Decomposition of Higher-Order Spectra for Blind Multiple-Input Deconvolution, Pattern Identification and Separation

Area of Science:

• Signal Processing
• Data Analysis
• Biomedical Engineering

Background:

• Higher-order spectra (HOS) capture phase information lost in power spectra, enabling waveform recovery.
• Identifying multiple, recurring transient waveforms with random delays is a significant challenge in signal processing.

Purpose of the Study:

• To develop a new HOS-based technique for identifying unknown transient waveforms.
• To enable waveform detection comparable to optimal matched filters without prior waveform information.
• To provide a method applicable to both deterministic and non-deterministic HOS signals.

Main Methods:

• Developed a novel technique for recovering filters from HOS.
• Applied HOS decomposition for additive separation of component processes in non-Gaussian signals.
• Utilized numerically stable operations: time shift, element-wise multiplication, and averaging.

Main Results:

• Waveform detection performance approaches that of an optimal matched filter.
• The method successfully applies to both deterministic and non-deterministic HOS.
• Demonstrated blind denoising, detection, and classification of heartbeats in ECG signals.

Conclusions:

• The new HOS technique offers improved waveform identification and signal separation.
• Its numerical stability and efficiency make it suitable for real-time applications.
• HOS decomposition provides a powerful tool for analyzing complex, real-world signals like ECGs.