
[0147] K-means++ clustering algorithm: An improved K-means clustering algorithm. This algorithm can disperse cluster centers as much as possible, thus efficiently selecting the center values of hidden layer nodes in the RBF neural network during the coarse adjustment stage.
[0148] Pseudo-inverse algorithms, also known as Moore-Penrose inverses or generalized inverses, are mathematical techniques that provide a "closest" solution to the inverse matrix when the original matrix is non-invertible (or singular). If the original matrix is invertible, the pseudo-inverse matrix is equal to the inverse matrix. In neural network training, pseudo-inverse algorithms are often used to solve problems caused by the non-invertibility of the weight matrix.
[0149] L-BFGS-B algorithm: An improved BFGS algorithm that uses a limited memory approach to handle multivariate function minimization problems with boundary constraints, significantly reducing storage and computation requirements compared to the BFGS algorithm.
[0150] In summary, the direct digital frequency synthesizer based on a staged optimization RBF neural network of this invention, by introducing the RBF neural network into the direct digital frequency synthesizer, makes the system more scalable and adaptable when handling complex and nonlinear frequency synthesis tasks. Simultaneously, by introducing two optimization stages—coarse tuning and fine tuning—on the basis of the RBF neural network, and rationally utilizing the K-means++ clustering algorithm and the L-BFGS-B optimization algorithm, the training process of the RBF neural network is deeply optimized. This overcomes the problems of accuracy instability and excessive computational resource consumption in the traditional RBF neural network training process, greatly improving the training efficiency and accuracy of the RBF neural network.
[0151] The above embodiments are only used to illustrate the possible solutions of the present invention, and are not intended to limit it; those skilled in the art, within the scope of the technology disclosed in the present invention, shall make equivalent substitutions or modifications according to the technical solutions and inventive concepts of the present invention, and such modifications or modifications shall be covered within the protection scope of the present invention.
Claims
1. A direct digital frequency synthesizer based on a staged optimization RBF neural network, characterized in that... ,include: A phase accumulator is used to generate a phase signal; The RBF neural network module is used to convert phase signals into amplitude signals; A digital-to-analog converter is used to convert digital amplitude information into low-frequency sawtooth signals; A low-pass filter is used to suppress high-frequency noise in sawtooth wave signals from digital-to-analog converters, converting the sawtooth wave signals into smooth analog signals. The RBF neural network module includes a hidden layer and an output layer. The hidden layer contains multiple nodes, each with a corresponding radial basis function. For each input phase information, each hidden layer node can map it to a corresponding feature value. The output layer is connected to the nodes of the hidden layer through weights. After multiplying the feature value of each node with its corresponding weight, the values obtained by multiplying all nodes are summed to obtain an amplitude value corresponding to the phase information. The training process of the RBF neural network module includes two optimization stages: coarse tuning and fine tuning. The coarse tuning stage includes: selecting the center values of the hidden layer nodes of the RBF neural network using the K-means++ clustering algorithm, calculating the width of the radial basis function based on the center values, initializing the hidden layer weights randomly, and updating these weights using a pseudo-inverse algorithm. After the coarse tuning stage, the output error is used to determine whether the requirements are met. If not, the fine tuning stage begins. The fine tuning stage includes: adjusting the optimal center values from the coarse tuning stage using the Limited-memory Broyden–Fletcher–Goldfarb–Shanno with Box constraints (L-BFGS-B algorithm) until the output error meets the requirements.
2. The direct digital frequency synthesizer according to claim 1, characterized in that: The phase accumulator includes a full adder and an accumulator register. The full adder is used to sum the input frequency word with the accumulation result of the previous cycle to obtain a new accumulation result. The accumulator register is used to store the output value of the full adder in each clock cycle and provide the accumulation input value for the full adder in the next cycle.
3. The direct digital frequency synthesizer according to claim 1, characterized in that, The radial basis function is an inverse square function, specifically in the form of: ,in Represents input phase information, This indicates the center of the node. This represents the width of the radial basis functions.
4. The direct digital frequency synthesizer according to claim 1, characterized in that: The adjustment range of the L-BFGS-B algorithm is ±1 of the center value in the coarse adjustment stage.
5. The direct digital frequency synthesizer according to claim 1, characterized in that: The digital-to-analog converter receives the digital amplitude signal output by the RBF neural network module, and after undergoing an internal D / A conversion process, converts the digital amplitude signal into a corresponding analog low-frequency sawtooth wave signal, which is then transmitted to the low-pass filter.
6. The direct digital frequency synthesizer according to claim 1, characterized in that: The low-pass filter is used to receive the analog low-frequency sawtooth wave signal output by the digital-to-analog converter. Through the design characteristics of the low-pass filter, the high-frequency noise components in the analog low-frequency sawtooth wave signal are suppressed, thereby outputting a smooth analog signal.