Windowed Spectrum Frequency Correction for Precise Signal Analysis
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Solution Overview
Problem
Current signal analysis methods, particularly those using Fourier transformation, face limitations in frequency resolution due to the Nyquist-Shannon sampling theorem and are prone to errors from the leakage effect, especially when signals are not recorded regularly, leading to imprecise determination of frequency and amplitude of sinusoidal components.
Innovation Solution
A method that corrects the frequency of signal components by using a frequency correction characteristic curve specific to the window function, determined from the amplitude ratios of the highest and second-highest spectral lines in the signal spectrum, to improve the accuracy of frequency analysis while minimizing computational effort.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the observation period is extended to improve frequency resolution, then frequency resolution is improved, but measurement time increases
Solution Approach 1:
The patent pre-calculates and stores correction values in a lookup table before signal analysis. The frequency correction values are computed once and stored, then directly retrieved during analysis without real-time calculation, eliminating the need for extended observation periods while achieving accurate frequency measurement
Solution Approach 2:
The patent replaces the traditional time-domain extension method (lengthening observation period) with a computational method (frequency correction using lookup tables). Instead of mechanically extending the measurement time, the system uses pre-computed correction factors to achieve the same resolution improvement instantaneously
2Measurement precision
If peak fitting is performed to improve frequency and amplitude accuracy, then accuracy is improved, but computational effort increases
Solution Approach 1:
The patent uses simple amplitude ratio calculations instead of complex peak fitting algorithms. By computing the ratio between the highest spectral line amplitude and adjacent spectral line amplitudes, the system achieves accurate frequency and amplitude determination with minimal computational resources, avoiding the heavy mathematical operations of curve fitting
Solution Approach 2:
The patent transforms the complex peak fitting problem into a simple parameter comparison task. Instead of fitting curves to determine parameters, the method directly uses the ratio of spectral line amplitudes as the determining parameter, fundamentally simplifying the computational approach while maintaining accuracy
3Object-generated harmful factors
If window functions are applied to reduce leakage effect, then leakage is reduced, but frequency accuracy deteriorates due to spectral line broadening
Solution Approach 1:
The patent extracts and compensates for the frequency shift caused by window functions. By calculating the frequency correction value based on the ratio of spectral line amplitudes and using a lookup table specific to each window function, the method removes the detrimental frequency shift effect while preserving the benefits of leakage reduction
Solution Approach 2:
The patent introduces frequency correction values as an intermediary element between the windowed spectrum and the final frequency measurement. These correction values, stored in lookup tables, mediate the relationship between the window function application and the accurate frequency determination, allowing both leakage reduction and frequency accuracy to coexist
Data Source
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AI summary
The invention relates to a method for analysing a signal, in which a spectrum of the signal to be analysed is provided, which spectrum is the result of a multiplication of the signal to be analysed by a predefined window function and a subsequent, in particular discrete or fast, Fourier transform, the highest spectral line and the adjacent second-highest spectral line (S2) are determined in the spectrum in the region of at least one local maximum, the amplitude (A1, A2) of the highest spectral line and of the second-highest spectral line is determined, at least one value dependent on the amplitude (A1) of the highest spectral line (S1) and on the amplitude (A2) of the second-highest spectral line (S2) is determined, a frequency correction value is determined for the frequency of the highest spectral line (S1) from the determined value using a frequency correction characteristic curve which was created for the predefined window function, and the frequency of the highest spectral line (S1) is corrected by the frequency correction value. The invention also relates to an apparatus for carrying out the method.