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

The timebase distortion present in an equivalent-time sampling oscilloscope introduces errors in the estimation of the values of the spectral components of a microwave signal when a classical discrete Fourier transform is used. A method is developed here to avoid these errors. The method is tested both in practice and with simulations. Two parts can be distinguished. At first, the timebase distortion is measured. This is done by digitizing a sinusoidal signal applied at the oscilloscope´s input, and by calculating the phase of the analytical signal of the digitized waveform. Other possible methods to measure the timebase distortion are discussed, and it is shown why the method used is the most appropriate for our specific application. The knowledge of the timebase distortion is then used to build a least squares error estimator for the values of the spectral components of a digitized microwave signal. An experimental verification is done, from which is concluded that the method effectively removes the spectral estimation errors due to a timebase distortion