Time-base nonlinearity determination using iterated sine-fit analysis

Sine-fit procedure for unevenly sampled, multiply clocked signals

“…In addition, it is easy to estimate the variance of the results [9], data may be unevenly spaced and in this case the spectral estimate acquires additional immunity from aliasing effects [10]. Sine-fit methods are often used to measure the performance of ADC circuits, but this is usually done with equally spaced samples and with nonlinear fitting algorithms to estimate frequency as well as amplitude and phase [5].…”

“…However, this is not always the case, and when signals are unevenly sampled and homodyne or heterodyne setups are used that involve multiple clocks, it is not possible to use the standard algorithms to produce accurate spectral density estimates. The PVLAS experiment, designed to perform a very delicate test of quantum electrodynamics (QED) [2,3] and to search for light pseudoscalar particles [4], is an example of a multiclock heterodyne scheme, and here it is shown how to implement an algorithm which generalizes the standard sine-fit [5] and Lomb-Scargle [6] procedures to obtain both amplitude and phase of important Fourier components of the physical signal, with an application to PVLAS data. The next section summarizes a few important facts, Sections 3 and 4 outline the theory, Section 5 reports the results obtained with test data, and Section 6 shows how the procedure has been implemented in the case of PVLAS.…”

Improved time-base for waveform parameter estimation

“…It is beyond the scope of this paper to provide an indepth discussion of this method, other than to note that only the fundamental harmonic is considered in the fit, and uniform weighting is used in the time-base distortion estimate. However, the auto-calibration circuitry provides no means of sampling the 19.4 MHz signal over multiple phases directly, as is required in [7]. The fit returns a 5 12-point, time-base distortion estimate array that contains approximately 10 repetitions of the ramp errors.…”

“…In step 3, The time-base distortion is extracted from the 19.4 MHz low-distortion sinewave data using the constantwaveshape constraint, iterated sine-fit method, described in [7]. It is beyond the scope of this paper to provide an indepth discussion of this method, other than to note that only the fundamental harmonic is considered in the fit, and uniform weighting is used in the time-base distortion estimate.…”

“…While its uncorrected performance is impressive, a new auto-calibration hardware and software scheme has been developed to further improve its timing linearity. The auto-calibration scheme employs a time-base error estimation algorithm similar to one proposed in [7], but with important additional details necessary when implementing the scheme as an embedded, steady-state, iterative process.…”