Abstract: A method and system provide for measuring a repeating waveform of a SUT. The method includes repeatedly sampling first and second copies of the SUT to provide first SUT waveforms including first noise introduced by a first digitizer and second SUT waveforms including second noise introduced by a second digitizer; pairing the first and second SUT waveforms to provide corresponding pairs of first and second digital samples; organizing the pairs of first and second digital samples into groups of sample pairs corresponding to sampling times; for each group, calculating a covariance of the first and second digital samples to estimate a signal variance of the SUT, and scaling the first and second digital samples to preserve a mean of the group while adjusting a variance of the group to match the estimated signal variance of the SUT at the corresponding sampling time; and reassembling the groups into the SUT waveform.

Abstract: A method and system are provided for reducing noise in a time domain waveform of a signal under test (SUT). The method includes performing cross-correlation of multiple first complex signals and multiple second complex signals, respectively, from the SUT to provide multiple cross-correlated signals, respectively, where the cross-correlated signals have amplitude components and no phase components from the SUT, and where the first and second complex signals include uncorrelated noise, respectively. The method further includes determining an average of the cross-correlated signals to provide an average cross-correlated signal with reduced uncorrelated noise; obtaining a representative phase component from one of the first complex signals or the second complex signals; and combining the representative phase component with the average cross-correlated signal to provide a representative complex signal corresponding to the SUT with reduced uncorrelated noise.

Abstract: A method of filtering a signal sampled by a sampler, for example, in an equivalent time oscilloscope includes applying a correction to an actual frequency response of the sampler, with respect to a reference frequency response, to a first frequency range of the sampled signal, and transitioning across a second frequency range of the sampled signal from the correction applied to the first frequency range to no correction of the actual frequency response of the sampler, the second frequency range being higher than the first frequency range. The method further includes compensating in a third frequency range of the sampled signal for excess gain incurred while applying the correction and transitioning from the correction to no correction in the first and second frequency ranges, respectively, so that statistics of asynchronous components of the sampled signal are preserved, the third frequency range being higher than the second frequency range.

Abstract: A direct determination equalizer system (“DDES”) for compensating for the deterministic effects of a transmission channel and a data source is disclosed. The DDES may include an equalizer having equalizer-tap coefficients, a cross-correlator configured to receive the first sampled signal and an ideal signal and in response produce a cross-correlated signal, and a processor in signal communication with the equalizer and the cross-correlator. The equalizer is configured to receive a first sampled signal and in response produce an equalized output data signal sequence and the processor is configured to determine the equalizer-tap coefficients from the cross-correlated signal.