Multiresolution Analysis TFDs Wavelets Etc PCG applications Heart

Multi-resolution Analysis TFDs, Wavelets Etc. PCG applications

Heart Sound Introduction

Recording PCG

S 2 signal n n Occurs because of blood flow and closure of Aortic and Pulmonary valves. Is composed of two sub signals n n n A 2 – created because of Aortic valve closure P 2 - created because of Pulmonary valve closure A 2 is characterized with lower frequencies than P 2 and is usually precedes it in time.

FT – Fourier Transform n n Fourier Transform returns the frequency components of the signal globaly. For example: n S 2 signal filtered in [20, 120]

FT – Fourier Transform n n n The corresponding FT: What does this give us? No Temporal info!

Short Time FT for changing signals n FT windowed: Window size 64 Window size 128 Window size 256

Short Time FT for changing signals n Uncertainty Principle n n n Each window N samples. N/2 coefficients signifying 0 -fs/2 frequencies. Space between coefficients

Multi-Resolution Analysis

Wavelet Transform - Intro n n Basis functions are compact in time and frequency. Basis function are created basic function called “Mother Wavelet”

Wavelet Transform - Intro n Basis function are created from mother wavelet through scaling and shifting

Wavelet Transform CTW Discrete

Wavelet Transform – PCG applications n Obaidat M. S. , J. Med. Eng. Tech. , 1993 Used wavelet transform for HS analysis:

Wavelet Transform – PCG applications n Reed T. R et al. Proceeding Signal and Image Processing -2005 Used Wavelet decomposition and reconstruction for PCA feature extraction and segmentation to Diastolic and systolic parts

Wavelet Transform – PCG applications n n 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 n Image Analysis: n n Feature Extraction Wavelet and Fractal connection – Self similarity

S-Transform n CTW with mother wavelet: n Properties: n n Not Orthogonal Directly invertible into the Fourier Transform Spectrum

S-Transform – PCG Application n 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.

Wigner-Ville Distribution n Mathematical definition: n Valuable: n because of preserving FT essence: n Is always pure real

Wigner-Ville Distribution n Problematic: n Cross components unlimited

Wigner-Ville Distribution – PCG Applications n Xu, Durand et al, IEEE transactions on biomedical engineering 2000, used WVD to extract A 2 and P 2 from S 2 signals and used this to estimate A 2 -P 2 interval

Wigner-Ville Distribution – PCG Applications n Seedahamed S. M. et al, Biomedical Signal Processing and control (Feb 2006). Use WVD to estimate IF (instantaneous frequency).

Chirplet Transform n 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 n 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 n n Currently trying to use TFDs and wavelet transform to extract interval time of A 2 -P 2. Currently working on using S-Transform for basis for a feature extraction algorithm