Performance of nonlinear smoothers in signal recovery

Abstract

Time series data can be decomposed as signal plus noise. A good smoother should be able to recover a smooth signal reasonably well from time series data. The performance of two classes of nonlinear smoothers in signal recovery is discussed in this paper. The first class is the well-known class of median smoothers. The other one is a relatively new class of smoothers based on extreme-order statistics, called lower-upper-lower-upper smoothers. Sinusoidal signals of different frequencies with contaminated normal noise and impulsive noise added were simulated. Members of the two classes of nonlinear smoothers were applied to remove the 'non-Gaussian' and impulsive noise. To this output linear smoothing was applied to remove the remaining Gaussian noise. By means of a simulation study, the success of the two classes of smoothers was investigated using as measures of success the least-squares regression of the smoothed sequence on the signal and the integrated mean square error. PERFORMANCE OF NONLINEAR SMOOTHERS IN SIGNAL RECOVERY 429 SIGNAL RECOVERYSignal recovery is the process by which a signal is recovered from a set of noisy time series data, generated at time t as data t = signal t +noise t

Modifications of 4253HT Smoother in Extracting Signal from Noise

“…The overall idea of the simulation procedure was from Conradie [23], where simulation was done 200 times in this study. Moreover, a signal used for the simulation process has been representing most real lifetime series data and has special functions such as Doppler, HeaviSine, Bumps, and Block, as follows: i. Doppler: The formula of this signal function originated from Donoho [24], where their contributions were reported by 𝑌𝑌 𝑖𝑖 [25] as their plots are shown in Figure 2.…”

Performance of 4253ht Smoother by Different Hannings: Application in Rainfall Data

“…The signal that was contaminated by normal noise was used during the simulation process to determine the performance of 4253HT smoother. All the simulation steps were done by referring to Conradie et al, (2009).…”

“…is frequency and 𝑝 is period, then 𝜙 is displacement. This is the similar signal used by Conradie et al, (2009) and Coles (2001) with the respective parameter values to yield a smooth and good curve: |𝛼| = 3, 𝜙 = 1, and 𝐷 = 0.7.…”

“…However, the efficacy of linear smoother is limited in certain conditions due to the nature in data smoothing such as a destruction by noise from heavy-tailed and unknown distribution [2]. To overcome this limitation, the nonlinear smoother is introduced as it has been proven to be more robust to heavy-tailed noise than the linear smoother based on previous studies [3,4,5,6].…”

“…Non-linear smoother such as running median was firstly introduced by Tukey (1977) and his works, later was extensively expanded by Rabiner et al, (1975). These non-linear smoothers are widely used in engineering practices, including image and speech processing applications [5,9]. Moreover, this method also was applied in signal processing by Masrelies and Martin (1977), and Azmi et al, (2018).…”