Pattern recognition (psychology)

Noise reduction

Mathematics

Discrete wavelet transform

Stationary wavelet transform

Continuous wavelet transform

Noise (video)

Image (mathematics)

Harmonic wavelet transform

Second-generation wavelet transform

Wavelet packet decomposition

Artificial intelligence

Wavelet transform

Programming language

SIGNAL (programming language)

Computer science

Wavelet

Telecommunications

Detector

Journal of Separation Science

Wavelet transform is a versatile time-frequency analysis technique, which allows localization of useful signals in time or space and separates them from noise. The detector output from any analytical instrument is mathematically equivalent to a digital image. Signals obtained in chemical separations that vary in time (e.g., high-performance liquid chromatography) or space (e.g., planar chromatography) are amenable to wavelet analysis. This article gives an overview of wavelet analysis, and graphically explains all the relevant concepts. Continuous wavelet transform and discrete wavelet transform concepts are pictorially explained along with their chromatographic applications. An example is shown for qualitative peak overlap detection in a noisy chromatogram using continuous wavelet transform. The concept of signal decomposition, denoising, and then signal reconstruction is graphically discussed for discrete wavelet transform. All the digital filters in chromatographic instruments used today potentially broaden and distort narrow peaks. Finally, a low signal-to-noise ratio chromatogram is denoised using the procedure. Significant gains (>tenfold) in signal-to-noise ratio are shown with wavelet analysis. Peaks that were not initially visible were recovered with good accuracy. Since discrete wavelet transform denoising analysis applies to any detector used in separation science, researchers should strongly consider using wavelets for their research.

Wavelet transforms in separation science for denoising and peak overlap detection