Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Statistical Methods in Waveform Metrology


Waveform metrology aims to develop new techniques and measurement services at bandwidths currently unattainable for waveform verification, to characterize high-speed electrical signals and equipments, and to enable metrology for high-speed applications in internet, wireless, remote sensing, and computing. The Statistical Engineering Division has developed statistical methods to support these efforts.


One of the methods developed is the timebase correction procedure for waveforms. A waveform is a representation of a signal varies with time. The most familiar waveform is the sine wave. Waveform measurements are required throughout the optical communications, computer, wireless communications, radar, and remote sensing industries. Waveform measurements are used to verify signal fidelity and standard compliance for the design and qualification of systems and components. High-speed sampling oscilloscopes are often used for displaying waveforms. Sampling oscilloscopes, however, suffer from several nonideal properties that must be characterized and compensated for. One of these effects is the timing error, which is the sum of a deterministic timebase distortion (TBD) and a random jitter. By taking advantage of a parallel design of many equivalent-time sampling oscilloscopes, which has the property that any jitter on the timebase delay generator is common to the sampling time of all the samplers in the oscilloscope mainframe, the systematic and random timebase errors can be estimated from a set of reference sinusoids. Consequently, the timebase errors in a simultaneously measured waveform of interest can be corrected, effectively replacing the timebase of the oscilloscope with a timebase provided by the measured sinusoids. The procedure corrects the timing errors that might be present with long waveforms or large jitter, and lowers the noise floor significantly in most measurements.

Major Accomplishments

SED staff have been involved in the Waveform Metrology program since 1998. SED staff have assisted in the development of a measurement service for waveform calibration that is traceable to fundamental physics through the NIST electro-optic sampling system. The calibration includes the whole measured waveform along with a covariance matrix that describes the covariance structure of the sampled points in the waveform epoch. In addition, the calibration supports test equipments that operate in both time and frequency domains. Many joint work on statistical signal processing techniques that are being used to correct for the effects of timing drift, time-base distortion, timing jitter in measurement, and uncertainty analysis of timebase errors, has been published and/or documented. A selected listing of joint work:

  1. "Correcting sampling oscilloscope timebase errors with a passively mode-locked laser phase locked to a microwave oscillator", IEEE Transactions on Instrumentation and Measurement, vol 59, 916-922, (2010).  
  2. "Uncertainty of timebase corrections", IEEE Transactions on Instrumentation and Measurement, vol 58, 3468-3472, (2009).
  3. "Calibration of sampling oscilloscopes with high-speed photodiodes", IEEE Transactions on Microwave Theory and Techniques, vol 54, 3173-3182, (2006).  
  4. "Compensation of random and systematic timing errors in sampling oscilloscopes", IEEE Transactions on Instrumentation and Measurement, vol. 55, 2146-2154, (2006).
Created October 4, 2010, Updated August 31, 2016