Overcome signal analysis limitations in CWT

With Continuous Wavelet Transform (CWT), users are able to analyse signals in communication technologies that people use every day, which provides insights into how improvements can be made in efficiency, performance, and more – but there are limitations. A new innovation has been created which overcomes the key issues users currently face – allowing the analysis of both time and frequency domains at the same time.

Continuous Wavelet or Waveform Regeneration (4)

Background

CWT is a mathematical transform technique which is used to investigate the varying time-frequency characteristics of non-stationary waveforms (the frequency of the waveform is adjusting continuously – for example, in communication channels where there is not just a constant frequency).

This currently provides:

At low frequencies – good frequency resolution, but poor time resolution;
At high frequencies – good time resolution, but poor frequency resolution.

These resolution limits work well for many non-stationary (real) waveforms, which have slowly changing vibrations punctured with momentary variations in frequency. However, there are occasions when users may wish to obtain both good frequency resolution and good time resolution at high or low frequencies, which is where the current technique falls short.

The solution

This issue can now be overcome through a new mathematical device – achieving both good frequency resolution and time resolution at the same time in both low and high frequencies. This is achieved by pre-processing the (complex) input waveform with CWT resolution inversion (which means completing CWT on both the original signal and an inverted signal).

This significant improvement in signal analysis ability can allow users an easier way to analyse multiple aspects of signals at the same time, regardless of the frequency level, and pinpoint where improvements can be made.

Key benefits

The process is straightforward and computationally very simple, without the need for a lot of processing.
Improved signal analysis from standard CWT is achieved.
This innovation overcomes a major limitation over existing CWT.

Potential applications

The mathematical method originated from the radio frequency (RF) electronics industry but can be used in almost any industry.

Signal analysis applications

Uses can include signal filtering and analysis, signal compression, transient detection, image processing or compression (possible e.g. laser printers), damping ratio of oscillating signals, seismic signal processing, partial differential equation solving, filter design, pattern recognition, and acoustic processing.

Electrocardiogram (ECG) analysis

This innovation could also potentially be used by medical professionals to analyse heart rates in patients.

Electrocardiogram in hospital surgery operating emergency room showing patient heart rate with blur team of surgeons background

Unlock users’ ability to achieve both good frequency resolution and time resolution at both low and high frequencies during CWT.

Intellectual property patent status