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RU-2861588-C1 - METHOD FOR INCREASING ACCURACY OF CONSTRUCTING DISCRETE SIGNAL SPECTRUM

RU2861588C1RU 2861588 C1RU2861588 C1RU 2861588C1RU-2861588-C1

Abstract

FIELD: digital signal processing. SUBSTANCE: method for constructing a discrete signal spectrum may include increasing the sampling rate by adding zeros between samples to reduce the time step, includes calculating the signal spectrum, analyzing the spectrum consisting in determining the first harmonic by isolating significant spectral components, filtering close frequencies and checking their multiplicity, determining the optimal number of samples, a multiple of the period of the first harmonic, by sequentially reducing the number of samples from the original number of samples to the number reduced by the period of the first harmonic in samples, calculating for each number of the discrete Fourier transform, determining in each spectrum the amplitude of the first harmonic and choosing the number at which this amplitude is maximum, calculating the spectrum with the optimal number of samples. It is used in telecommunications, acoustics, vibration diagnostics, radar and other technical fields where high-precision estimation of signal spectral characteristics is required. EFFECT: minimising spectrum leakage, increasing the accuracy of constructing a signal spectrum. 4 cl

Inventors

  • Pavlovskii Sergei Anatolevich
  • Smirnov Aleksei Vladimirovich
  • Elsukov Aleksei Aleksandrovich
  • Morokhina Daria Dmitrievna

Dates

Publication Date
20260506
Application Date
20250529

Claims (9)

  1. 1. A method for constructing the spectrum of a discrete signal with an initial number of samples N and an initial sampling frequency SR , which includes the use of a discrete Fourier transform, characterized in that the signal spectrum is calculated using the discrete Fourier transform; the obtained spectrum is analyzed to isolate the spectral component and its multiples for which the sum of the amplitudes is maximum, and the period of this component in samples is calculated; the optimal number of samples, a multiple of the calculated period, is determined by successively reducing the length of the signal and selecting the length at which the amplitude of the isolated component in the spectrum is maximum; the final spectrum is calculated using the discrete Fourier transform for a signal containing a certain optimal number of samples, wherein the spectrum analysis and/or the period determination can be performed using variable parameters.
  2. 2. The method according to paragraph 1, characterized in that the optimal number of samples is determined by successively decreasing the number of signal samples from the initial number of samples to a number reduced by the calculated period in samples, calculating for each number the discrete Fourier transform and the amplitude of the selected spectral component as the maximum value in a given frequency range, for example, ±2 spectral samples from its index, and selecting the number at which the amplitude is maximum.
  3. 3. The method according to paragraph 1 or 2, characterized in that the spectral component and its multiples are determined by analyzing the signal spectrum by analyzing the signal spectrum, including:
  4. a) identification of spectral components (frequency indices of the discrete Fourier transform), the amplitude of which exceeds the threshold equal to the maximum of the product of the maximum amplitude of the spectrum by the coefficient A (0.05-0.2) and the product of the median of the amplitudes by the coefficient B (2-6);
  5. b) filtering of closely located selected spectral components (frequency indices of the discrete Fourier transform) located at a distance of C (1-3) spectral samples, preserving the component (index) with the maximum amplitude;
  6. c) checking the remaining indices for multiplicity by checking the proximity of the index ratios to integers with a tolerance proportional to the spectral resolution , For example, ;
  7. d) summation of the amplitudes of multiple components and selection of the component with the minimum index and maximum sum of amplitudes;
  8. d) calculation of the period of the selected signal component in samples as a rounded ratio of N to its index.
  9. 4. The method according to any one of paragraphs 1-3, characterized in that before analyzing the spectrum, in order to increase the accuracy of calculating the period, the initial sampling frequency of the signal is increased by a factor of U (2-16) , adding U-1 zeros between samples, increasing the number of samples to N⋅U and the sampling frequency to SR⋅U , wherein in the subsequent spectral analysis only the first copy of the spectrum up to SR/2 is taken into account.

Description

Field of technology to which the invention relates The invention relates to the field of digital signal processing, in particular to methods of spectral analysis of discrete signals used in telecommunications, acoustics, vibration diagnostics, radar and other technical fields where a highly accurate assessment of the spectral characteristics of signals is required. State of the art There are known methods for constructing the spectrum of a discrete signal using the discrete Fourier transform (DFT), which involve multiplying the signal by a weighting function (e.g., a Hann or Hamming window) to reduce spectral spreading. These methods have drawbacks associated with distortion of the amplitudes of spectral components and the dependence of the result on the choice of weighting function. The aim of the invention is to increase the accuracy of constructing the spectrum of a discrete signal of the predominant spectral component and its multiples by determining the number of samples that is a multiple of the period of the spectral component and by reducing the time step of the discrete signal by increasing the initial sampling frequency for a more accurate selection of the specified number of samples. Disclosure of invention The proposed method for increasing the accuracy of constructing the spectrum of a discrete signal with an initial number of samples N and a sampling frequency SR includes the following steps instead of the traditional multiplication of the signal by a weighting function. Step 1: Upsampling (optional) To increase the accuracy of selecting the number of samples that is a multiple of the spectral component period, the original signal sampling frequency is increased by a factor of U (2-16). This is achieved by adding U-1 zeros between samples, which increases the number of samples to N⋅U and the sampling frequency to SR⋅U. Reducing the time step allows for a more precise determination of the optimal number of samples. In subsequent spectral analysis, only the first copy of the spectrum is taken into account. to eliminate the influence of repeating copies of the spectrum. Step 2. Calculating the signal spectrum The spectrum of the signal is calculated using the discrete Fourier transform, using either the original parameters (N and SR) or the increased parameters (N⋅U and SR⋅U) if upsampling was applied in step 1. The resulting spectrum is used for further analysis of the harmonic components. Step 3. Spectrum analysis to determine the period of the spectral component The spectral component and its period are determined by analyzing the signal spectrum as follows: a) spectral indices are identified whose amplitude exceeds a threshold equal to the maximum of the product of the maximum amplitude of the spectrum by the coefficient A (0.05-0.2) and the product of the median of the amplitudes by the coefficient B (2-6); b) filter closely spaced spectral indices located at a distance of C (1-3) spectral counts, preserving the index with the maximum amplitude; c) check the remaining indices for multiplicity by assessing the proximity of the index ratios to integers greater than or equal to 1, with a tolerance proportional to the spectral resolution (or at higher sampling rates), for example, ; d) sum up the amplitudes of multiple indices and select the minimum index with the maximum sum as the index of the spectral component; d) calculate the period of the spectral component in samples as the ratio of the number of samples (N or N⋅U) to the index of the spectral component, rounded to an integer. Step 4. Determining the optimal number of samples The optimal number of signal samples, a multiple of the spectral component period, is determined by successively reducing the signal length from the initial number of samples (N or N⋅U) to a number reduced by the spectral component period in samples. For each length, the discrete Fourier transform is calculated, and the spectral component amplitude is determined as the maximum value in a given frequency range, for example, ±2 spectral samples from the spectral component index. The length at which the amplitude is maximum is selected as the optimal number of samples. Step 5. Calculating the spectrum with the optimal number of samples The final signal spectrum is calculated using a discrete Fourier transform, using the optimal number of samples determined in step 4. This ensures the construction of a spectrum of the spectral component and its multiples with minimal spreading and high accuracy in determining the frequencies and amplitudes of harmonics. Advantages of the invention 1. Increasing the accuracy of constructing the spectrum of a discrete signal of the predominant spectral component and its multiples by selecting a number of samples that is a multiple of the period of the spectral component, minimizing spectrum spreading. 2. Increasing the accuracy of selecting the number of samples by increasing the initial sampling frequency, which reduces the time step of