Timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation

Abstract

The application relates to the technical field of audio signal processing, and discloses a timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation, which comprises the following steps: performing nonlinear operation on an actual independent variable of a logarithmic function by using the logarithmic function to generate an intermediate signal with harmonic components; performing smooth compression on the intermediate signal by using a soft knee saturation function constructed by a fixed saturation threshold and an exponential function to obtain a saturation shaping signal; performing frequency response correction on the saturation shaping signal by using a cascaded equalization filter to obtain an equalization signal; and performing protection limiting on the equalization signal to obtain an audio signal. The application can independently adjust the harmonic intensity, saturation depth and frequency response by using the hierarchical processing of logarithmic nonlinear mapping, fixed threshold soft knee saturation and cascaded equalization, and can realize stable and reproducible electronic tube power amplifier timbre simulation with low calculation complexity, and is suitable for real-time audio processing.

Description

Technical Field

[0001] This application relates to the field of audio signal processing technology, and in particular to a timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation. Background Technology

[0002] In the field of digital audio signal processing, vacuum tube power amplifiers (tube amplifiers) are highly favored in high-fidelity audio equipment, headphone amplifiers, and recording equipment due to their warm, smooth tone and rich harmonic structure. This unique tone mainly stems from the non-linear transmission characteristics and progressive saturation behavior of vacuum tubes, as well as the adjustment of frequency response by the output transformer and power supply filter circuit, resulting in a significant difference in sound perception compared to transistor amplifiers.

[0003] With the development of digital audio technology, software simulation of tube power amplifier timbre has become a key application in effects processors, plugins, and embedded systems, requiring the reproduction of nonlinear harmonics, smooth overload transitions, and specific frequency responses without relying on hardware.

[0004] Existing algorithms often employ static nonlinear mapping, soft clipping, or polynomial fitting, but they still have shortcomings in areas such as harmonic amplitude correlation, even-order harmonic generation, and independence of saturation transition. First, the harmonic distribution of fixed transfer functions (such as hyperbolic tangent and arctangent) is relatively fixed, making it difficult to reflect the gradual enrichment of harmonics as the input amplitude changes; even-order harmonics usually require additional bias or asymmetric coefficients, easily introducing gain-bias coupling. Second, common soft clipping mixes compression and distortion, lacking a clear linear operating region; small signal dynamics are easily compressed, making it impossible to simulate the transition from linear amplification to saturation; hard clipping's abrupt changes at the threshold generate too many high-order harmonics and sharp distortion. Polynomial fitting and lookup table interpolation are difficult to use a small number of parameters to coherently control the linear, nonlinear, and saturation regions, and high-order fitting may introduce oscillations. While circuit-level modeling is accurate, it is computationally complex and involves many parameters, hindering real-time adjustment. Furthermore, frequency response correction is often coupled with nonlinear processing; adjusting the frequency response affects distortion characteristics, leading to complex tone tuning and difficulty in stable reproduction. Summary of the Invention

[0005] In view of this, this application provides a timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation, which enables harmonic generation, saturation transition and frequency response correction to be modeled and adjusted independently, and achieves harmonic distribution that naturally changes with the input amplitude, smooth saturation processing under a fixed threshold and controllable overall timbre correction with low computational complexity.

[0006] This application discloses a timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation, which includes: Step 1: Adjust the gain of the input audio sample values ​​to obtain the signal to be processed; Step 2: Limit the amplitude of the signal to be processed and protect the lower limit of the independent variable of the logarithmic function to obtain the actual independent variable of the logarithmic function; Step 3: Use the logarithmic function to perform nonlinear operations on the actual independent variable of the logarithmic function to generate an intermediate signal with harmonic components; Step 4: The intermediate signal is smoothed and compressed using a soft-knee saturation function constructed from a fixed saturation threshold and an exponential function to obtain a saturated shaped signal; Step 5: Correct the frequency response of the saturated shaped signal using cascaded equalization filters to obtain an equalized signal; Step 6: Protect and limit the equalization signal, and output the audio signal; Step 7: When the input audio is a multi-channel signal, execute the processing flow of steps 1 to 6 for each channel.

[0007] Further, step 1 includes: Calculate the signal to be processed using the following formula;

[0008] in, The signal obtained after adjusting the input level is the signal to be processed; The current input audio sample value; This is the input gain coefficient, used to control the signal amplitude of the input signal before it enters the nonlinear processing stage.

[0009] Further, step 2 includes: Using a limiting function Signal to be processed Limited to the range Inside, the signal is restricted. The calculation formula is:

[0010] in, For domain restriction coefficients, A positive number less than 1; Using the maximum value function The independent variable of the logarithmic function By performing lower bound protection, the actual independent variable of the logarithmic function is obtained. The calculation formula is:

[0011] in, This is the lower bound protection coefficient of the logarithmic function. It is a positive number greater than 0.

[0012] Further, step 3 includes: The following formula is used to perform a logarithmic nonlinear mapping operation to obtain the harmonic-generated signal, i.e., the intermediate signal containing harmonic components. :

[0013] in, For the restricted signal, The actual independent variable of the logarithmic function, It is the natural logarithm function. This is the harmonic intensity control coefficient, used to adjust the proportion of logarithmic nonlinear components in the output signal.

[0014] Further, step 4 includes: Based on the intermediate signal containing harmonic components The amplitude range is used to obtain the saturated shaped signal using the corresponding calculation rules. : when hour, ; when hour, ; when hour, ; in, For a fixed saturation threshold, For the natural constant An exponential function with base 0.

[0015] Furthermore, in step 5, one or more second-order IIR equalization filters are cascaded to achieve timbre equalization processing; The calculation formula for a single second-order IIR equalizer is:

[0016] In the formula, For the first The output signal of the current sampling point of the equalization filter This is the equalization filter number. The sampling point number, For the first The input signal of the current sampling point of the equalization filter , , These are the forward filter coefficients of the equalization filter. , These are the feedback filter coefficients of the equalization filter; When multiple filters are cascaded, the output of the previous equalizer is used as the input of the next equalizer, and the input of the first equalizer is a saturated-shaped signal. The output of the last equalizer filter is the equalizer signal. .

[0017] Furthermore, the coefficients of the second-order IIR equalized filter are determined by the filter's center frequency. Quality Factor Gain and audio sampling rate Calculated; When the center frequency of the equalization filter Approaching or exceeding the audio sampling rate When the corresponding upper limit of the processable frequency is reached, the equalizer is configured in pass-through mode. The calculation formula for pass-through mode is as follows: .

[0018] Further, step 6 includes: According to the equalization signal The amplitude range is protected and limited to output audio signals. ; when hour, ; when hour, ; when hour, ; in, To protect the amplitude limiting threshold.

[0019] Further, step 7 includes: For the Input sampling signal for each channel Execute steps 1 through 6 sequentially to obtain the result. The final output sampling signal of each channel ; In multi-channel processing, all channels share the same input gain coefficient. Domain restriction coefficient The lower limit protection coefficient of the independent variable of the logarithmic function Harmonic intensity control coefficient Fixed saturation threshold Protection threshold It also includes equalization filter parameters, and each channel independently stores the filter's historical state.

[0020] Furthermore, prior to step 1, the procedure also includes: Calculate the equalizer filter coefficients based on the current audio sampling rate and clear all equalizer filter history states; when switching audio sources or re-initializing the processing state, only the equalizer filter history states are cleared, and the sampling rate and equalizer filter coefficients are not changed.

[0021] Due to the adoption of the above technical solution, this application has the following advantages: 1. This application combines logarithmic nonlinear mapping, fixed-threshold soft-knee saturation shaping, tone equalization, and output protection to enable audio signals to simultaneously achieve harmonic generation, smooth saturation, and frequency response correction during digital processing. This method utilizes logarithmic nonlinear mapping to introduce harmonic components that vary with the input amplitude, allowing the output signal to maintain a relatively natural dynamic performance at small amplitudes and gradually exhibit richer harmonic characteristics at larger amplitudes. Simultaneously, the fixed-threshold soft-knee saturation function preserves the linear transmission region within the threshold range and smoothly compresses signals exceeding the threshold, thereby avoiding abrupt distortion caused by hard clipping.

[0022] 2. By setting harmonic generation, saturation compression, and frequency response correction as independent processing stages, this application reduces the coupling between different timbre parameters, allowing harmonic intensity, saturation initiation position, and frequency response to be adjusted independently. This makes the algorithm debugging process clearer, enabling adjustments to relevant parameters according to different target timbre requirements while maintaining the stability and reproducibility of the processing results.

[0023] 3. This application reduces the risk of logarithmic operation anomalies, filter coefficient anomalies, and output amplitude overflow by using domain protection, lower limit protection of the logarithmic function's independent variable, equalization pass-through processing under low sampling rate conditions, and protection limiting. This improves the stability of the algorithm under different input levels, different sampling rates, and multi-channel processing conditions. This method does not rely on frequency domain transformation, convolution operations, or iterative solutions to complex circuit equations, and can complete sample-by-sample processing with low computational complexity, making it suitable for timbre simulation applications in real-time audio processing systems.

[0024] 4. This application can achieve a digital timbre simulation effect with the characteristics of a vacuum tube power amplifier based on a simple algorithm structure, controllable parameters and low computational load, so that the output audio can simultaneously have harmonic performance that varies with amplitude, smooth saturation transition under a fixed threshold and adjustable overall frequency response characteristics. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments recorded in the embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings.

[0026] Figure 1 This is a flowchart illustrating a timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation, according to an embodiment of this application. Detailed Implementation

[0027] The present application will be further described in conjunction with the accompanying drawings and embodiments. The described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments obtained by those skilled in the art should fall within the protection scope of the embodiments of the present application.

[0028] See Figure 1 This application provides an embodiment of a timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation, which includes: Step 1: Input level adjustment: Adjust the gain of the input audio sample value to obtain the signal to be processed; Step 2: Domain protection: Amplitude limiting is applied to the signal to be processed, and lower limit protection is applied to the independent variable of the logarithmic function to obtain the actual independent variable of the logarithmic function; Step 3: Logarithmic nonlinear mapping: Using the logarithmic function to perform nonlinear operations on the actual independent variable of the logarithmic function to generate an intermediate signal with harmonic components; Step 4: Fixed threshold soft knee saturation shaping: The intermediate signal is smoothed and compressed using a soft knee saturation function constructed from a fixed saturation threshold and an exponential function to obtain a saturated shaped signal; Step 5: Tone Equalization Processing: The frequency response of the saturated shaped signal is corrected by cascaded equalization filters to obtain an equalized signal; Step 6: Protective Limiting: Protectively limit the equalization signal and output the audio signal; Step 7: Multi-channel processing: When the input audio is a multi-channel signal, the processing flow of steps 1 to 6 is executed for each channel.

[0029] This application is used to perform sample-by-sample processing on the input audio signal, generate harmonic components with amplitude correlation through logarithmic nonlinear mapping, and smooth and compress signals exceeding the preset saturation threshold through a fixed threshold soft knee saturation function. Combined with timbre equalization and protection limiting, an output audio signal with the timbre characteristics of the target power amplifier is obtained.

[0030] Optionally, step 1 includes: Calculate the signal to be processed using the following formula;

[0031] in, The signal obtained after adjusting the input level is the signal to be processed; The current input audio sample value; This is the input gain coefficient, used to control the signal amplitude of the input signal before it enters the nonlinear processing stage.

[0032] Step 1 serves to preprocess the input signal, ensuring that the subsequent logarithmic nonlinear mapping and fixed-threshold soft-knee saturation processing are within a suitable operating range. This is achieved by adjusting... This allows control over the degree to which the input signal drives nonlinear mapping and saturation shaping. When When the input signal is large, it is more likely to enter the nonlinear region and saturation region; when When the value is smaller, the output is closer to a linear tone. It can be set according to the target timbre intensity, input signal level, and system output margin.

[0033] Optionally, step 2 includes: Using a limiting function Signal to be processed Limited to the range Inside, the signal is restricted. The calculation formula is:

[0034] in, For domain restriction coefficients, A positive number less than 1; Using the maximum value function The independent variable of the logarithmic function By performing lower bound protection, the actual independent variable of the logarithmic function is obtained. The calculation formula is:

[0035] in, This is the lower bound protection coefficient of the logarithmic function. It is a positive number greater than 0.

[0036] Step 2 serves to prevent the independent variable of the logarithmic function from being zero or negative, thereby avoiding infinity, non-numerical, or abnormal outputs. This is because subsequent logarithmic nonlinear mappings include... ,when Logarithmic operations can cause numerical problems when the value is close to or exceeds 1. Therefore, by... and The dual protection ensures that the algorithm remains stable even under extreme input conditions.

[0037] Optionally, step 3 includes: The following formula is used to perform a logarithmic nonlinear mapping operation to obtain the harmonic-generated signal, i.e., the intermediate signal containing harmonic components. :

[0038] in, For the restricted signal, The actual independent variable of the logarithmic function, It is the natural logarithm function. This is the harmonic intensity control coefficient, used to adjust the proportion of logarithmic nonlinear components in the output signal.

[0039] Step 3 is used to generate harmonics from the input signal by utilizing the nonlinear characteristics of the logarithmic function. Used to adjust the intensity of harmonic generation, when When the value is large, the proportion of logarithmic nonlinear components increases, and the harmonic components in the output signal are enhanced; when When the value is reduced, the output signal becomes closer to the original linear signal. This logarithmic nonlinear mapping is based on the following mathematical relationship: ,in

[0040] in, Represents a normalized variable that satisfies the domain conditions; , They represent The second and third powers; the ellipsis indicates a higher power term.

[0041] This mathematical relationship shows that the logarithmic function can introduce power terms of different orders into the output signal in a closed-form expression. Since the coefficients of power terms of different orders decrease as the order increases, this mapping allows higher-order harmonics to gradually weaken relative to lower-order harmonics. Furthermore, this mapping is not a completely odd-symmetric function about the origin; the mapping relationships for positive and negative inputs are different. Therefore, it can form an asymmetric harmonic structure in the output signal, making the output signal contain even-order harmonic components.

[0042] Step 3 independently models the harmonic generation process of the audio signal, providing an intermediate signal with the target harmonic structure for subsequent saturation transition processing.

[0043] Optionally, step 4 includes: Based on the intermediate signal containing harmonic components The amplitude range is used to obtain the saturated shaped signal using the corresponding calculation rules. : when hour, ; when hour, ; when hour, ; in, A fixed saturation threshold is used to determine the critical amplitude at which a signal transitions from the linear region to the saturated compression region; For the natural constant An exponential function with base 0.

[0044] Step 4 serves to simulate the smooth transition of an audio signal from a linear transmission state to a saturated state. When lie in When within range, output Equal to input That is, the signal maintains linear transmission without saturation compression; when Greater than At that time, only for values ​​exceeding the positive threshold The portion is smoothly compressed; when Less than At that time, only for values ​​exceeding the negative threshold The portion is smoothly compressed.

[0045] In step 4, A fixed threshold parameter is used, which does not dynamically change with the instantaneous amplitude of a single sampling point during processing. This is achieved by setting... It can control where saturation occurs. When the value is large, the linear region is wide, and the signal is less likely to enter the saturation region; When the value is small, the linear region is narrower, the signal is more likely to enter the saturation region, and the saturation effect is more obvious.

[0046] The soft-knee saturation function establishes a smooth compression relationship through an exponential function, preventing the signal from being directly truncated after exceeding the threshold, thus avoiding the amplitude abrupt changes caused by hard clipping at the threshold. Unlike the logarithmic nonlinear mapping in step three, this step mainly controls the saturation transition and compression mode. By separating harmonic generation and saturation compression into two consecutive but independent steps, they can be adjusted separately. and This allows for the separate control of harmonic intensity and saturation depth.

[0047] Optionally, in step 5, one or more second-order IIR equalization filters are cascaded to achieve timbre equalization processing; The calculation formula for a single second-order IIR equalizer is:

[0048] In the formula, For the first The output signal of the current sampling point of the equalization filter This is the equalization filter number. The sampling point number, For the first The input signal of the current sampling point of the equalization filter , , These are the forward filter coefficients of the equalization filter. , These are the feedback filter coefficients of the equalization filter; When multiple filters are cascaded, the output of the previous equalizer is used as the input of the next equalizer, and the input of the first equalizer is a saturated-shaped signal. The output of the last equalizer filter is the equalizer signal. .

[0049] Optionally, when multiple equalizers are cascaded, the output of the previous equalizer is used as the input of the next equalizer. Let there be M equalizers in total, then:

[0050] ,in

[0051]

[0052] in, Indicates the total number of cascaded equalizers; This represents the saturated and shaped signal of the current sampling point obtained in step 4. This represents the signal after processing by all equalization filters.

[0053] The coefficients of each equalizer filter can be determined based on the center frequency, quality factor, gain, and sampling rate. Let the first equalizer be... The center frequency of each equalizer filter is The quality factor is The gain is The current sampling rate is Then the filter coefficients can be determined according to , , and Calculated.

[0054] in, Indicates the first The target operating frequency position of the equalization filter; Indicates the first Bandwidth control parameters of an equalizer filter The larger the value, the narrower the operating bandwidth. The smaller the value, the wider the operating bandwidth; Indicates the first The gain parameter of each equalizer is used to control the boost or attenuation magnitude of this frequency band. This indicates the sampling rate of the audio system.

[0055] Step 5 aims to correct the frequency response of the audio signal after nonlinear mapping and soft knee saturation. This is achieved by setting different... , and It allows for independent adjustment of the low-frequency, mid-frequency, or high-frequency ranges to achieve a target tonal balance in the output signal. For example, a low-frequency equalizer can be set to enhance low-frequency thickness, while a high-frequency equalizer can be set to reduce high-frequency energy, resulting in a smoother tone.

[0056] In step 5, the tone equalization processing is independent of the aforementioned harmonic generation and saturation compression. When adjusting the equalization parameters, the steps in step 3 remain unchanged. It does not change the steps in step 4. This allows for separate control of harmonic intensity, saturation position, and frequency response.

[0057] Optionally, the coefficients of the second-order IIR equalized filter are determined by the filter's center frequency. Quality Factor Gain and audio sampling rate Calculated; When the center frequency of the equalization filter Approaching or exceeding the audio sampling rate When the corresponding upper limit of the processable frequency is reached, the equalizer is configured in pass-through mode. The calculation formula for pass-through mode is as follows: The purpose of pass-through processing is to avoid abnormal coefficients or unstable outputs caused by inappropriate filter center frequency settings under low sampling rate conditions.

[0058] Optionally, step 6 includes: According to the equalization signal The amplitude range is protected and limited to output audio signals. ; when hour, ; when hour, ; when hour, ; in, To protect the amplitude limiting threshold.

[0059] Step 6 serves to prevent the signal, after being processed by logarithmic nonlinear mapping, soft knee saturation shaping, and tone equalization, from exceeding the system's allowed output range. It can be set according to the output range of the normalized audio system. This protection limit is mainly used as a safety protection measure and is not used as a primary means of shaping tone.

[0060] Optionally, step 7 includes: For the Input sampling signal for each channel Execute steps 1 through 6 sequentially to obtain the result. The final output sampling signal of each channel ; In multi-channel processing, all channels share the same input gain coefficient. Domain restriction coefficient The lower limit protection coefficient of the independent variable of the logarithmic function Harmonic intensity control coefficient Fixed saturation threshold Protection threshold It also includes equalization filter parameters, and each channel independently stores the filter's historical state.

[0061] Alternatively, each channel is processed according to the following procedure: →Input level adjustment→Domain protection→Logarithmic nonlinear mapping→Fixed threshold soft knee saturation shaping→Tone equalization processing→Protective limiting→

[0062] in, Indicates the vocal tract number; Indicates the sampling point number; Indicates the first The current input sample value for each channel; Indicates the first The current output sample value of each channel.

[0063] In multi-channel processing, all channels can share the same input gain coefficient. Domain restriction coefficient The lower limit protection coefficient of the independent variable of the logarithmic function Harmonic intensity control coefficient Fixed saturation threshold Protection threshold and equalization filter parameters , , However, the filter history of each channel should be saved separately.

[0064] Step 7 aims to ensure that multi-channel audio has consistent timbre processing parameters, while avoiding mutual interference between filter states of different channels, thereby maintaining channel independence and stereo stability.

[0065] This application's method supports both mono and stereo audio processing. For stereo audio, the left and right channels share the same equalization filter coefficients, but each maintains independent filter state variables. Each channel undergoes independent sample-by-sample processing according to steps 1 to 6 described above.

[0066] Optionally, before step 1, the method further includes: Calculate the equalizer filter coefficients based on the current audio sampling rate, and clear all equalizer filter history states. When switching audio sources or re-initializing the processing state, only the historical state of the equalizer filter is cleared, without changing the sampling rate and equalizer filter coefficients.

[0067] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.

Claims

1. A timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation, characterized in that, include: Step 1: Adjust the gain of the input audio sample values ​​to obtain the signal to be processed; Step 2: Limit the amplitude of the signal to be processed and protect the lower limit of the independent variable of the logarithmic function to obtain the actual independent variable of the logarithmic function; Step 3: Use the logarithmic function to perform nonlinear operations on the actual independent variable of the logarithmic function to generate an intermediate signal with harmonic components; Step 4: The intermediate signal is smoothed and compressed using a soft-knee saturation function constructed from a fixed saturation threshold and an exponential function to obtain a saturated shaped signal; Step 5: Correct the frequency response of the saturated shaped signal using cascaded equalization filters to obtain an equalized signal; Step 6: Protect and limit the equalization signal, and output the audio signal; Step 7: When the input audio is a multi-channel signal, execute the processing flow from Step 1 to Step 6 for each channel respectively; Step 3 includes: Perform a logarithmic nonlinear mapping operation according to the following formula to obtain the signal after harmonic generation, i.e., the intermediate signal with harmonic components. : in, For the restricted signal, The actual independent variable of the logarithmic function, It is the natural logarithm function. This is the harmonic intensity control coefficient, used to adjust the proportion of logarithmic nonlinear components in the output signal; Step 4 includes: Based on the intermediate signal containing harmonic components The amplitude range is used to obtain the saturated shaped signal using the corresponding calculation rules. : when hour, ; when hour, ; when hour, ; in, For a fixed saturation threshold, For the natural constant An exponential function with base 0.

2. The timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation according to claim 1, characterized in that, Step 1 includes: Calculate the signal to be processed using the following formula; in, The signal obtained after adjusting the input level is the signal to be processed; The current input audio sample value; This is the input gain coefficient, used to control the signal amplitude of the input signal before it enters the nonlinear processing stage.

3. The timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation according to claim 1, characterized in that, Step 2 includes: Using a limiting function Signal to be processed Limited to the range Inside, the signal after restriction is obtained. The calculation formula is: in, For domain restriction coefficients, A positive number less than 1; Using the maximum value function The independent variable of the logarithmic function By performing lower bound protection, the actual independent variable of the logarithmic function is obtained. The calculation formula is: in, This is the lower bound protection coefficient of the logarithmic function. It is a positive number greater than 0.

4. The timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation according to claim 1, characterized in that, In step 5, one or more second-order IIR equalization filters are cascaded to achieve timbre equalization processing. The calculation formula for a single second-order IIR equalizer is: In the formula, For the first The output signal of the current sampling point of the equalization filter This is the equalization filter number. The sampling point number, For the first The input signal of the current sampling point of the equalization filter , , These are the forward filter coefficients of the equalization filter. , These are the feedback filter coefficients of the equalization filter; When multiple filters are cascaded, the output of the previous equalizer is used as the input of the next equalizer, and the input of the first equalizer is a saturated-shaped signal. The output of the last equalizer filter is the equalizer signal. .

5. The timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation according to claim 4, characterized in that, The coefficients of the second-order IIR equalized filter are determined by the filter's center frequency. Quality Factor Gain and audio sampling rate Calculated; When the center frequency of the equalization filter Approaching or exceeding the audio sampling rate When the corresponding upper limit of the processable frequency is reached, the equalizer is configured in pass-through mode. The calculation formula for pass-through mode is as follows: .

6. The timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation according to claim 1, characterized in that, Step 6 includes: According to the equalization signal The amplitude range is protected and limited to output audio signals. ; when hour, ; when hour, ; when hour, ; in, To protect the amplitude limiting threshold.

7. The timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation according to claim 1, characterized in that, Step 7 includes: For the Input sampling signal for each channel Execute steps 1 through 6 sequentially to obtain the result. The final output sampling signal of each channel ; In multi-channel processing, all channels share the same input gain coefficient. Domain restriction coefficient The lower limit protection coefficient of the independent variable of the logarithmic function Harmonic intensity control coefficient Fixed saturation threshold Protection threshold It also includes equalization filter parameters, and each channel independently stores the filter's historical state.

8. The timbre simulation method based on logarithmic nonlinear mapping and fixed threshold soft knee saturation according to claim 1, characterized in that, Before step 1, the following are also included: Calculate the equalizer filter coefficients based on the current audio sampling rate and clear all equalizer filter history states; when switching audio sources or re-initializing the processing state, only the equalizer filter history states are cleared, and the sampling rate and equalizer filter coefficients are not changed.

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