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Technology Details
Limitations of Previous Methods
Many applications that involve signal or data processing require the use of transforms such as the Fast Fourier Transform (FFT) or Discrete Fourier Transform (DFT). These transforms allow a signal or data set that satisfies certain conditions to be converted to the frequency domain. Once in the frequency domain, the signal or data set can be analyzed, encoded, or modulated for transmission. The transform can then be used again to return the signal to the time domain once decoded or demodulated.
The methods described above can be applied to linear and stationary signals and data. However, they cannot be applied to nonlinear or nonstationary signals or data sets. A Wavelet Transform can be used on nonlinear signals with gradual inter-wave frequency modulation but cannot be used with signals that have intra-wave modulation (i.e., a group of signals that vary over time). When used with nonlinear and nonstationary signals, current transform methods and technologies may result in reduced quality or accuracy.
Given that many applications in communications, sonar, seismic analysis, acoustics, optics, and medicine require the analysis of multiple signals that are nonlinear and/or nonstationary, new transform technologies are needed.
How HHT Resolves Limitations with Previous Methods
HHT technology has resolved this limitation. It allows for the accurate transform of nonlinear and/or nonstationary signals, while maintaining the highest level of accuracy. In addition, this technology also provides the same results as the Fourier Transform when applied to linear signals; thus, HHT offers a complete solution to all signal processing needs.
The HHT algorithms accurately analyze physical signals via the following steps:
Compared to current transform methods and technologies, HHT offers improved accuracy and yields results with more physical meaning than existing analysis tools that tend to obscure or discard valuable information.
Many applications that involve signal or data processing require the use of transforms such as the Fast Fourier Transform (FFT) or Discrete Fourier Transform (DFT). These transforms allow a signal or data set that satisfies certain conditions to be converted to the frequency domain. Once in the frequency domain, the signal or data set can be analyzed, encoded, or modulated for transmission. The transform can then be used again to return the signal to the time domain once decoded or demodulated.
The methods described above can be applied to linear and stationary signals and data. However, they cannot be applied to nonlinear or nonstationary signals or data sets. A Wavelet Transform can be used on nonlinear signals with gradual inter-wave frequency modulation but cannot be used with signals that have intra-wave modulation (i.e., a group of signals that vary over time). When used with nonlinear and nonstationary signals, current transform methods and technologies may result in reduced quality or accuracy.
Given that many applications in communications, sonar, seismic analysis, acoustics, optics, and medicine require the analysis of multiple signals that are nonlinear and/or nonstationary, new transform technologies are needed.
How HHT Resolves Limitations with Previous Methods
HHT technology has resolved this limitation. It allows for the accurate transform of nonlinear and/or nonstationary signals, while maintaining the highest level of accuracy. In addition, this technology also provides the same results as the Fourier Transform when applied to linear signals; thus, HHT offers a complete solution to all signal processing needs.
The HHT algorithms accurately analyze physical signals via the following steps:
Instantaneous frequencies are calculated based on the Empirical Mode Decomposition method when intrinsic mode functions (IMFs) are generated for complex data.
A Hilbert transform converts the local energy and instantaneous frequency derived from the IMFs to a full energy-frequency-time distribution of the data (i.e., a Hilbert spectrum).
The physical signal is filtered by reconstruction from selected IMFs.
A curve can be fitted to the filtered signal. (Curve fitting might not have been possible with the original, unfiltered signal.)
Compared to current transform methods and technologies, HHT offers improved accuracy and yields results with more physical meaning than existing analysis tools that tend to obscure or discard valuable information.
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