A High-Performance Training-Free Pipeline for Robust Random Telegraph Signal Characterization via Adaptive Wavelet-Based Denoising and Bayesian Digitization Methods

TL;DR

RTS signals, especially with pink noise and multi-trap configurations, challenge accurate extraction of transition amplitudes $\Delta_{RTS}$ and dwell-time distributions $\bar{\tau}_{high}$, $\bar{\tau}_{low}$. The authors present a training-free pipeline that couples adaptive DTCWT denoising with a Bayesian digitizer (with KDE-based level identification) to infer discrete RTS levels and subsequently fit exponential dwell-time models. The method autonomously selects DTCWT parameters via rules linking decomposition level $K$ to signal length $L$ and threshold $T$ to spectral entropy $H_S$, enabling robust operation without neural networks. Benchmarking on synthetic RTS data with up to $N_{trap}=3$ and both white and pink noise demonstrates superior trap-number accuracy, reduced $\Delta_{RTS}$ and dwell-time errors, and a roughly 83x speedup, with modest memory overhead, and it extends to real CNT device signals.

Abstract

Random telegraph signal (RTS) analysis is increasingly important for characterizing meaningful temporal fluctuations in physical, chemical, and biological systems. The simplest RTS arises from discrete stochastic switching events between two binary states, quantified by their transition amplitude and dwell times in each state. Quantitative analysis of RTSs provides valuable insights into microscopic processes such as charge trapping in semiconductors. However, analyzing RTS becomes considerably complex when signals exhibit multi-level structures or are corrupted by background white or pink noise. To address these challenges and support high-throughput RTS analysis, we introduce a modular and scalable signal processing pipeline combining dual-tree complex wavelet transform (DTCWT) denoising with a Bayesian digitization strategy. The adaptive DTCWT-based denoiser incorporates autonomous parameter selection rules for its decomposition level and thresholds, optimizing white noise suppression without manual tuning. Complementing this denoiser, our probabilistic digitizer effectively resolves binary trap states even under residual notorious background pink noise. The overall approach enables robust performance across varying noise levels and multi-trap scenarios, improving mean dwell time estimation and RTS reconstruction over classical and neural baselines. The method is up to 83x faster, training-free, and suitable for real-time or large-scale analysis. Evaluations confirm its generalizability, speed, and reliability, providing a strong foundation for future fully adaptive and automated RTS pipelines.

Figures (8)

• Figure 1: (a) A noiseless simple 2-level RTS with the definition of $\Delta_{\text{RTS}}$, ${\tau}_{\text{high}}$, and ${\tau}_{\text{low}}$. Examples of processed synthesized RTS with noisy RTS (grey), denoised RTS (blue), and digitized RTS by our DTCWT + Bayesian method (red) on middle subplot, cropped for better visualization; kernel density estimation (KDE) plot on left subplot; time-lag plot on right subplot for the entire RTS duration. (b) The workflow of our three-stage RTS analysis pipeline. (c) 1-trap RTS with $\eta_{\text{wn}}=10\%$. (d) 2-trap RTS with $\eta_{\text{wn}}=20\%$. (e) 3-trap RTS with $\eta_{\text{wn}}=30\%$. (f) 1-trap RTS with $\eta_{\text{pn}}=10\%$. (g) 2-trap RTS with $\eta_{\text{pn}}=10\%$. (h) 3-trap RTS with $\eta_{\text{pn}}=10\%$.
• Figure 2: Comparison of SNR (denoising quality) on benchmarked algorithms. RTS samples spanning ground truth $N_{\text{trap}}=1,2,3$, and $\eta_{\text{wn}},\eta_{\text{pn}}=1\%\sim30\%$ for white (a) and pink noise (b), respectively. RTS sample lengths fixed at $L = 100{,}000$ time steps.
• Figure 3: Comparison of $N_{\text{trap}}$ error (denoising quality) on benchmarked algorithms. RTS samples spanning ground truth $N_{\text{trap}}=1,2,3$, and $\eta_{\text{wn}},\eta_{\text{pn}}=1\%\sim30\%$ for white (a) and pink noise (b), respectively. RTS sample lengths fixed at $L = 100{,}000$ steps. The darkened diagonal subplots indicate correct detections, namely, $N_{\text{trap, truth}} = N_{\text{trap, detected}}$. The values in each column of each method sum to 100% of all RTS samples at the same ground truth $N_{\text{trap}}$ and $\eta_{\text{wn}},\eta_{\text{pn}}$ level. The bottom-left subplots indicate overestimation, while the top-right subplots reflect underestimation.
• Figure 4: Comparison of $\Delta_{\text{RTS}}$ error (denoising quality) on benchmarked algorithms. RTS samples spanning ground truth $N_{\text{trap}}=1,2,3$, and $\eta_{\text{wn}}=1\%\sim30\%$ for white (a) and pink noise (b), respectively. RTS sample lengths fixed at $L = 100{,}000$ steps. Error statistics of individual traps are separated into subplots. Each subplot contains results from up to 50 synthetic RTSs, provided the corresponding trap was correctly detected. The subplot layout is organized as follows: The top row, left subplot shows error distribution for the single trap in $N_{\text{trap}} = 1$ samples. The top row, middle and right subplots display errors for the two individual traps, labeled as the first and second traps, in $N_{\text{trap}} = 2$ synthetic RTSs. The bottom row shows errors for the first, second, and third traps in $N_{\text{trap}} = 3$ synthetic RTSs.
• Figure 5: Comparison of RMSE (digitization quality) on benchmarked algorithms. RTS samples spanning ground truth $N_{\text{trap}}=1,2,3$, and $\eta_\text{wn},\eta_\text{pn} = 1\%\sim30\%$ for white (a) and pink noise (b), respectively. Each RTS sample is fixed at a length of $L = 100{,}000$ time steps. Error statistics of individual traps are presented in separate subplots.