Principal Component Compression Method for Covariance Matrices Used for Uncertainty Propagation

We investigate a principal component analysis approach for compressing the covariance matrices derived from real-time and sampling oscilloscope measurements. The objective of reducing the data storage requirements to scale proportional to the trace length n rather than n² is achieved, making the approach practical for representing results and uncertainties in either the time or frequency domain. Simulation results indicate that the covariance matrices can be represented in a compact form with negligible error. Mathematical manipulation of the compressed matrix can be achieved without the need to reconstruct the full covariance matrix. We have demonstrated compression of data sets containing up to 10000 complex frequency components.