An Introduction to S-Transform for Time-Frequency Analysis S.K. Steve Chang SKC-2009.

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Presentation transcript:

An Introduction to S-Transform for Time-Frequency Analysis S.K. Steve Chang SKC-2009

Question: Do we live in… Time-Domain or Frequency-Domain? SKC-2009

Time Domain vs Frequency Domain Time information is lost Frequency (Hz) Spectrum Time (Seconds) Waveform SKC-2009

Spectrogram (time-Frequency) Time (Seconds) Frequency (HZ) SKC-2009

Fourier Transform & Short Time Fourier Transform Window SKC-2009

STFT Fourier Transform SKC-2009

STFT: Fixed Window, Fixed Resolution Window Length Frequency Resolution Time Resolution SKC-2009

Example (400 msec sample) SKC-2009

(T=25 ms) Poor Frequency Resolution SKC-2009

(T=125 ms) Fixed Resolution SKC-2009

(T=375 ms) Fixed Resolution SKC-2009

(T=1000 ms) Poor High Frequency Time Resolution SKC-2009

S-Transform & Short Time Fourier Transform SKC-2009

Gaussian Window for S-Transform Function of Frequency SKC-2009

Gaussian Window for S-Transform High Frequency Low Frequency Time Shifted SKC-2009

and from SKC-2009

Two Chirps and Two Bursts S-T STFT Wigner SKC-2009

S-Transform and Wavelet Transform Mother Wavelet: SKC-2009

S-Transform is not Wavelet Transform Mother Wavelet does not have zero mean: Morlet’s Wavelet Phase Correction SKC-2009

Generalized S-Transform Resolution p TimeFrequency Standard Deviation SKC-2009

Generalized S-Transform: Bi-Gaussian SKC-2009

Generalized S-Transform: Bi-Gaussian Sharper Front Edge For Arrival Time Sacrifice Frequency Resolution SKC-2009

Generalized S-Transform: Bi-Gaussian Sharper Arrival Time SKC-2009

Generalized S-Transform: Your Own SKC-2009

Generalized S-Transform: Your Own Constraint: SKC-2009

Examples - Applications Engine Knock Pressure STFT S-Transform with New Window S-Transform SKC-2009

Power Disturbance Detection Power Disturbance Contour Stationary Phase Power Disturbance SKC-2009

Earthquake Detection Noisy Signal Time-Frequency Filter Inverse S-Transform Earthquake Signal SKC-2009

Earthquake Seismology Original Data Filter 1 Filter 2 S-Filters SKC-2009

Seismic Data STFTS- Transform Seismic Trace SKC-2009

Medical: Forearm Blood Flow Rest Activities Occlusion SKC-2009

Geomagnetic Storm Induced Current SKC-2009

Gear Vibration Signal Decoposition Helicopter Rotor under Fatigue Test Transient Components SKC-2009

Image Analysis Original ImageDominant Frequency SKC-2009

S-Transform We live in Time-Frequency World. Similar to Short-Time Fourier Transform Similar to Continuous Wavelet Transform Generalized S-Transform: Many Different Window Choices Time-Frequency Analysis: Many Applications SKC-2009