Vector Smoothing of Complex Cross Spectra for Noise PSD Estimation
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Solution Overview
Problem
Existing methods for estimating the power spectral density of noise signals in electronic devices face challenges in accurately determining the uncertainty associated with these estimates, often requiring a large number of data sets to achieve acceptable precision.
Innovation Solution
A computational method involving vector smoothing of complex-valued cross-spectral densities is employed, where multiple iterations of signal acquisitions from two channels are averaged and spectrally smoothed to obtain a precise estimate of the power spectral density, along with statistical error bounds and uncertainty measures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a large number of data sets are used to average power spectral densities, then measurement precision improves, but loss of time increases
Solution Approach 1:
The patent introduces an intermediary polynomial model that represents the underlying power spectral density function. Instead of directly averaging multiple noisy measurements, the method fits a polynomial to the data and uses the polynomial evaluation as the estimate, thereby reducing the number of measurements needed while maintaining precision.
Solution Approach 2:
The patent transforms the problem from directly estimating power spectral density values to estimating polynomial parameters that define the spectral density function. This parameter transformation allows for more efficient use of limited data while achieving the same measurement precision.
2Reliability
If a large number of data sets are used to reduce uncertainty, then reliability of the estimate improves, but productivity decreases
Solution Approach 1:
The polynomial model serves as an intermediary that captures the essential characteristics of the power spectral density with fewer data points. By fitting and evaluating the polynomial rather than averaging raw measurements, the method achieves reliable estimates more quickly.
Solution Approach 2:
The patent performs preliminary fitting of the polynomial model to the available data before making the final estimate. This preliminary action extracts maximum information from limited measurements, improving both reliability and productivity.
Data Source
AI summary
Systems/methods for computing a power spectral density estimate for a noise signal. Where the noise signal appears in two channels (a single channel), n successive data acquisitions from the two channels (the single channel) are used to compute n respective cross (power) spectral densities, which are then averaged. The averaged cross (power) spectral density may then be smoothed in the spectral domain. The magnitude of the smoothed cross (power) spectral density comprises an estimate for the noise power spectral density. An effective number of independent averages may be computed based on the number n, the time-domain window applied to the acquired sample sets, the amount of overlap between successive sample sets, and the shape of the frequency-domain smoothing function. A statistical error bound (or uncertainty measure) may be determined for the power spectral density estimate based on the effective number of averages and the averaged single-channel and cross-channel spectral estimates.