Accurate spectral estimation based on measurements with a distorted-timebase digitizer

To accurately measure amplitude and phase of the spectral components of a multispectral microwave signal an equivalent time broadband sampling oscilloscope with an appropriate triggering can be used. A method is described which allows an accurate estimation of the values of the spectral components of a signal, with significant timebase error present in a digitized sine wave. Once this error is characterized one complex function, called kernel, is calculated for each frequency component present in the signal. This kernel will be dependent on the timebase error and the set of frequencies. It is constructed so that the result of an inner product between kernel and measured signal equals the value of the spectral component with the associated frequency. These kernels are stored and used for calculating accurate spectral estimations of signals present at the scopes input port, by calculating the inner products between the different kernels and the measured signals. When properly applied the use of windowing techniques can improve accuracy.<
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