Image Processing with Complex Daubechies Wavelets
Journal of Mathematical Imaging and Vision
SIAM Journal on Scientific Computing
Time-frequency localization with the Hartley S-transform
Signal Processing
Shift invariant properties of the dual-tree complex wavelet transform
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 03
Orthogonal complex filter banks and wavelets: some properties anddesign
IEEE Transactions on Signal Processing
Localization of the complex spectrum: the S transform
IEEE Transactions on Signal Processing
The wavelet transform, time-frequency localization and signal analysis
IEEE Transactions on Information Theory
Computational Signal Processing with Wavelets
Computational Signal Processing with Wavelets
The Condition Monitoring and Performance Evaluating of Digital Manufacturing Process
ICIRA '08 Proceedings of the First International Conference on Intelligent Robotics and Applications: Part II
Rule based system for power quality disturbance classification incorporating S-transform features
Expert Systems with Applications: An International Journal
Need for speed: fast Stockwell transform (FST) with O(N) complexity
ICICS'09 Proceedings of the 7th international conference on Information, communications and signal processing
The discrete orthonormal Stockwell transform for image restoration
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
A user study of visualization effectiveness using EEG and cognitive load
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
Power quality analysis using Discrete Orthogonal S-transform (DOST)
Digital Signal Processing
ECG signal enhancement using S-Transform
Computers in Biology and Medicine
Expert Systems with Applications: An International Journal
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The S-transform is a time-frequency representation known for its local spectral phase properties. A key feature of the S-transform is that it uniquely combines a frequency dependent resolution of the time-frequency space and absolutely referenced local phase information. This allows one to define the meaning of phase in a local spectrum setting, and results in many desirable characteristics. One drawback to the S-transform is the redundant representation of the time-frequency space and the consumption of computing resources this requires (a characteristic it shares with the continuous wavelet transform, the short time Fourier transform, and Cohen's class of generalized time-frequency distributions). The cost of this redundancy is amplified in multidimensional applications such as image analysis. A more efficient representation is introduced here as a orthogonal set of basis functions that localizes the spectrum and retains the advantageous phase properties of the S-transform. These basis functions are defined to have phase characteristics that are directly related to the phase of the Fourier transform spectrum, and are both compact in frequency and localized in time. Distinct from a wavelet approach, this approach allows one to directly collapse the orthogonal local spectral representation over time to the complex-valued Fourier transform spectrum. Because it maintains the phase properties of the S-transform, one can perform localized cross spectral analysis to measure phase shifts between each of multiple components of two time series as a function of both time and frequency. In addition, one can define a generalized instantaneous frequency (IF) applicable to broadband nonstationary signals. This is the first time a channel IF has been integrated in an orthogonal local spectral representation. A direct comparison between these basis functions and complex wavelets is performed, highlighting the advantages of this approach. The relationship between this basis set and the fully redundant S-transform is demonstrated highlighting the ability to arbitrarily sample the time-frequency space. The introduction of this basis set leads to efficient analysis routines that may find use in a wide range of fields.