A Multiple Interpolation Algorithm to Improve Resampling Accuracy in Data Triggers

Abstract

To address the problem of low trigger accuracy during trigger resampling and variable sampling rate trigger resampling using a fixed sampling rate analog-to-digital converter (ADC), this paper proposes an interpolation method combining sinc interpolation and linear interpolation to improve accuracy, based on a digital trigger. After behavior simulation verification and actual field programmable gate array (FPGA) test verification, the data collected by two 3GSps 12-bit ADCs were subjected to 8-times sinc interpolation followed by 16-times linear interpolation processing, after which the original trigger resampling accuracy was increased by 128 times and the sampling rate could be realized to vary between 100 MHz and 1 GHz. A signal–noise ratio (SNR) of 46.80 dBFS, a spurious free dynamic range (SFDR) of 45.91 dB, and an effective number of bits (ENOB) of 7.48 bits were obtained by direct trigger resampling without algorithm processing in the behavior simulation. Meanwhile, an SNR of 58.98 dBFS, an SFDR of 60.96 dB, and an ENOB of 9.42 bits were obtained by trigger resampling after algorithm processing. Due to the influence of analog link signal loss and signal interference on the development board, an SNR, SFDR and ENOB of 51.97 dBFS, 61.26 dB, and 8.32 bits, respectively, were obtained from the trigger resampling in the FPGA test. The experimental results show that the algorithm has not only improved the triggering accuracy but has also improved the SNR, SFDR, and ENOB parameters.

Feasibility of Low Latency, Single-Sample Delay Resampling: A New Kriging Based Method

“…A detailed design of a Farrow filter is described in [1]. A further recent application [11] provided resampling and trigger event detection for signals up to a sampling rate of 1 GHz. Aside from digital oscilloscopes, precise triggering is required in medical tomography applications.…”

“…The auxiliary variable µ can be ignored. Kriging requires a matrix inversion of order n + 1, with the matrix in (11) representing the statistical distance between the input samples. The weights and the matrix depend only on the location of the input samples, not on their values.…”

“…The output points use all the same input samples with identical time differences between them. The left side matrix in (11) for Kriging remains constant, as well as the denominator in (6) for Margolis. The inversion of the Kriging matrix can be pre-calculated.…”

“…Kriging and Margolis both used pre-calculation to reduce CPU time. The inverse Kriging matrix (11) and a table for the denominator in (6) was calculated once per input sample and applied to ten output samples, as described in Section 3.5. The average CPU time per output sample was 380 µs for Kriging (HW = 25) and 620 µs (HW = 18) for Margolis including pre-calculation.…”

“…Margolis requires the evaluation of n 2 terms in Equation ( 6) with O(n 2 ). Both algorithms have the same complexity of O(n 2 ) for the additional operations per output sample, either for multiplying the inverted Kriging matrix with the vector on the right side of (11), or for evaluation of the numerator in (6). The latter one is more expensive due to the sine function, leading to a higher total t CPU for Margolis.…”