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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

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Multi-resolution Analysis


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multi resolution analysis

Multi-resolution Analysis

TFDs, Wavelets Etc.PCG applications

s2 signal
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
FT – Fourier Transform
  • Fourier Transform returns the frequency components of the signal globaly.
  • For example:
    • S2 signalfiltered in[20,120]
ft fourier transform1
FT – Fourier Transform
  • The corresponding FT:
  • What does this give us?
  • No Temporal info!
short time ft for changing signals
Short Time FT for changing signals
  • FT windowed:

Window size 64

Window size 128

Window size 256

short time ft for changing signals1
Short Time FT for changing signals
  • Uncertainty Principle
    • Each window N samples.
    • N/2 coefficients signifying 0-fs/2 frequencies.
    • Space between coefficients
multi resolution analysis1
Multi-Resolution Analysis

Chirplet

Transform

Wavelet

Transform

Wigner-Ville

Distribution

wavelet transform intro
Wavelet Transform - Intro
  • Basis functions are compact in time and frequency.
  • Basis function are created basic function called “Mother Wavelet”
wavelet transform intro1
Wavelet Transform - Intro
  • Basis function are created from mother wavelet through scaling and shifting
wavelet transform
Wavelet Transform

CTW Discrete

wavelet transform pcg applications
Wavelet Transform – PCG applications
  • Obaidat M.S., J. Med. Eng. Tech., 1993Used wavelet transform for HS analysis:
wavelet transform pcg applications1
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
wavelet transform pcg applications2
Wavelet Transform – PCG applications
  • Liang, H.   Hartimo, I.   Signal Process. & Comput. Technol. Lab., Helsinki Univ. of Technol., EspooUsed 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
Wavelet Transform - Applications
  • Image Analysis:
    • Feature Extraction
    • Wavelet and Fractal connection – Self similarity
s transform
S-Transform
  • CTW with mother wavelet:
  • Properties:
    • Not Orthogonal
    • Directly invertible into the Fourier Transform Spectrum
s transform pcg application
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.
wigner ville distribution
Wigner-Ville Distribution
  • Mathematical definition:
  • Valuable:
    • because of preserving FT essence:
    • Is always pure real
wigner ville distribution1
Wigner-Ville Distribution
  • Problematic:
    • Cross components unlimited
wigner ville distribution pcg applications
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 applications1
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
chirplet transform applications
Chirplet Transform - Applications
  • O’Neill J.C. et al gave and algorithm to create sparse representation of signal using max likelihood estimation of chirplets
my work
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