Noise Power Spectral Density Estimation Using Coherence-Based Error Bounds
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Solution Overview
Problem
Existing methods for estimating the power spectral density of noise signals in electronic devices are inefficient, requiring large numbers of data sets to achieve acceptable uncertainty, and lack effective methods for determining uncertainty and error bounds in noise measurements.
Innovation Solution
A computational method involving vector smoothing of complex-valued cross-spectral densities in the frequency domain, which includes averaging and spectral smoothing of cross-spectral densities from multiple two-channel acquisitions, along with calculations for 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 productivity deteriorates due to the time required to acquire and process numerous data sets
Solution Approach 1:
The patent introduces a coherence function as an intermediary metric that characterizes the correlation between two noise channels. By computing the coherence function alongside the cross-spectral densities, the system can determine statistical error bounds without requiring excessive averaging, thus reducing acquisition time while maintaining measurement precision.
Solution Approach 2:
The patent replaces the mechanical approach of simply averaging many independent measurements with a computational approach that uses spectral smoothing and coherence-based error bounding. This substitution allows for more efficient estimation of uncertainty bounds, reducing the need for large numbers of data sets and thereby improving productivity.
2Measurement precision
If spectral smoothing is applied to cross-spectral densities, then measurement precision improves through better noise characterization, but device complexity increases due to additional computational operations
Solution Approach 1:
The patent applies spectral smoothing selectively rather than uniformly across all frequency ranges. By smoothing only where necessary to reduce variance in the power spectral density estimates, the method achieves improved measurement precision without the full computational overhead of complete spectral smoothing, thus managing device complexity more effectively.
3Measurement precision
If two-channel acquisitions are used with cross-spectral density computation, then measurement precision improves for noise signals present in both channels, but device complexity increases due to simultaneous dual-channel acquisition requirements
Solution Approach 1:
The patent converts the presence of interfering noise signals, which would normally degrade measurements, into a beneficial feature. By using two channels where each contains different interfering noises but both contain the target noise, the cross-spectral density computation automatically suppresses uncorrelated interfering noises while preserving the correlated target noise, thereby improving measurement precision.
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.