Multi-resolution Analysis

TFDs, Wavelets Etc.PCG applications

Heart Sound Introduction

Recording PCG

S2 signal

Occurs because of blood flow and closure of Aortic and Pulmonary valves.

Is composed of two sub signals A2 – created because of Aortic valve closure P2 - created because of Pulmonary valve closure

A2 is characterized with lower frequencies than P2 and is usually precedes it in time.

FT – Fourier Transform

Fourier Transform returns the frequency components of the signal globaly.

For example: S2 signal

filtered in[20,120]

FT – Fourier Transform

The corresponding FT:

What does this give us?

No Temporal info!

Short Time FT for changing signals

FT windowed:

Window size 64 Window size 128 Window size 256

Short Time FT for changing signals

Uncertainty Principle Each window N samples. N/2 coefficients signifying 0-fs/2 frequencies. Space between coefficients

/ 2

( / 2 1)s sf f

N N

Multi-Resolution Analysis

Wavelet Transform - Intro

Basis functions are compact in time and frequency.

Basis function are created basic function called “Mother Wavelet”

Wavelet Transform - Intro

Basis function are created from mother wavelet through scaling and shifting

Wavelet Transform

CTW Discrete

Wavelet Transform – PCG applications

Obaidat M.S., J. Med. Eng. Tech., 1993Used wavelet transform for HS analysis:

Wavelet Transform – PCG applications Reed T.R et al.

Proceeding Signal and Image Processing -2005Used Wavelet decomposition and reconstruction for PCA feature extraction and segmentation to Diastolic and systolic parts

D1

D2

D3

D4

D5

D6

D7

D8

Normal Heart Signal

D1

D2

D3

D4

D5

D6

D7

D8

D1

D2

D3

D4

D5

D6

D7

D8

Normal Heart Signal

Wavelet Transform – PCG applications Liang, H.   Hartimo, I.  

Signal Process. & Comput. Technol. Lab., Helsinki Univ. of Technol., Espoo Used Wavelet Decomposition and Reconstruction of PCG as input to an ANN for study of murmurs.

There are several other works doing the same for detection of different HS conditions

Wavelet Transform - Applications

Image Analysis: Feature Extraction

Wavelet and Fractal connection – Self similarity

S-Transform

CTW with mother wavelet:

Properties: Not Orthogonal Directly invertible into the Fourier Transform

Spectrum

S-Transform – PCG Application G Livanos*, N Ranganatha, J

Jiang, Computers in Cardiology 2000.Showed that S-Transform can perform best for the needs of a user who needs a simple and clear display of intensity, frequency and timing, in comparison to Morlet wavelet and STFT.

Mathematical definition:

Valuable: because of preserving FT essence:

Is always pure real

Wigner-Ville Distribution

Wigner-Ville Distribution

Problematic: Cross components unlimited

Wigner-Ville Distribution – PCG Applications

Xu, Durand et al, IEEE transactions on biomedical engineering 2000, used WVD to extract A2 and P2 from S2 signals and used this to estimate A2-P2 interval

Wigner-Ville Distribution – PCG Applications Seedahamed S.M. et al, Biomedical Signal Processing and

control (Feb 2006).Use WVD to estimate IF (instantaneous frequency).

Chirplet Transform

Instead of wavelet basis function that can be scaled and shifted Chirplet Transform uses basis functions that derive for chirps where the phase changes too.

Chirplet Transform - Applications O’Neill J.C. et al gave and algorithm to create sparse

representation of signal using max likelihood estimation of chirplets

Chirplet Transform - Applications

My work

Currently trying to use TFDs and wavelet transform to extract interval time of A2-P2.

Currently working on using S-Transform for basis for a feature extraction algorithm