Quantitative assessment of linear noise-reduction filters for spectroscopy
| Autor: | Long V. Le, Young C. Kim, David E. Aspnes |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Signal Processing (eess.SP)
Noise reduction FOS: Physical sciences 02 engineering and technology Applied Physics (physics.app-ph) 01 natural sciences Parseval's theorem 010309 optics symbols.namesake Optics Distortion 0103 physical sciences FOS: Electrical engineering electronic engineering information engineering Electrical Engineering and Systems Science - Signal Processing Fourier series Mathematics business.industry Filter (signal processing) Physics - Applied Physics 021001 nanoscience & nanotechnology Atomic and Molecular Physics and Optics Noise Fourier transform symbols 0210 nano-technology business Algorithm Linear filter |
| DOI: | 10.48550/arxiv.2010.00987 |
| Popis: | Linear noise-reduction filters used in spectroscopy must strike a balance between reducing noise and preserving lineshapes, the two conflicting requirements of interest. Here, we quantify this tradeoff by capitalizing on Parseval’s Theorem to cast two measures of performance, mean-square error (MSE) and noise, into reciprocal- (Fourier-) space (RS). The resulting expressions are simpler and more informative than those based in direct- (spectral-) space (DS). These results provide quantitative insight not only into the effectiveness of different linear filters, but also information as to how they can be improved. Surprisingly, the rectangular (“ideal” or “brick wall”) filter is found to be nearly optimal, a consequence of eliminating distortion in low-order Fourier coefficients where the major fraction of spectral information is contained. Using the information provided by the RS version of MSE, we develop a version that is demonstrably superior to the brick-wall and also the Gauss-Hermite filter, its former nearest competitor. |
| Databáze: | OpenAIRE |
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