Cavity light force chaotic acceleration sensing system and calibration method

Abstract

The invention discloses a cavity light force chaotic acceleration sensing system and a calibration method, is applied to the technical field of sensors, and aims to solve the problem that the existing cavity light force acceleration sensor is difficult to keep stable measurement performance when the frequency and amplitude of acceleration to be detected are both small. Working parameters of the cavity light power system provided by the invention are accurately adjusted to enter a chaotic state; external acceleration acts on the micro-mechanical oscillator, so that the cavity length of the optical resonant cavity is slightly changed, and the chaotic light field is modulated; the photoelectric detection module captures the modulated chaotic light field and converts the modulated chaotic light field into an electric signal; and the signal processing module analyzes the electric signal, establishes a quantitative mapping relation between the acceleration and amplitude, frequency, phase and frequency spectrum changes, inverts the acceleration by using a multi-feature fusion technology, and completes calibration. The system has excellent sensitivity and precision, is particularly suitable for high-precision measurement of micro acceleration, and can be widely applied to the fields of aerospace, precise instruments and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to sensor technology, in particular to a chaotic acceleration sensing system based on cavity optomechanics. Specifically, the present application relates to detecting acceleration by combining cavity optomechanics effects with chaotic dynamics, using changes in amplitude, frequency, phase and spectrum of chaotic light field. BACKGROUND

[0002] With the development of technology, existing acceleration sensors such as capacitive and piezoelectric types have certain limitations in high-precision measurement, low-frequency measurement and high-sensitivity applications. Especially in the detection of small acceleration, it is often affected by noise interference, temperature changes and other external environmental factors, resulting in a decrease in measurement accuracy.

[0003] Cavity optomechanics technology is widely used in acceleration sensors due to its high sensitivity. However, existing cavity optomechanics acceleration sensors can provide high sensitivity, but when facing small acceleration frequency and amplitude, traditional methods are difficult to maintain stable measurement performance.

[0004] The introduction of chaotic dynamics provides a new way to improve the accuracy and stability of the system. By observing the changes in amplitude, frequency, phase and spectrum of chaotic light field, the changes in acceleration signal can be effectively detected. Chaotic systems have strong sensitivity and robustness to external disturbances, so they can provide more accurate and stable acceleration measurement results. SUMMARY

[0005] To solve the above technical problems, the present application proposes a cavity optomechanics chaotic acceleration sensing system that combines cavity optomechanics principles with chaotic dynamics to achieve high-sensitivity detection of acceleration by monitoring changes in amplitude, frequency, phase and spectrum of chaotic light field.

[0006] One of the technical solutions adopted by the present application is: a cavity optomechanics chaotic acceleration sensing system, comprising: a vacuum cavity, a laser source, a photodetector module and a signal processing module; the vacuum cavity includes an optical resonant cavity and a micromechanical oscillator rigidly connected to the optical resonant cavity; the laser provided by the laser source enters the optical resonant cavity through an optical fiber, and when the vacuum cavity is in a chaotic state, the micromechanical oscillator completes chaotic modulation on the laser entering the optical resonant cavity under the action of acceleration, the photodetector module obtains the laser signal after chaotic modulation through the optical fiber, and the signal processing module analyzes the acceleration information based on the laser signal obtained by the photodetector module.

[0007] The vacuum cavity further comprises a base, and one part of the photonic crystal microcavity is rigidly connected to the micromechanical oscillator, and the other part of the photonic crystal microcavity is fixed on the base.

[0008] The micromechanical oscillator includes a movable mass block and a cantilever beam. A portion of the photonic crystal microcavity is rigidly connected to the movable mass block, which is fixed to the free end of the cantilever beam. The other end of the cantilever beam is fixed to the base support structure.

[0009] By adjusting various parameters of the vacuum chamber, the vacuum chamber is brought into a chaotic state.

[0010] The process of achieving chaotic modulation of laser light incident on an optical resonant cavity by a micromechanical oscillator under acceleration excitation is as follows: when external acceleration is applied to the vacuum cavity in a chaotic state, the micromechanical oscillator is driven to generate displacement through the optical-mechanical coupling effect, thereby disturbing the optical resonance condition of the vacuum cavity and directly modulating the output of the chaotic light field.

[0011] The parameters of the vacuum cavity include the resonant wavelength of the optical resonant cavity, the mechanical frequency of the micromechanical oscillator, the effective mass of the movable mass block, the input laser power, the input laser wavelength, and the vacuum-optical-mechanical coupling strength.

[0012] The vacuum chamber parameters must meet the following requirements:

[0013] The resonant wavelength of the optical resonant cavity is located within the C-band range of optical communication;

[0014] The mechanical frequency of the micromechanical oscillator is between 1 MHz and 800 GHz;

[0015] The effective mass of the movable mass block is kilograms to Between kilograms;

[0016] The input laser power ranges from 1 microwatt to 100 milliwatts;

[0017] The detuning between the input laser wavelength and the resonant wavelength of the optical resonant cavity is between 0.1 picometers and 10 nanometers;

[0018] The vacuum optomechanical coupling strength is between 500 Hz and 10 GHz.

[0019] The second technical solution adopted in this invention is: a cavity optical force chaotic acceleration calibration method, comprising:

[0020] S1, Adjust the operating parameters of the cavity optical system to a specific value to bring the system into a chaotic state;

[0021] S2, A small external acceleration acts on the micromechanical oscillator, producing a small displacement, which causes a change in the cavity length of the optical resonant cavity, and in turn causes a shift in the resonant frequency of the optical resonant cavity, thereby causing a dynamic change in the chaotic optical field. The amplitude of the external acceleration signal should ensure that the system remains in the chaotic state induced by cavity-optical-mechanical coupling.

[0022] S3, use the photoelectric detection module to capture the chaotically modulated light field signal and convert it into an electrical signal, and then use the signal processing module to extract the features of the electrical signal, including but not limited to amplitude features, frequency features, phase features and spectral features, etc.

[0023] S4. Establish a quantitative mapping relationship between multi-feature changes and acceleration. Through multi-feature weighted fusion technology, achieve accurate inversion of acceleration values ​​and complete the calibration of the accelerometer.

[0024] The beneficial effects of this invention are as follows: The cavity optical-mechanical chaotic acceleration sensing system of this invention achieves acceleration detection by introducing changes in the amplitude, frequency, phase, and spectrum of a chaotic optical field. Specifically: the operating parameters of the cavity optical-mechanical system are precisely adjusted to induce a chaotic state; external acceleration acts on a micromechanical oscillator, causing a minute change in the cavity length of the optical resonant cavity, modulating the chaotic optical field; the photoelectric detection module captures the modulated chaotic optical field and converts it into an electrical signal; the signal processing module analyzes the electrical signal, establishes a quantitative mapping relationship between acceleration and changes in amplitude, frequency, phase, and spectrum, and uses multi-feature fusion technology to invert the acceleration and complete calibration; the system of this invention has the following advantages:

[0025] 1. High sensitivity: By utilizing the nonlinear characteristics of chaos, the system can respond very sensitively to changes in acceleration, especially in the range of small accelerations;

[0026] 2. Strong robustness: Chaotic dynamics can effectively resist external noise and disturbances, maintaining high measurement accuracy;

[0027] 3. High precision: Through multiple analyses of changes in amplitude, frequency, phase, and spectrum, this invention can provide more accurate acceleration detection results, making it particularly suitable for applications in fields such as high-precision inertial navigation.

[0028] 4. Wide applicability: This invention is applicable to aerospace, precision instruments and other fields. Attached Figure Description

[0029] Figure 1 is a schematic diagram of the core sensing unit structure of the cavity optical chaotic acceleration sensing system of the present invention.

[0030] Figure 2 is a schematic diagram of the complete system device of the cavity optical chaotic acceleration sensing system of the present invention.

[0031] Figure 3 is a flowchart of the cavity optical force chaotic acceleration calibration method of the present invention.

[0032] Figure 4 is a chaotic phase diagram of the system of the present invention corresponding to parameter combination one.

[0033] Figure 5 is the chaotic phase diagram of the system of the present invention corresponding to parameter combination two.

[0034] Figure 6 is the chaotic phase diagram of the system of the present invention corresponding to parameter combination three.

[0035] Figure 7 is the chaotic phase diagram of the system of the present invention corresponding to parameter combination four. Detailed Implementation

[0036] like Figure 1 The key component of the sensor, the vacuum cavity, is shown. It includes a photonic crystal microcavity, a micromechanical oscillator, and a base. One part of the photonic crystal microcavity is rigidly connected to the micromechanical oscillator, and the other part of the photonic crystal microcavity is fixed on the base.

[0037] like Figure 1 As shown, the micromechanical oscillator includes a movable mass block and a cantilever beam. A portion of the photonic crystal microcavity is rigidly connected to the movable mass block, which is fixed to the free end of the cantilever beam. The other end of the cantilever beam is fixed to the base support structure.

[0038] Under acceleration, the cantilever beam bends, causing displacement of the movable mass block, which in turn causes a change in the cavity length of the photonic crystal microcavity. This change in cavity length modulates the optical field within the cavity, forming a coupling relationship between the optical signal and the mechanical displacement.

[0039] As shown in Figure 2, the cavity optical-mechanical chaotic acceleration sensing system of the present invention includes a vacuum cavity, a laser source, a photoelectric detection module and a signal processing module. The components are connected by optical fiber and electrical connection to form a closed-loop detection system. The core utilizes the chaotic dynamic characteristics induced by cavity optical-mechanical coupling to achieve high-sensitivity acceleration measurement.

[0040] The vacuum cavity includes an optical resonant cavity and a micromechanical oscillator. The portion of the vacuum cavity connecting the two optical fibers is a tapered coupling fiber. The function of the tapered coupling fiber is to couple the laser output from the laser source into the optical resonant cavity and then couple it out of the optical resonant cavity, transmitting the chaotic light field output from the optical resonant cavity to the photoelectric detection module. Those skilled in the art will understand that the tapered fiber, through its gradually tapering structure, achieves efficient coupling with the optical resonant cavity, thereby optimizing the transmission and modulation efficiency of the optical signal.

[0041] The optical resonant cavity is a two-dimensional photonic crystal microcavity, which has a high quality factor and can provide a stable optical mode. The cavity is rigidly connected to a micromechanical oscillator, and the cavity length changes linearly with the displacement of the oscillator, thereby inducing a shift in the cavity resonant frequency. This shift serves as an external perturbation input to the chaotic system, directly modulating the output of the chaotic optical field.

[0042] The micromechanical oscillator, combined with the optical resonant cavity, can generate minute displacements under minute acceleration, thereby inducing changes in the amplitude and spectrum of the chaotic light field.

[0043] The output wavelength of the laser source is precisely matched to the resonant wavelength of the optical resonant cavity, and it supports detuning adjustment with picometer- to nanometer-level precision near the resonant wavelength. By dynamically fine-tuning the frequency detuning between the laser and the cavity, the system is ensured to operate stably within the chaotic threshold range induced by cavity-optical-mechanical coupling, laying the foundation for high-sensitivity modulation of acceleration signals.

[0044] The photoelectric detection module uses a high-bandwidth, low-noise photodiode, which can efficiently capture the light field intensity signal after chaotic modulation and linearly convert it into an electrical signal. This electrical signal completely preserves the dynamic characteristics of the chaotic system and the coupling information related to the acceleration input, providing high signal-to-noise ratio raw data support for the subsequent signal processing module.

[0045] The signal processing module consists of a high-speed data acquisition card and a host computer. The workflow is as follows: First, the chaotic characteristic electrical signal output by the photoelectric detection module is acquired in real time by the high-speed data acquisition card and the data is stored. Then, the characteristic changes such as amplitude, frequency, phase and spectrum are extracted. Combined with the chaotic dynamics characteristic analysis, a quantitative mapping relationship between the changes in amplitude, frequency, phase and spectrum and acceleration is established. Finally, the acceleration is accurately inverted through this mapping model.

[0046] The working principle and process of the cavity optical-mechanical chaotic acceleration sensing system of the present invention are as follows: When acceleration is applied to the micromechanical oscillator, the oscillator is displaced, which in turn causes a slight change in the cavity length. These changes lead to changes in the optical frequency within the optical cavity, and through the nonlinear behavior of the chaotic system, manifest as changes in the amplitude, frequency, phase, and spectrum of the chaotic optical field. The signal processing module can extract acceleration information in real time by detecting and analyzing these changes.

[0047] In practical implementation, the signal processing module performs real-time calculations on the electrical signal output by the photoelectric detection module based on the chaotic dynamic characteristics of the cavity-optical-mechanical coupling system. This module synchronously captures the variation patterns of the amplitude, frequency, phase, and spectrum of the chaotic signal, establishing a coupling mapping model between multiple characteristic parameters and acceleration. This effectively suppresses the influence of environmental noise and system interference on the measurement results, thereby significantly improving the sensitivity, accuracy, and stability of acceleration measurement.

[0048] like Figure 3 As shown, the present invention also provides a method for calibrating cavity optical chaotic acceleration, comprising:

[0049] S1, Adjust the operating parameters of the cavity optical system to specific values ​​to induce a chaotic state; adjusting the parameters of the cavity optical system to specific values ​​includes:

[0050] S11, The resonant wavelength of the optical resonant cavity is designed to be within the C-band range of optical communication;

[0051] S12, the mechanical frequency of the micromechanical oscillator is designed to be between 1 MHz and 800 GHz;

[0052] S13, the effective mass of the movable mass block is designed to be within... kilograms to Between kilograms;

[0053] S14, adjust the input laser power between 1 microwatt and 100 milliwatts;

[0054] S15, Adjust the input laser wavelength so that the detuning between it and the resonant wavelength of the optical resonant cavity is between 0.1 picometers and 10 nanometers;

[0055] S16, adjust the vacuum optomechanical coupling strength between 500 Hz and 10 GHz;

[0056] S17. The parameters of the cavity optical-mechanical system must strictly meet S11, S12, S13, S14, S15, and S16 to ensure that the system operates in the chaotic region induced by cavity optical-mechanical coupling.

[0057] S2, A small external acceleration acts on the micromechanical oscillator, producing a small displacement, which causes a change in the cavity length of the optical resonant cavity, and consequently shifts the resonant frequency of the optical resonant cavity, thus causing dynamic changes in the chaotic optical field. The amplitude of the external acceleration signal should not exceed the maximum range of the cavity optical-mechanical chaotic acceleration sensing system; the process of chaos generation is as follows:

[0058] A1. In a cavity optomechanical system, the interaction between the optical field and the micromechanical oscillator causes a change in the cavity length of the optical resonant cavity through laser input;

[0059] A2. There is a nonlinear coupling between the optical field in the optical resonant cavity and the micromechanical oscillator, which leads to complex nonlinear effects in the dynamic behavior of the cavity optical-mechanical system;

[0060] A3. The material of the optical resonator will cause changes in the carrier density. Specifically, when the optical resonator uses silicon, the laser generates carriers through the two-photon absorption effect, which modulates the optical field in the cavity and further induces nonlinear interactions between the optical field, the mechanical oscillator and the carriers.

[0061] A4. The nonlinear interaction between light, force, and charge carriers induces chaotic behavior under specific parameter conditions and produces changes proportional to acceleration, including but not limited to changes in amplitude, frequency, phase, and spectrum.

[0062] The maximum range of a cavity optical chaotic accelerometer system refers to the range of external acceleration signals that the system can stably and without distortion detect. In practical applications, this range depends on the specific device; different device parameters result in different ranges.

[0063] S3, use the photoelectric detection module to capture the chaotically modulated light field signal and convert it into an electrical signal, and then use the signal processing module to extract the values ​​of the electrical signal, including but not limited to amplitude, frequency, phase and spectrum values.

[0064] The changes in amplitude, frequency, phase, and spectrum of the chaotic light field in step S3 are detected through the following steps:

[0065] B1, the photoelectric detection module captures the light field intensity signal transmitted through the optical fiber in real time;

[0066] B2 converts the captured optical signal into an electrical signal and amplifies it.

[0067] B3 processes the electrical signal through the signal processing module, extracting values ​​such as amplitude, frequency, phase, and spectrum. Specifically, it includes the following steps:

[0068] B31, statistically analyzes the amplitude, frequency, phase, and spectrum of electrical signals;

[0069] B32, establish the correspondence between changes in amplitude, frequency, phase and spectrum values ​​and actual acceleration changes;

[0070] S4 employs a multi-feature weighted fusion technique using a neural network regression algorithm. Using "extracted multi-feature data" and "corresponding actual acceleration values" as training samples, it learns the correlation strength between each feature and acceleration changes, automatically determining the optimal weight for each feature. The features are then weighted and fused according to their optimal weights. A mapping relationship between the fused comprehensive features and acceleration is established. Substituting the real-time acquired multi-feature data, the corresponding acceleration value is retrieved. This retrieved acceleration value is used as the acceleration value measured by the cavity optical-mechanical chaotic accelerometer system, thus completing the calibration of the cavity optical-mechanical chaotic accelerometer system. The neural network regression algorithm is a known existing technology and will not be described in detail here.

[0071] To better illustrate the present invention, some typical practical parameter combinations are provided below to demonstrate the application of cavity optical-mechanical chaotic systems:

[0072] Parameter combination one: The resonant wavelength of the optical resonant cavity is 1570.3 nm, the mechanical frequency of the micromechanical oscillator is 110 MHz, and the effective mass of the movable mass block is... The system has a weight of 1 kg, an input laser power of 1.2 mW, a detuning of 4 picometers, and a vacuum optomechanical coupling strength of 690 kHz. This parameter combination ensures that the cavity optomechanical system operates stably in a chaotic state and can output parameters such as... Figure 4 The chaotic phase diagram shown below, in which This represents the output port power of the tapered coupled optical fiber, measured in femtojoules (fJ). It represents the change in temperature inside the cavity, and the unit is Kelvin (K).

[0073] Parameter combination two: The resonant wavelength of the optical resonant cavity is 1530 nm, the mechanical frequency of the micromechanical oscillator is 10 MHz, and the effective mass of the movable mass block is... The system has a weight of 1 kg, an input laser power of 100 mW, a detuning of 15 picometers, and a vacuum optomechanical coupling strength of 600 kHz. This parameter combination ensures that the cavity optomechanical system operates stably in a chaotic state and can output parameters such as... Figure 5 The chaotic phase diagram shown below, in which This represents the output power of the tapered-coupled optical fiber, measured in femtojoules (fJ). It represents the change in temperature inside the cavity, and the unit is Kelvin (K).

[0074] Parameter combination three: The resonant wavelength of the optical resonant cavity is 1530 nm, the mechanical frequency of the micromechanical oscillator is 1 MHz, and the effective mass of the movable mass block is... The system has a weight of 1 kg, an input laser power of 100 mW, a detuning of 15 picometers, and a vacuum optomechanical coupling strength of 600 kHz. This parameter combination ensures that the cavity optomechanical system operates stably in a chaotic state and can output parameters such as... Figure 6 The chaotic phase diagram shown below, in which This represents the output power of the tapered-coupled optical fiber, measured in femtojoules. This represents the change in temperature within the cavity, measured in Kelvin.

[0075] Parameter combination four: The resonant wavelength of the optical resonant cavity is 1625 nanometers, the mechanical frequency of the micromechanical oscillator is 1 MHz, and the effective mass of the movable mass block is... The system has a weight of 1 kg, an input laser power of 100 mW, a detuning of 5 picometers, and a vacuum optomechanical coupling strength of 840 kHz. This parameter combination ensures that the cavity optomechanical system operates stably in a chaotic state and can output parameters such as... Figure 7 The chaotic phase diagram shown below, in which This represents the output power of the tapered-coupled optical fiber, measured in femtojoules. This represents the change in temperature within the cavity, measured in Kelvin.

[0076] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A cavity optical force chaotic acceleration sensing system, characterized in that, include: Vacuum cavity, laser source, photoelectric detection module and signal processing module; the vacuum cavity includes an optical resonant cavity and a micromechanical oscillator rigidly connected to the optical resonant cavity; The laser provided by the laser source enters the optical resonant cavity through an optical fiber. When the vacuum cavity is in a chaotic state, the micromechanical oscillator performs chaotic modulation on the laser entering the optical resonant cavity under the action of acceleration. The photoelectric detection module acquires the laser signal after chaotic modulation through the optical fiber. The signal processing module analyzes the laser signal acquired by the photoelectric detection module to obtain acceleration information.

2. The cavity optical force chaotic acceleration sensing system according to claim 1, characterized in that, The vacuum cavity also includes a base, a part of the optical resonant cavity is rigidly connected to the micromechanical oscillator, and the other part of the optical resonant cavity is fixed on the base.

3. The cavity optical chaotic acceleration sensing system according to claim 2, characterized in that, The micromechanical oscillator includes a movable mass block and a cantilever beam. A portion of the optical resonant cavity is rigidly connected to the movable mass block of the micromechanical oscillator. The movable mass block is fixed to the free end of the cantilever beam, and the other end of the cantilever beam is fixed to the base.

4. The cavity optical chaotic acceleration sensing system according to claim 3, characterized in that, By adjusting various parameters of the vacuum cavity, the vacuum cavity is brought into a chaotic state. These parameters include the resonant wavelength of the optical resonant cavity, the mechanical frequency of the micromechanical oscillator, the effective mass of the movable mass block, the input laser power, the input laser wavelength, and the vacuum-optical-mechanical coupling strength.

5. A cavity optical chaotic acceleration sensing system according to claim 4, characterized in that, The parameters of the vacuum cavity that induce a chaotic state must meet the following requirements: The resonant wavelength of the optical resonant cavity is located within the C-band range of optical communication; The mechanical frequency of the micromechanical oscillator is between 1 MHz and 800 GHz; The effective mass of the movable mass block is kilograms to Between kilograms; The input laser power ranges from 1 microwatt to 100 milliwatts; The detuning between the input laser wavelength and the resonant wavelength of the optical resonant cavity is between 0.1 picometers and 10 nanometers; The vacuum optomechanical coupling strength is between 500 Hz and 10 GHz.

6. The cavity optical chaotic acceleration sensing system according to claim 5, characterized in that, The process of achieving chaotic modulation of laser light incident on an optical resonant cavity by a micromechanical oscillator under acceleration excitation is as follows: when external acceleration is applied to the vacuum cavity in a chaotic state, the micromechanical oscillator is driven to generate displacement through the optical-mechanical coupling effect, thereby disturbing the optical resonance condition of the vacuum cavity and directly modulating the output of the chaotic light field.

7. A cavity optical force chaotic acceleration calibration method for a cavity optical force chaotic acceleration sensing system according to any one of claims 1-6, characterized in that, include: S1. Adjust the working parameters of the vacuum chamber to a specific value to make the vacuum chamber enter a chaotic state; S2. A small external acceleration acts on the micromechanical oscillator, producing a small displacement, which causes a change in the cavity length of the optical resonant cavity, and in turn causes a shift in the resonant frequency of the optical resonant cavity, thereby causing a dynamic change in the chaotic optical field. S3. Use a photoelectric detection module to capture the chaotically modulated light field signal and convert it into an electrical signal, and then use a signal processing module to extract the features of the electrical signal. S4. Establish a quantitative mapping relationship between the feature changes of the electrical signal extracted in step S3 and the acceleration. Through multi-feature weighted fusion technology, achieve accurate inversion of acceleration values ​​and complete the calibration of the accelerometer.

8. The cavity optical force chaotic acceleration calibration method according to claim 7, characterized in that, The vacuum cavity operating parameters that cause the vacuum cavity to enter a chaotic state include the resonant wavelength of the optical resonant cavity, the mechanical frequency of the micromechanical oscillator, the effective mass of the movable mass block, the input laser power, the input laser wavelength, and the vacuum-optical-mechanical coupling strength.

9. The cavity optical force chaotic acceleration calibration method according to claim 8, characterized in that, The operating parameters of the vacuum cavity that induce a chaotic state must meet the following requirements: The resonant wavelength of the optical resonant cavity is located within the C-band range of optical communication; The mechanical frequency of the micromechanical oscillator is between 1 MHz and 800 GHz; The effective mass of the movable mass block is kilograms to Between kilograms; The input laser power ranges from 1 microwatt to 100 milliwatts; The detuning between the input laser wavelength and the resonant wavelength of the optical resonant cavity is between 0.1 picometers and 10 nanometers; The vacuum optomechanical coupling strength is between 500 Hz and 10 GHz.

10. A cavity optical force chaotic acceleration calibration method according to claim 9, characterized in that, The characteristics of electrical signals include, but are not limited to, amplitude characteristics, frequency characteristics, phase characteristics, and spectral characteristics.

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