HHT based Instrumental Glitch Trigger Generation

Project Description and Goal

Introduction: Hilbert-Huang Transform (HHT)

• HHT is a recently suggested empirical data transform based on adaptive bases. So it is very useful for analyzing non-linear and/or non-stationary data. The HHT consists of two main parts: 1) empirical mode decomposition (EMD) 2) Hilbert spectral analysis (HSA). The EMD can decompose the original data into some appropriate data sets that contributes to some frequency bands. Basically the EMD is described by a sifting processes with , which shows that the EMD performs the subtraction between the original data (or the previously generated data) and its average of envelopes, repeatedly, called intrinsic mode functions (IMF), expressed by and . And the normalized squared difference (NSD) between two successive sifting operations is defined as

,

which should be small. The stoppage criterion of this process is determined by comparing between the NSD and the predetermined value - if NSD is smaller than a predetermined value, the process is stopped.

• The Hilbert transform of the EMDed data consists of the amplitude and phase parts and we see that the original data can be expressed by the summation of the whole IMFs, which is .

  • Comparing to the (Fast) Fourier Transform (FFT), , we easily see that the HHT deals with the time-variant amplitude and phase data with adaptive bases. We compare the HHT to other two different transforms in the following table.

Preliminary Analysis of HHT

Trigger Generation Method

Simulation Results

Comparison to Klein-Welle and Other Methods