Abstract
This article introduces the methods of Fourier and wavelet analysis for enhancing data quality in typical chemometric and process analytics applications. Fourier analysis has been popular for many decades but is best suited for enhancing signals where most features are localized in frequency. In contrast, wavelet analysis is appropriate for signals that contain features localized in both time and frequency domains. It also retains the benefits of Fourier analysis such as orthonormality and computational efficiency. Practical algorithms for off-line and on-line denoising are described and compared via simple examples. These algorithms can be used for off-line or on-line applications in order to mitigate the impact of additive Gaussian as well as non-Gaussian noise.
| Original language | English (US) |
|---|---|
| Title of host publication | Comprehensive Chemometrics |
| Subtitle of host publication | Chemical and Biochemical Data Analysis, Second Edition: Four Volume Set |
| Publisher | Elsevier |
| Pages | 179-204 |
| Number of pages | 26 |
| Volume | 3 |
| ISBN (Electronic) | 9780444641656 |
| DOIs | |
| State | Published - Jan 1 2020 |
| Externally published | Yes |
Keywords
- Bayesian estimation
- Data quality
- Data rectification
- Filtering
- Fourier analysis
- Gaussian and non-Gaussian noise
- Kalman filtering
- Model-based denoising
- Multiscale analysis
- Off-line and online denoising
- Outliers
- Smoothing
- Wavelet analysis
- Wavelet thresholding
- Windowed Fourier analysis
ASJC Scopus subject areas
- General Chemistry