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Software for compact covariance matrix uncertainty

This software was developed as part of EURAMET Joint Research Project IND16 'Metrology for ultrafast electronics and high-speed communications' (Ultrafast).

Measurement uncertainties associated with a waveform measured in the time or frequency domain can be represented by a covariance matrix. But the size of the covariance matrix grows as the square of the length of the measured waveform. Digital Sampling Oscilloscopes typically provide waveforms with lengths of up to 5 000 points, yielding large, but manageable, covariance matrices. However, Real-Time Digital Oscilloscopes can acquire waveforms with lengths of greater than 106 points giving large covariance matrices that are difficult to store and manipulate.

The software can be used to provide a compact representation of the large covariance matrices associated with waveform measurements. In addition, modules are include to support the propagation of the covariance matrix through the measurement functions defined by various algebraic manipulations of the waveform measurements so that impedance match corrections and calibration corrections can be applied.

The software is written in MATLAB and includes a User Guide and Software Licence Agreement. A separate software package based on these algorithms has been developed in Python and is available from the project website

This work was funded by the UK National Measurement Office under the Physical Programme and by EURAMET under the EMRP Industry 2010 Programme, which is jointly funded by the EMRP participating countries within EURAMET and the European Union.

05 Nov 2015


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