Determination of uncertainty measure for estimate of noise power spectral density
View Patent ↗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.
1. A method comprising:
determining at a computational device a measure of uncertainty for an estimate of a power spectral density of a noise signal, wherein the estimate is determined by computing an average of n power spectral densities derived from n respective sets of samples of the noise signal, wherein each of the n power spectral densities is computed based on a corresponding one of the sample sets, wherein said determining the uncertainty measure includes computing the uncertainty measure based on the number n, wherein said determining the uncertainty measure includes computing an effective number of independent averages corresponding to said power spectral density estimate based on data including the number n and a relative amount of overlap between successive ones of the n sample sets, wherein the uncertainty measure is computed based on the effective number of independent averages; and
storing the uncertainty measure in a memory.
2. The method of claim 1 , wherein said determining the power spectral density estimate includes spectrally smoothing the average of the n power spectral densities to obtain a spectrally smoothed power spectral density, wherein said determining the uncertainty measure includes computing an effective number of independent averages corresponding to said power spectral density estimate based on data including:
the number n; information specifying a time-domain window that is applied to each of the n sample sets; and information specifying a filter used to perform said spectral smoothing;
wherein the uncertainty measure is computed based on the effective number of independent averages.
3. The method of claim 2 , wherein parameters of the filter vary with frequency.
4. The method of claim 1 , further comprising:
utilizing the computational device to further implement:
displaying a graph of the estimate of the power spectral density of the noise signal; and
displaying a graphical indication of the uncertainty measure in association with the displayed graph.
5. The method of claim 1 , further comprising:
receiving user input specifying the number n.
6. The method of claim 1 , wherein the computational device is a processor configured to execute program instructions stored in the memory.
7. The method of claim 1 , wherein the computation device comprises one or more programmable hardware elements.
8. A non-transitory memory medium storing program instructions, wherein the program instructions, when executed by a processor, cause the processor to implement:
determining a measure of uncertainty for an estimate of a power spectral density of a noise signal, wherein the estimate is determined by computing an average of n power spectral densities derived from n respective sets of samples of the noise signal, wherein each of the n power spectral densities is computed based on a corresponding one of the sample sets, wherein said determining the uncertainty measure includes computing the uncertainty measure based on the number n, wherein said determining the uncertainty measure includes computing an effective number of independent averages corresponding to said power spectral density estimate based on data including the number n and a relative amount of overlap between successive ones of the n sample sets, wherein the uncertainty measure is computed based on the effective number of independent averages; and
storing the uncertainty measure in a memory.
9. The memory medium of claim 8 , wherein said determining the power spectral density estimate includes spectrally smoothing the average of the n power spectral densities to obtain a spectrally smoothed power spectral density, wherein said determining the uncertainty measure includes computing an effective number of independent averages corresponding to said power spectral density estimate based on data including:
the number n; information specifying a time-domain window that is applied to each of the n sample sets; and information specifying a filter used to perform said spectral smoothing;
wherein the uncertainty measure is computed based on the effective number of independent averages.
10. The memory medium of claim 9 , wherein parameters of the filter vary with frequency.
11. The memory medium of claim 8 , wherein the program instructions, when executed by the processor, cause the processor to further implement:
displaying a graph of the estimate of the power spectral density of the noise signal; and displaying a graphical indication of the uncertainty measure in association with the displayed graph.
12. The memory medium of claim 8 , wherein the program instructions, when executed by the processor, cause the processor to further implement:
receiving user input specifying the number n.
13. The memory medium of claim 8 , wherein the memory medium is a semiconductor-based memory.
14. A system comprising:
a memory storing program instructions; and
a processor configured to access the program instructions from the memory and execute the program instructions, wherein the program instructions, when executed by the processor, cause the processor to implement:
determining a measure of uncertainty for an estimate of a power spectral density of a noise signal, wherein the estimate is determined by computing an average of n power spectral densities derived from n respective sets of samples of the noise signal, wherein each of the n power spectral densities is computed based on a corresponding one of the sample sets, wherein said determining the uncertainty measure includes computing the uncertainty measure based on the number n, wherein said determining the uncertainty measure includes computing an effective number of independent averages corresponding to said power spectral density estimate based on data including: the number n and a relative amount of overlap between successive ones of the n sample sets, wherein the uncertainty measure is computed based on the effective number of independent averages;
storing the uncertainty measure in a memory medium.
15. The system of claim 14 , wherein the program instructions, when executed by the processor, further cause the processor to implement:
displaying a graph of the estimate of the power spectral density of the noise signal; and
displaying a graphical indication of the uncertainty measure in association with the displayed graph.
16. The system of claim 14 , wherein said determining the power spectral density estimate includes spectrally smoothing the average of the n power spectral densities to obtain a spectrally smoothed power spectral density, wherein said determining the uncertainty measure also includes computing an effective number of independent averages corresponding to said power spectral density estimate based on data including:
the number n;
information specifying a time-domain window that is applied to each of the n sample sets; and
information specifying a filter used to perform said spectral smoothing;
wherein the uncertainty measure is computed based on the effective number of independent averages.
17. The system of claim 16 , wherein parameters of the filter vary with frequency.