HILBERT HUANG TRANSFORM

BY

MAYUR SHELKE

SATYAVRAT WAGLE

PRATEEK NAGRAS

GAURAV VIKHE

INTRODUCTION

The Hilbert–Huang transform (HHT) is a way to decompose a signal into so-called intrinsic mode functions (IMF), and obtain instantaneous frequency data.

It is designed to work well for data that is non-stationary and nonlinear.

In contrast to other common transforms like the Fourier transform, the HHT is more like an algorithm (an empirical approach) that can be applied to a data set, rather than a theoretical tool.

Why we need HHT

The HHT provides a new method of analyzing non-stationary and nonlinear time series data.

The transform doesn’t impose a linear behavior on the input signal and hence a true representation of data is obtained.

It enables us to study input data in time, frequency and energy domains

Fourier Wavelet Hilbert

Basis a priori a priori Adaptive

Frequency convolution: global uncertainty

convolution: regional uncertainty

differentiation: local certainty

Presentation energy-frequency energy-time-frequency energy-time-frequency

Non-linear no no yes

Non- stationary no yes yes

Feature extraction

No discrete: no continuous: yes yes

Theoretical base

theory complete theory complete empirical

LITERATURE SURVEY

“Time-Frequency Analysis and Wave Transform Term Paper”

Po-Hong Wu

N. E. Huang, Z. Shen and S. R. Long, et al., ―The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time Series Analysis＂ , Proc. Royal Society, vol. 454, pp.903-995, London, 1998.

Md. Khademul Islam Molla, Akimasa Sumi and M. Sayedur Rahman, ―Analysis of Temperature Change under Global Warming Impact using Empirical Mode Decomposition

THE ALGORITHM

VARIANTS IN USING ALGORITHM

The algorithm can vary in two main aspects

Them being

1. The stoppage criteria used.

2. The degree of the splining equation.

We would be using Cubic spline and we have put in user defined iterations in our code, so the flexibility of choosing a stoppage criteria is available

RESULTS TILL DATE

We have read papers and tried to understand the methodology in which HHT is used in the mentioned systems.

A general understanding of how the transform can be used in systems ranging from fiscal to climatic.

A code to calculate IMF has been written

We are in the need of a real time system to apply our result to. Also a verification of our obtained results is needed.

PLAN FOR THE NEXT SEMESTER

We would be applying our program to a system whose behavior we already know

We would test our code on part of the said system and analyze whether it works for the remaining part.

After having a conclusive result we would then apply our program for a real time system and use HHT for analysis as well as prediction of behavior.

THANK YOU