A method and system for signal amplitude deviation compensation
By calculating the normalized frequency offset and the rectangular window spectrum function model, the FFT amplitude deviation is directly compensated, which solves the signal amplitude deviation problem caused by non-integer period sampling and improves the accuracy and efficiency of spectrum analysis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHWEST CHINA RES INST OF ELECTRONICS EQUIP
- Filing Date
- 2026-03-17
- Publication Date
- 2026-06-30
AI Technical Summary
In high-precision spectrum analysis and RF receiver channel calibration, the amplitude deviation of the FFT calculation signal caused by non-integer period sampling seriously affects the measurement accuracy and system calibration accuracy. Existing methods are either inefficient or computationally intensive.
By calculating the normalized frequency offset of a known signal, the FFT amplitude deviation is directly compensated based on the rectangular window spectrum function model. Simple mathematical operations are used, making it suitable for fast and automatic amplitude calibration at multiple frequency points.
It enables fast and accurate compensation of FFT amplitude deviation under rectangular window conditions, improving measurement consistency and system performance while reducing computational burden and resource consumption.
Smart Images
Figure CN122307303A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of spectrum calibration technology, and more specifically, to a method and system for compensating for signal amplitude deviation. Background Technology
[0002] In applications such as high-precision spectrum analysis and RF receiver channel calibration, it is often necessary to accurately measure the amplitude of a sinusoidal signal at a known frequency. A common process involves the analog-to-digital converter (ADC) sampling the signal, directly extracting a finite-length sample (i.e., applying a rectangular window), and then performing an FFT to calculate its spectral amplitude. However, when the sampling sequence length is not an integer multiple of the signal period, spectral leakage and the picket-fence effect inevitably occur, leading to a significant deviation between the spectral amplitude calculated by the FFT and the true amplitude of the signal. This deviation severely affects the measurement accuracy of channel amplitude consistency and the accuracy of system calibration.
[0003] In existing technologies, non-rectangular window functions such as the Hanning window and Hamming window are often used to suppress spectral leakage. However, this reduces spectral resolution and introduces new amplitude attenuation, requiring additional correction. Another approach is to increase the number of FFT points by padding with zeros in the time domain to mitigate the picket fence effect, but this significantly increases computational complexity. For calibration scenarios with known precise input frequencies, the above-mentioned general methods are inefficient or not direct enough. Therefore, a solution is needed that can quickly and accurately compensate for FFT amplitude deviations under rectangular window conditions for known frequencies. Summary of the Invention
[0004] This invention aims to provide a signal amplitude deviation compensation method and system to solve the problem of signal amplitude deviation from the true amplitude caused by non-integer period sampling under rectangular window truncation conditions. This method can directly compensate for the deviation through a calculation model given the precise frequency of the signal, without changing the window function or adding a large amount of computation. It is particularly suitable for applications requiring rapid and automatic amplitude calibration at multiple frequency points. To achieve the above objective, this invention proposes a signal amplitude deviation compensation method and system.
[0005] In a first aspect, this application provides a signal amplitude deviation compensation method, applied to a spectrum analysis system that uses a rectangular window to truncate a single-frequency sinusoidal signal, comprising: Obtain the true frequency of the input signal Sampling frequency of the spectrum analysis system and the number of Fast Fourier Transform sampling points ; Based on the actual frequency Sampling frequency and the number of Fast Fourier sampling points Calculate the true frequency Normalized frequency offset relative to the Fast Fourier Discrete Grid; Determine whether the normalized frequency offset is zero; If the offset is zero, then the amplitude deviation compensation value is determined to be zero; If the offset is non-zero, then the amplitude deviation compensation value is calculated based on the normalized frequency offset and the spectral function model of the rectangular window. Obtain the original signal amplitude value after performing Fast Fourier Transform calculation on the input signal; The original signal amplitude value is compensated using the amplitude deviation compensation value to obtain the compensated signal amplitude value.
[0006] Preferably, the expression for calculating the normalized frequency offset is:
[0007] in, This represents the rounding function. This expression characterizes the normalized distance between the true spectral line of the input signal and the nearest Fourier discrete spectral line index, with a value range of [-0.5, 0.5). Preferably, the expression for calculating the amplitude deviation compensation value is:
[0008] in, This indicates taking the absolute value.
[0009] Preferably, determining whether the normalized frequency offset is a zero offset includes: If the normalized frequency offset is less than the preset tolerance threshold, it is determined to be zero offset; If the normalized frequency offset is less than the preset tolerance threshold, it is determined to be a non-zero offset.
[0010] Preferably, the expression for the compensated signal amplitude value is:
[0011] in, This represents the original signal amplitude value.
[0012] In the numerical domain, the above equation can be equivalent to:
[0013] Preferably, the number of Fast Fourier sampling points is obtained based on the number of frequency points and frequency of the input signal. The It is an integer power of 2.
[0014] Preferably, in acquiring the true frequency of the input signal Previously, the method also included: performing analog-to-digital conversion on the input signal to obtain a discrete time series.
[0015] Preferably, obtaining the original signal amplitude value obtained after fast Fourier transform calculation of the input signal includes: The discrete-time series is truncated by adding a rectangular window to extract the number of Fast Fourier Transform sampling points. ; Perform an N-point Fast Fourier Transform and take the one-sided spectrum; Multiply the complex modulus value of the corresponding single-sided frequency point by 2 / N to obtain the original signal amplitude value.
[0016] Preferably, when the method is used for multiple input signals, it obtains their true frequencies. For i=1, 2, ..., M, perform batch compensation, including: For each frequency point Calculate the corresponding normalized frequency offset and amplitude deviation compensation value independently; For each frequency point, the original signal amplitude value is individually compensated using the corresponding amplitude deviation compensation value.
[0017] The second aspect is a signal amplitude deviation compensation system, comprising: The parameter input module is used to obtain the true frequency of the input signal, the system sampling frequency, and the number of fast Fourier sampling points; The offset analysis module is used to calculate the normalized frequency offset of the input signal based on the true frequency, sampling frequency, and FFT points. The deviation calculation module, connected to the offset analysis module, is used to determine the amplitude deviation value in the logarithmic domain based on the offset and the rectangular window spectrum characteristic model when the offset is non-zero. The amplitude acquisition module is used to acquire the raw amplitude value after performing a fast Fourier transform on the input signal; The compensation synthesis module, connected to the deviation calculation module and the amplitude acquisition module, is used to compensate the original amplitude value using the amplitude deviation value and output the corrected final amplitude value.
[0018] The beneficial effects of this invention are as follows: This invention starts directly from the mathematical model of spectral leakage of a rectangular window, calculates the theoretical deviation for known signal frequencies, and has high compensation accuracy and clear physical meaning.
[0019] Computationally efficient and resource-saving: No zero-padding in the time domain (which increases the number of FFT points) or complex window functions are required, avoiding the significant computational overhead and reduced spectral resolution associated with these methods. Only a small number of multiplication, division, logarithmic, and trigonometric function operations are needed, resulting in a very light computational burden.
[0020] Facilitates automation and batch processing: The algorithm has a clear flow and each frequency point is processed independently, making it very suitable for integration into automated test systems (ATE) or embedded calibration software to perform rapid and continuous amplitude calibration on multiple channels and multiple frequency points, significantly improving production efficiency.
[0021] Improved system performance: As shown in the specific implementation, after applying the present invention, the amplitude measurement deviation between channels is significantly smoothed and reduced over a wide frequency band, improving the consistency of measurement and the overall performance of the system.
[0022] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description
[0023] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0024] Figure 1 This is a flowchart of a signal amplitude deviation compensation method provided in an embodiment of the present invention; Figure 2 This is a structural block diagram of a signal amplitude deviation compensation system provided in an embodiment of the present invention. Detailed Implementation
[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0026] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.
[0027] English definition: ADC analog-to-digital converter FFT (Fast Fourier Transform) Example 1: See Figure 1 This embodiment details a signal amplitude deviation compensation method, which is applied to a spectrum analysis system that uses a rectangular window to truncate a single-frequency sinusoidal signal.
[0028] Step S1: Obtain the true frequency of the input signal Sampling frequency of the spectrum analysis system and the number of Fast Fourier Transform sampling points .
[0029] Step S2, based on the actual frequency Sampling frequency and the number of Fast Fourier sampling points Calculate the true frequency Normalized frequency offset relative to the Fast Fourier Discrete Grid; The expression for calculating the normalized frequency offset is:
[0030] in, This represents the rounding function.
[0031] Step S3: Determine whether the normalized frequency offset is zero offset; If the normalized frequency offset is less than the preset tolerance threshold, it is determined to be zero offset; if it is zero offset, the amplitude deviation compensation value is determined to be zero. If the normalized frequency offset is less than the preset tolerance threshold, it is determined to be a non-zero offset; if it is a non-zero offset, the amplitude deviation compensation value is calculated based on the normalized frequency offset and the spectrum function model of the rectangular window. The expression for calculating the amplitude deviation compensation value is as follows:
[0032] in, This indicates taking the absolute value.
[0033] Step S4: Obtain the original signal amplitude value after the input signal is calculated by Fast Fourier Transform; The input signal is converted from analog to digital to obtain a discrete time series.
[0034] The step of obtaining the original signal amplitude value after fast Fourier transform calculation of the input signal includes: The discrete-time series is truncated by adding a rectangular window to extract the number of Fast Fourier Transform sampling points. ; Perform an N-point Fast Fourier Transform and extract the single-sided spectrum; obtain the number of Fast Fourier sampling points based on the number of frequency points and frequency of the input signal. The It is an integer power of 2; Multiply the complex modulus value of the corresponding single-sided frequency point by 2 / N to obtain the original signal amplitude value.
[0035] Step S5: Use the amplitude deviation compensation value to compensate the original signal amplitude value to obtain the compensated signal amplitude value; The expression for the compensated signal amplitude value is:
[0036] in, This represents the original signal amplitude value.
[0037] When the method is used to obtain the true frequency of multiple input signals, it is applied to the input signal. For i=1, 2, ..., M, perform batch compensation, including: For each frequency point Calculate the corresponding normalized frequency offset and amplitude deviation compensation value independently; For each frequency point, the original signal amplitude value is individually compensated using the corresponding amplitude deviation compensation value.
[0038] Example 2: See Figure 2 Compensating for a single frequency point requires inputting a series of single-frequency test signals with known frequencies and amplitudes (e.g., from 1300MHz to 2300MHz in 100MHz steps) into the system. After sampling by an ADC and processing by an FFT, the frequency response of each channel is evaluated. Due to spectral leakage in the FFT, direct measurements exhibit fluctuating deviations, affecting calibration accuracy.
[0039] Step S1: Using the true frequency of the input signal Taking 1400MHz as an example, the sampling frequency of the spectrum analysis system , =5000MHz, preset number of Fast Fourier Transform sampling points , =1024.
[0040] Step S2, based on the actual frequency Sampling frequency and the number of Fast Fourier sampling points Calculate the true frequency The normalized frequency offset relative to the Fast Fourier Discrete Grid; the expression for the normalized frequency offset is:
[0041] Right now, =1400 / 5000×1024 round(1400 / 5000×1024)≈286.72 287= 0.28 Step S3: Determine whether the normalized frequency offset is zero offset; Judgment If the offset is not 0, and is non-zero, then based on the normalized frequency offset and the spectral function model of the rectangular window, the amplitude deviation compensation value is calculated. The expression for the amplitude deviation compensation value is:
[0042] in, This indicates taking the absolute value.
[0043] Right now, =20×log10(sin(π×( 0.28)) / π×( 0.28))≈ 1.686dB Sufficient significant figures are usually retained in calculations.
[0044] Step S4: Obtain the original signal amplitude value obtained after the input signal is calculated by Fast Fourier Transform; Assuming that after applying a rectangular window to the ADC sampled signal and performing a 1024-point FFT, the original amplitude value of the spectrum near 1400MHz is obtained as the AFFT (linear value).
[0045] Step S5: Use the amplitude deviation compensation value to compensate the original signal amplitude value to obtain the compensated signal amplitude value; Convert the original amplitude to decibels: (dB)==20×log10( ).
[0046] The compensation range is then:
[0047] =AFFT(dB) ( 1.686) = AFFT(dB) + 1.686dB This result is closer to the true amplitude of the signal.
[0048] Example 3: Batch compensation was performed on 11 frequency points from 1300MHz to 2300MHz (in 100MHz steps).
[0049] The actual frequency of each frequency point is sequentially... Calculate its corresponding normalized frequency offset independently. and amplitude deviation compensation value Because the offset between each frequency point and the FFT grid is different, the calculated... They are also different (for example, the 1500MHz frequency point). Approaching 0, its It's also close to 0).
[0050] Each calculated separately Compensation for the original FFT amplitude value at the corresponding frequency point .
[0051] Performance Verification: Before compensation, the amplitude deviation at the 11 frequency points fluctuated wildly between approximately -1.8dB and +0.05dB. After compensation using the method of this invention, the amplitude deviation was significantly smoothed and controlled within a very small range of approximately -0.05dB to +0.32dB, fully demonstrating the effectiveness of this invention. Even when the step density was increased to 10MHz (101 frequency points), the deviation after compensation (-0.5dB ~ +0.32dB) was far better than before compensation (-5dB ~ +2.5dB), showing the good adaptability of this invention to dense frequency points.
[0052] Example 4 This embodiment provides a signal amplitude deviation compensation system, including: The parameter input module 001 is used to obtain the true frequency of the input signal, the system sampling frequency, and the number of fast Fourier sampling points; Offset analysis module 002 is used to calculate the normalized frequency offset of the input signal based on the true frequency, sampling frequency and FFT points; The deviation calculation module 003 is connected to the offset analysis module and is used to determine the amplitude deviation value in the logarithmic domain based on the offset and the rectangular window spectrum characteristic model when the offset is non-zero. Amplitude acquisition module 004 is used to acquire the original amplitude value after performing fast Fourier calculation on the input signal; The compensation synthesis module 005 is connected to the deviation calculation module and the amplitude acquisition module, and is used to compensate the original amplitude value using the amplitude deviation value, and output the corrected final amplitude value.
[0053] Regarding the apparatus in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated upon here.
[0054] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
[0055] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A signal amplitude deviation compensation method, characterized by, The method, applied in a spectrum analysis system that uses a rectangular window to truncate a single-frequency sinusoidal signal, includes: Acquiring true frequency of input signal Sampling frequency of spectrum analysis system And fast fourier sample point number ; based on the true frequency , a sampling frequency , and a number of fast Fourier samples , a normalized frequency offset of the true frequency relative to a fast Fourier discrete grid; Determine whether the normalized frequency offset is zero; If the offset is zero, then the amplitude deviation compensation value is determined to be zero; If the offset is non-zero, then the amplitude deviation compensation value is calculated based on the normalized frequency offset and the spectral function model of the rectangular window. Obtain the original signal amplitude value after the input signal is calculated by Fast Fourier Transform; The original signal amplitude value is compensated using the amplitude deviation compensation value to obtain the compensated signal amplitude value.
2. The method of claim 1, wherein, The expression for calculating the normalized frequency offset is: in, This represents the rounding function.
3. The signal amplitude deviation compensation method according to claim 1, characterized in that, The expression for calculating the amplitude deviation compensation value is: in, This indicates taking the absolute value.
4. The signal amplitude deviation compensation method according to claim 1, characterized in that, The step of determining whether the normalized frequency offset is a zero offset includes: If the normalized frequency offset is less than the preset tolerance threshold, it is determined to be zero offset; If the normalized frequency offset is less than the preset tolerance threshold, it is determined to be a non-zero offset.
5. The signal amplitude deviation compensation method according to claim 1, characterized in that, The expression for the compensated signal amplitude value is: in, This represents the original signal amplitude value.
6. The signal amplitude deviation compensation method according to claim 1, characterized in that, The number of Fast Fourier sampling points is obtained based on the number of frequency points and frequency of the input signal. The It is an integer power of 2.
7. The signal amplitude deviation compensation method according to claim 1, characterized in that, Obtaining the true frequency of the input signal Previously, the method also included: performing analog-to-digital conversion on the input signal to obtain a discrete time series.
8. The signal amplitude deviation compensation method according to claim 7, characterized in that, The step of obtaining the original signal amplitude value after fast Fourier transform calculation of the input signal includes: The discrete-time series is truncated by adding a rectangular window to extract the number of Fast Fourier Transform sampling points. ; Perform an N-point Fast Fourier Transform and take the one-sided spectrum; Multiply the complex modulus value of the corresponding single-sided frequency point by 2 / N to obtain the original signal amplitude value.
9. A signal amplitude deviation compensation method according to claim 1, characterized in that, When the method is used to obtain the true frequency of multiple input signals, it is applied to the input signal. For i=1, 2, ..., M, perform batch compensation, including: For each frequency point Calculate the corresponding normalized frequency offset and amplitude deviation compensation value independently; For each frequency point, the original signal amplitude value is individually compensated using the corresponding amplitude deviation compensation value.
10. A signal amplitude deviation compensation system, characterized in that, include: The parameter input module is used to obtain the true frequency of the input signal, the system sampling frequency, and the number of fast Fourier sampling points; The offset analysis module is used to calculate the normalized frequency offset of the input signal based on the true frequency, sampling frequency, and FFT points. The deviation calculation module, connected to the offset analysis module, is used to determine the amplitude deviation value in the logarithmic domain based on the offset and the rectangular window spectrum characteristic model when the offset is non-zero. The amplitude acquisition module is used to acquire the raw amplitude value after performing a fast Fourier transform on the input signal; The compensation synthesis module, connected to the deviation calculation module and the amplitude acquisition module, is used to compensate the original amplitude value using the amplitude deviation value and output the corrected final amplitude value.