CN116972900B - Under-sampling-based broadband sinusoidal signal amplitude measurement method and device - Google Patents
Under-sampling-based broadband sinusoidal signal amplitude measurement method and device Download PDFInfo
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Abstract
The technical scheme adopted by the invention is as follows: a broadband sinusoidal signal amplitude measuring method and equipment based on undersampling, the method includes the following steps: preprocessing the acquired broadband sinusoidal signals; undersampling the preprocessed broadband sinusoidal signal, finding out a frequency band with only one current broadband sinusoidal signal amplitude in the frequency spectrum, and forming an undersampled broadband sinusoidal signal; and calculating the energy of the undersampled broadband sinusoidal signal in the corresponding frequency band in the power spectral density to obtain the amplitude of the broadband sinusoidal signal in the time domain. The invention can improve the detection precision and efficiency of the broadband sinusoidal signal amplitude.
Description
Technical Field
The invention belongs to the technical field of digital signal processing, and particularly relates to a broadband sinusoidal signal amplitude measurement method and device based on undersampling.
Background
In the field of information transmission and processing, sine wave signals take a significant role. By accurately measuring the signal amplitude, the energy information of the signal can be obtained, the quality of the signal can be estimated, and basic data can be provided for optimizing the system performance. Therefore, sinusoidal signal amplitude measurement is widely used in various fields. As in power systems, the magnitude of the current and voltage are important factors in determining the efficiency and stability of power transmission. In a wireless communication system, the amplitude of a signal may provide important information about the signal transmission distance and the possible interference situation. In digital communication, by measuring the signal amplitude, the signal-to-noise ratio of the signal in the transmission process is calculated, so that a more effective noise suppression strategy is conveniently formulated. In radar and ultrasound imaging systems, distance and position information of an unknown object is detected by measuring the amplitude of reflected signals. In the field of medical imaging, ultrasonic imaging technology generates a corresponding image by measuring the amplitude of a signal reflected from the inside of a human body, which is of great importance for both diagnosis and treatment of diseases.
In summary, the measurement of the amplitude of the sine wave signal has important application in various fields, and provides a wide background and application prospect for researching the measurement of the amplitude of the signal. To date, the widely used sinusoidal signal amplitude measurement method is as follows:
1. the method based on real-time sampling converts an analog signal into a digital signal. The amplitude of the sinusoidal signal is measured by fourier transforming the digital signal from the time domain to the frequency domain. The method is based on the sampling theorem, namely that the sampling frequency is at least required to be twice as high as the frequency of the signal to be measured, and the measurement accuracy is increased along with the increase of the sampling frequency. Therefore, the hardware cost of the measurement method increases as the bandwidth of the measurement method increases.
2. The signal amplitude is measured based on a precision detection circuit. The measuring principle is that the sine signal to be measured is conditioned by a circuit to obtain a sine signal which is matched with the input dynamic range of an ADC (analog-digital converter). The signal outputs a DC signal with amplitude information through a diode detection circuit. And then the DC signal is sampled by an ADC (analog-digital converter) to calculate the amplitude of the original sinusoidal signal. The measurement accuracy of the measurement method mainly depends on the linear relation between the output signal voltage and the input signal amplitude of the detection circuit. The diode detection capability is greatly affected by frequency change, and the higher the frequency is, the larger the diode detection error is, so that the measurement bandwidth of the method is limited.
3. The AIC (analog information conversion) method based on compressed sensing theory measures signal amplitude. The method is based on the principle that the amplitude of a signal is estimated by minimizing the square sum of reconstruction errors, the signal is sparsely represented by an algorithm based on L1 norm minimization, the reconstructed signal is compared with a sampling signal by using a least square method, the square sum of the reconstruction errors is calculated, and the error function is minimized to optimize the reconstruction of the signal, so that the amplitude of the signal is estimated. However, the software of the scheme has large calculation amount and high requirement on hardware calculation force, and is difficult to popularize and use in more occasions.
Disclosure of Invention
The invention aims to solve the defects in the background art, and provides a broadband sinusoidal signal amplitude measurement method and device based on undersampling, which can improve the detection precision and efficiency of the broadband sinusoidal signal amplitude.
The technical scheme adopted by the invention is as follows: a broadband sinusoidal signal amplitude measuring method based on undersampling comprises the following steps:
preprocessing the acquired broadband sinusoidal signals;
undersampling the broadband sinusoidal signal after preprocessing, finding out a frequency band with only one current width sinusoidal signal amplitude in the frequency spectrum, and forming an undersampled broadband sinusoidal signal;
and calculating the energy of the undersampled width sinusoidal signal in the corresponding frequency band in the power spectral density to obtain the amplitude of the broadband sinusoidal signal in the time domain.
In the above technical scheme, the method further comprises the following steps: estimating the frequency of the acquired broadband sinusoidal signals to obtain corresponding compensation rules; and carrying out frequency compensation on the calculated amplitude of the broadband sinusoidal signal in the time domain based on a compensation rule.
In the above technical solution, the process of preprocessing the collected wideband sinusoidal signal includes: amplifying or attenuating, AC coupling, impedance matching and low-pass filtering the broadband sinusoidal signal;
amplification or attenuation of the wideband sinusoidal signal is used to match the amplitude of the acquired wideband sinusoidal signal with the input dynamic range of the device performing undersampling;
the alternating current coupling is used for changing the direct current component in the acquired broadband sinusoidal signal into 0, so that the energy of the broadband sinusoidal signal is only related to the amplitude;
impedance matching is used for matching the acquired broadband sinusoidal signals with the impedance of the device for performing undersampling;
the low-pass filtering is used for suppressing noise of the high-frequency end of the acquired broadband sinusoidal signal.
In the above technical solution, the process of calculating the energy of the frequency band corresponding to the undersampled width sinusoidal signal in the power spectral density includes:
calculating to obtain a corresponding autocorrelation function according to the undersampled broadband sinusoidal signal;
performing Fourier transformation on the obtained autocorrelation function to obtain power spectral density;
determining a power maximum and a corresponding frequency based on the power spectral density;
determining the full-width half-height frequency bandwidth according to the maximum power value;
and subtracting the calculated result of the background noise from the power spectrum density, and integrating the frequency in an integration interval formed according to the frequency and the frequency bandwidth corresponding to the power maximum value to obtain the energy of the acquired broadband sinusoidal signal on the frequency domain.
In the technical scheme, the amplitude of the sinusoidal signal in the time domain is calculated by the energy of the acquired broadband sinusoidal signal in the frequency domain through the Paswal theorem.
In the above technical solution, the process of determining the power maximum value and the corresponding frequency based on the power spectral density includes: based on the power spectrum density, a corresponding power maximum value is found through a traversal algorithm, and then a frequency value at the maximum power is obtained according to a corresponding relation provided in the power spectrum.
In the above technical solution, the process of determining the full-width half-maximum frequency bandwidth according to the power maximum value includes: determining a power maximum P based on an image of the power spectral density m The method comprises the steps of carrying out a first treatment on the surface of the Finding a power value of 1/2P based on an image of the power spectral density m Is a frequency bin of the frequency bin; the frequency difference between the two frequency points is the full-width half-height frequency bandwidth delta f.
In the above technical solution, the expression of the integration interval formed according to the frequency and the frequency bandwidth corresponding to the maximum power is:
f m ±δf;
wherein f m A frequency corresponding to a power maximum determined based on the power spectral density; δf is the full-width half-height frequency bandwidth.
In the technical scheme, the analog-digital converter with low sampling rate is adopted to undersample the preprocessed broadband sinusoidal signal.
The invention also provides undersampling-based broadband sinusoidal signal amplitude measurement equipment, which comprises a signal preprocessing module, an AD acquisition module and a microcontroller;
the signal preprocessing module is used for preprocessing the acquired broadband sinusoidal signals;
the AD acquisition module is used for undersampling the preprocessed broadband sinusoidal signals, finding out a frequency band with only one current width sinusoidal signal amplitude in the frequency spectrum, and forming undersampled broadband sinusoidal signals;
the microcontroller is used for calculating the energy of the undersampled width sinusoidal signal corresponding to the frequency band in the power spectral density to obtain the amplitude of the broadband sinusoidal signal in the time domain.
The beneficial effects of the invention are as follows: the invention provides an undersampling-based broadband sinusoidal signal amplitude measurement method and device, which are characterized in that after undersampling is carried out on signals by adopting an ADC (analog-digital converter) with low sampling rate, the amplitude of the sinusoidal signals is measured by combining a spectrum analysis theoretical algorithm, the constraint of the Nyquist sampling theorem is broken through, and the accurate measurement of the broadband sinusoidal signal amplitude is realized by adopting a low-cost hardware design.
Further, the method and the device can compensate the amplitude calculated by the algorithm according to the corresponding compensation rule when the equipment performs amplitude measurement by the compensation rule obtained by frequency estimation, so that the accuracy of amplitude measurement is improved.
Furthermore, the invention adds a corresponding signal preprocessing flow in the amplitude measurement flow, which is convenient for setting the measuring range of the measuring method and the measuring device, and can also perform corresponding noise reduction treatment on the signal, thereby enhancing the accuracy and the applicability of the measuring result.
Furthermore, the energy of the broadband sinusoidal signal in the frequency domain is calculated through the calculation of the power spectral density so as to solve the amplitude, and the process has low requirements on the hardware of the acquisition equipment and high calculation accuracy.
Furthermore, the amplitude of the signal in the time domain is obtained through frequency domain energy calculation, the limit of the Nyquist sampling theorem can be broken through, the signal is sampled and recovered by using a low sampling rate, and the sampling rate requirement of the analog-to-digital converter is reduced.
Furthermore, the power maximum value required by calculating the signal amplitude can be accurately found based on the power spectral density through the traversal algorithm, so that the complexity of the algorithm is reduced.
Furthermore, the invention determines the frequency value at the maximum power through the power spectrum density, can accurately find the frequency bandwidth, and reduces the calculated amount of the algorithm.
Furthermore, the invention determines the integration interval according to the frequency corresponding to the full-width half-height frequency bandwidth and the power maximum value to perform subsequent signal amplitude calculation, thereby better improving the measurement accuracy.
Furthermore, the invention collects the signal to be measured by utilizing the undersampling mode, thereby reducing the sampling rate requirement of the analog-digital converter of the measuring device and reducing the production cost.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention;
FIG. 2 is a diagram illustrating a frequency aliasing phenomenon in an embodiment;
FIG. 3 is a graph of the actual sinusoidal signal spectrum under undersampling in an exemplary embodiment;
FIG. 4 is a schematic diagram of an equipment module of an embodiment;
FIG. 5 is a schematic flow chart of a method according to an embodiment;
fig. 6 is a graph of the output results of the apparatus of the embodiment.
Detailed Description
The invention will now be described in further detail with reference to the drawings and specific examples, which are given for clarity of understanding and are not to be construed as limiting the invention.
As shown in fig. 1, the method for measuring the amplitude of the broadband sinusoidal signal based on undersampling comprises the following steps:
s1, preprocessing an acquired broadband sinusoidal signal;
s2, undersampling the preprocessed broadband sinusoidal signal, finding out a frequency band with only one current width sinusoidal signal amplitude in a frequency spectrum, and forming an undersampled broadband sinusoidal signal;
s3, calculating the energy of the undersampled width sinusoidal signal in the power spectral density corresponding to the frequency band to obtain the amplitude of the broadband sinusoidal signal in the time domain;
s4, performing frequency estimation on the acquired broadband sinusoidal signals to obtain corresponding compensation rules; and carrying out frequency compensation on the calculated amplitude of the broadband sinusoidal signal in the time domain based on a compensation rule.
The core algorithm of the invention is a broadband sinusoidal signal amplitude measurement method based on undersampling. And carrying out spectrum analysis processing on the digital signal obtained by undersampling, converting the sine signal amplitude information in the time domain into energy information in the frequency domain, and calculating the amplitude of the original signal by calculating the signal energy in the frequency domain.
Specifically, in step S1, the process of preprocessing the acquired wideband sinusoidal signal includes: amplifying or attenuating, AC coupling, impedance matching and low-pass filtering the broadband sinusoidal signal;
amplification or attenuation of the wideband sinusoidal signal is used to match the amplitude of the acquired wideband sinusoidal signal to the input dynamic range of the device performing undersampling (analog-to-digital converter), improving the resolution of the analog-to-digital converter sampling.
The alternating current coupling is used for changing the direct current component in the acquired broadband sinusoidal signal into 0, so that the energy of the broadband sinusoidal signal is only related to the amplitude;
the impedance matching is used for matching the acquired broadband sinusoidal signals with the impedance of the device for performing undersampling, and the phenomena of reflection, standing waves and the like caused by the fact that the input signals are not matched with the impedance of the measuring device are prevented, so that amplitude measurement is affected.
The low-pass filtering is used for inhibiting noise at the high-frequency end of the acquired broadband sinusoidal signal, so that interference caused by the noise at the high-frequency end is inhibited, and the accuracy and precision of measuring the amplitude of the sinusoidal signal are improved.
Specifically, in step S2, the pre-processed wideband sinusoidal signal is undersampled by using a low sampling rate analog-to-digital converter, and the sampled digital signal may be used to calculate the sinusoidal signal amplitude.
When the nyquist sampling theorem is not satisfied, frequency aliasing occurs in the frequency spectrum, and a signal component of a high frequency is erroneously recognized as a low frequency signal, so that an erroneous frequency appears in the frequency spectrum. Specifically, assume that the wideband sinusoidal signal to be measured is x (t) =acos (2pi f 0 t) at a sampling frequency f s . The frequency will appear in the whole frequency spectrum as(n is an integer) as shown in fig. 2.
Since the spectrum can only observe the frequency after aliasing to be between 0 and 0Signals in between, so that the sampling frequency needs to satisfy 0.ltoreq.nf s ±f 0 ≤f s /2. Relieve->Or-f 0 /f s <n≤-f 0 /f s +1/2。
From the analysis, no matter f s And f 0 How the relation between the two inequalities is that the integer n satisfies the two inequalities has and has only one value, namely that only one spectral line corresponding to the frequency exists in the frequency spectrum. However, due to spectral leakage and the presence of the grating effect, the spectral line of this frequency becomes a band in actual measurement, as shown in fig. 3.
In the frequency aliasing process caused by undersampling, only the frequency of the sinusoidal signal is changed, the amplitude information of the sinusoidal signal is not affected, and only a frequency band capable of reflecting the amplitude of the sinusoidal signal exists in the frequency spectrum. The spectrum of the undersampled digital signal can thus be analyzed and sinusoidal signal amplitude measurements can be made.
Specifically, in step S3, the process of calculating the energy of the frequency band corresponding to the undersampled width sinusoidal signal in the power spectral density includes:
calculating to obtain a corresponding autocorrelation function according to the undersampled broadband sinusoidal signal;
performing Fourier transformation on the obtained autocorrelation function to obtain power spectral density;
determining a power maximum and a corresponding frequency based on the power spectral density;
determining the full-width half-height frequency bandwidth according to the maximum power value;
and subtracting the calculated result of the background noise from the power spectrum density, and integrating the frequency in an integration interval formed according to the frequency and the frequency bandwidth corresponding to the power maximum value to obtain the energy of the acquired broadband sinusoidal signal on the frequency domain.
Preferably, if the wideband sinusoidal signal to be calculated is x (t) =acos (2pi f) 0 t), then the autocorrelation function R x The method comprises the following steps:
wherein f 0 Represents the frequency of the wideband sinusoidal signal x (T), a represents the amplitude of x (T), and T represents the period of x (T).
Obtaining the power spectral density P of the sinusoidal signal to be detected according to the Fourier transform relation x (f) The method comprises the following steps:
when calculating the energy of the signal under test according to the power spectral density, the power maximum P is first determined m And the frequency f corresponding to the power m 。
After the power spectrum density is calculated, the power maximum value is found by a traversal algorithm, and then the power maximum value is obtained according to the corresponding relation provided in the power spectrumAnd obtaining a frequency value at the maximum power. Then according to P m The calculation formula for determining the frequency bandwidth δf of FWHM (full width half maximum) is as follows:
is the standard deviation
The power maximum P may also be determined based on an image of the power spectral density m The method comprises the steps of carrying out a first treatment on the surface of the Finding a power value of 1/2P based on an image of the power spectral density m Is a frequency bin of the frequency bin; the frequency difference between the two frequency points is the full-width half-height frequency bandwidth delta f.
Noise floor P may exist due to noise and other interference of some environments and hardware itself noise 。
In band f m And in +/-delta f/2, integrating the frequency by subtracting the noise floor from the power spectrum density to obtain the energy of the sinusoidal signal with the width to be detected on the frequency domain. Finally, the energy is subjected to the Paswal theorem to obtain the amplitude of the broadband sinusoidal signal in the time domain.
From the paswal theorem, the energy of a signal is equal in time and frequency domains, i.e., the relation is satisfied:
where N represents the period of the undersampled wideband sinusoidal signal X (N), X (k) represents the discrete fourier transform of X (N), X (N) =acos (2pi f) 0 n), a represents the amplitude of the wideband sinusoidal signal.For the energy in the signal frequency domain,representing the energy of the signal in the time domain.
Therefore, the energy of the wide-band sinusoidal signal in the time domain is obtained through the energy of the wide-band sinusoidal signal to be detected in the frequency domain, and the amplitude of the wide-band sinusoidal signal is obtained through calculation.
Specifically, in step S4, the present invention performs measurement calculation on signals with known amplitude values and different frequency bands by using the existing frequency estimation method, and then finds out a corresponding compensation rule corresponding to the frequency band according to the calculation result and the error of the known amplitude values. Then when the broadband sinusoidal signal to be measured is measured, the frequency range of the signal to be measured can be estimated approximately, and the calculated amplitude value is compensated based on the corresponding frequency compensation rule, so that the accuracy of amplitude measurement is further improved.
The invention also provides an undersampled broadband sinusoidal signal amplitude measurement device, which is shown in fig. 4 and comprises a signal preprocessing module, an AD acquisition module and a microcontroller;
the signal preprocessing module is used for preprocessing the acquired broadband sinusoidal signals;
the AD acquisition module is used for undersampling the preprocessed broadband sinusoidal signals, finding out a frequency band with only one current width sinusoidal signal amplitude in the frequency spectrum, and forming undersampled broadband sinusoidal signals;
the microcontroller is used for calculating the energy of the undersampled width sinusoidal signal corresponding to the frequency band in the power spectral density to obtain the amplitude of the broadband sinusoidal signal in the time domain.
The signal preprocessing module is composed of a multi-stage operational amplifier circuit, a low-pass filter and a high-pass filter. The multistage operational amplification circuit realizes the functions of impedance matching, signal amplification or attenuation and the like of a signal to be tested. The low pass filter implements ac coupling of the signal under test. The high pass filter is used to reduce the interference of the high frequency signal to the measurement.
The AD acquisition module adopts an ADC chip with low sampling rate to realize undersampling of the sine signal to be detected.
The microcontroller module is composed of a memory, a spectrum analysis module, a frequency compensation module, a communication module and a peripheral driver and is used for controlling the AD acquisition module, performing spectrum analysis and calculation, realizing a communication interface, driving a display and the like.
The software functions of the microcontroller module include controlling the AD acquisition module, implementing an amplitude measurement algorithm, communicating and driving a display, etc., and the flowchart is shown in FIG. 5.
The AD acquisition module sends the undersampled broadband sinusoidal signal to the memory. The control chip of the microcontroller module firstly judges whether the data volume stored in the memory meets the requirement, and the data volume is more than 8192 points, namely the data volume is considered to meet the requirement. After meeting the requirements, all acquired digital signals are sent to a spectrum analysis module for executing a sine signal amplitude measurement algorithm.
In the process of executing the sine signal amplitude measurement algorithm, the spectrum analysis module firstly carries out autocorrelation operation on the digital signal, and carries out Fourier transformation on the obtained autocorrelation function to obtain the power spectrum density. Then determining a power maximum value and a corresponding frequency thereof based on the power spectral density; determining the full-width half-height frequency bandwidth according to the maximum power value; and subtracting the calculated result of the background noise from the power spectrum density, and integrating the frequency in an integration interval formed according to the frequency and the frequency bandwidth corresponding to the power maximum value to obtain the energy of the acquired broadband sinusoidal signal on the frequency domain. Finally, based on the Paswal theorem, the energy value is converted into the amplitude of the sinusoidal signal and output.
When the non-measuring equipment does not input the broadband sinusoidal signal to be measured, the spectrum analysis module detects a noise signal according to the environment where the spectrum analysis module is positioned, and the noise floor is obtained through calculation.
In order to further improve the accuracy of amplitude detection, a frequency compensation module is added in the software design of the microcontroller, and frequency compensation is carried out on the amplitude measured value output by the spectrum analysis module.
The frequency estimation method based on the Chinese remainder theorem utilizes a CRT reconstruction algorithm in a closed form to carry out frequency estimation on the measured signals, then utilizes the amplitude measurement device to test the signals under a large number of frequencies, and can add a frequency compensation part into the microcontroller after finding out the corresponding compensation rule. And firstly, carrying out frequency estimation on the signals received by the memory in the frequency compensation module, then carrying out amplitude detection by utilizing the spectrum analysis algorithm, and finally carrying out frequency compensation on the amplitude measured value output by the spectrum analysis module according to a compensation rule set by advanced detection, thereby obtaining a more accurate measured value.
The microcontroller outputs the amplitude value of the broadband sinusoidal signal obtained by measurement to the upper computer through the communication module, and sends the amplitude value to the display module for display through the peripheral drive.
The present embodiment has been verified by outputting sinusoidal signals of different frequency amplitudes through a high-precision signal generator, and the test instrument used mainly is the signal generator.
The undersampled broadband sinusoidal signal amplitude measuring equipment provided by the embodiment is utilized for detection display. At a sampling frequency of 560kHz, the amplitude measurement of the broadband sinusoidal signal is realized, the bandwidth of the measuring device reaches 10MHz, the amplitude measurement error in the bandwidth is within 5%, and the test result is shown in figure 6.
The following are several related parameters currently available on the market for measuring wideband sinusoidal ac millivoltmeters:
| model number | Frequency bandwidth | Measurement error | Price of |
| TH1912 | 5Hz-5MHz | 5% | 2170 yuan |
| UT631 | 10Hz-2MHz | 5% | 1368 yuan |
The amplitude measuring method and the amplitude measuring equipment can reduce the sampling rate requirement of the measuring instrument on the analog-digital converter, thereby reducing the cost. The cost spent in device manufacturing and experimental detection is within two hundred yuan according to the method, and the comparison of the test result of the method and the parameters in the table can be seen.
What is not described in detail in this specification is prior art known to those skilled in the art.
Claims (7)
1. A broadband sinusoidal signal amplitude measuring method based on undersampling is characterized in that: the method comprises the following steps:
preprocessing the acquired broadband sinusoidal signals, wherein the process comprises the following steps: amplifying or attenuating, AC coupling, impedance matching and low-pass filtering the broadband sinusoidal signal; amplification or attenuation of the wideband sinusoidal signal is used to match the amplitude of the acquired wideband sinusoidal signal with the input dynamic range of the device performing undersampling; the alternating current coupling is used for changing the direct current component in the acquired broadband sinusoidal signal into 0, so that the energy of the broadband sinusoidal signal is only related to the amplitude; impedance matching is used for matching the acquired broadband sinusoidal signals with the impedance of the device for performing undersampling; the low-pass filtering is used for suppressing noise of the high-frequency end of the acquired broadband sinusoidal signal;
undersampling the broadband sinusoidal signal after preprocessing, finding out a frequency band with only one current width sinusoidal signal amplitude in the frequency spectrum, and forming an undersampled broadband sinusoidal signal;
calculating to obtain a corresponding autocorrelation function according to the undersampled broadband sinusoidal signal;
performing Fourier transformation on the obtained autocorrelation function to obtain power spectral density;
determining a power maximum and a corresponding frequency based on the power spectral density;
determining the full-width half-height frequency bandwidth according to the maximum power value;
subtracting the calculated result of the noise floor from the power spectrum density, and integrating the frequency in an integration interval formed according to the frequency and the frequency bandwidth corresponding to the power maximum value to obtain the energy of the acquired broadband sinusoidal signal on the frequency domain;
and calculating the energy of the acquired broadband sinusoidal signal in the frequency domain through the Paswal theorem to obtain the amplitude of the sinusoidal signal in the time domain.
2. A method according to claim 1, characterized in that: the method also comprises the following steps: performing frequency estimation on the acquired broadband sinusoidal signals to obtain corresponding compensation rules; and carrying out frequency compensation on the calculated amplitude of the broadband sinusoidal signal in the time domain based on a compensation rule.
3. A method according to claim 1, characterized in that: the process of determining the power maxima and their corresponding frequencies based on the power spectral density includes: based on the power spectrum density, a corresponding power maximum value is found through a traversal algorithm, and then a frequency value at the maximum power is obtained according to a corresponding relation provided in the power spectrum.
4. A method according to claim 1, characterized in that: the process of determining the full-width half-maximum frequency bandwidth from the power maximum comprises: determining a power maximum P based on an image of the power spectral density m The method comprises the steps of carrying out a first treatment on the surface of the Finding a power value for an image based on power spectral densityIs a frequency bin of the frequency bin; the frequency difference between the two frequency points is the full-width half-height frequency bandwidth delta f.
5. A method according to claim 1, characterized in that: the expression of the integration interval formed according to the frequency and the frequency bandwidth corresponding to the power maximum value is:
f m ±δf；
wherein f m A frequency corresponding to a power maximum determined based on the power spectral density; δf is the full-width half-height frequency bandwidth.
6. A method according to claim 1, characterized in that: and undersampling the preprocessed broadband sinusoidal signal by adopting an analog-digital converter with a low sampling rate.
7. An undersampled wideband sinusoidal signal amplitude measurement device, characterized in that: the system comprises a signal preprocessing module, an AD acquisition module and a microcontroller;
the signal preprocessing module is used for preprocessing the acquired broadband sinusoidal signals, and the process comprises the following steps: amplifying or attenuating, AC coupling, impedance matching and low-pass filtering the broadband sinusoidal signal;
amplification or attenuation of the wideband sinusoidal signal is used to match the amplitude of the acquired wideband sinusoidal signal with the input dynamic range of the device performing undersampling;
the alternating current coupling is used for changing the direct current component in the acquired broadband sinusoidal signal into 0, so that the energy of the broadband sinusoidal signal is only related to the amplitude;
impedance matching is used for matching the acquired broadband sinusoidal signals with the impedance of the device for performing undersampling;
the low-pass filtering is used for suppressing noise of the high-frequency end of the acquired broadband sinusoidal signal;
the AD acquisition module is used for undersampling the preprocessed broadband sinusoidal signals, finding out a frequency band with only one current width sinusoidal signal amplitude in the frequency spectrum, and forming undersampled broadband sinusoidal signals;
the microcontroller is used for calculating and obtaining a corresponding autocorrelation function according to the undersampled broadband sinusoidal signal; performing Fourier transformation on the obtained autocorrelation function to obtain power spectral density; determining a power maximum and a corresponding frequency based on the power spectral density; determining the full-width half-height frequency bandwidth according to the maximum power value; subtracting the calculated result of the noise floor from the power spectrum density, and integrating the frequency in an integration interval formed according to the frequency and the frequency bandwidth corresponding to the power maximum value to obtain the energy of the acquired broadband sinusoidal signal on the frequency domain; and calculating the energy of the acquired broadband sinusoidal signal in the frequency domain through the Paswal theorem to obtain the amplitude of the sinusoidal signal in the time domain.
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