What is a Relevant Signal-to-Noise Ratio for Numerical Differentiation?
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909465669795840 |
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| author | Verma, Shashank Almuhaihi, Mohammad Bernstein, Dennis S. |
| author_facet | Verma, Shashank Almuhaihi, Mohammad Bernstein, Dennis S. |
| contents | In applications that involve sensor data, a useful measure of signal-to-noise ratio (SNR) is the ratio of the root-mean-squared (RMS) signal to the RMS sensor noise. The present paper shows that, for numerical differentiation, the traditional SNR is ineffective. In particular, it is shown that, for a harmonic signal with harmonic sensor noise, a natural and relevant SNR is given by the ratio of the RMS of the derivative of the signal to the RMS of the derivative of the sensor noise. For a harmonic signal with white sensor noise, an effective SNR is derived. Implications of these observations for signal processing are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | What is a Relevant Signal-to-Noise Ratio for Numerical Differentiation? Verma, Shashank Almuhaihi, Mohammad Bernstein, Dennis S. Systems and Control In applications that involve sensor data, a useful measure of signal-to-noise ratio (SNR) is the ratio of the root-mean-squared (RMS) signal to the RMS sensor noise. The present paper shows that, for numerical differentiation, the traditional SNR is ineffective. In particular, it is shown that, for a harmonic signal with harmonic sensor noise, a natural and relevant SNR is given by the ratio of the RMS of the derivative of the signal to the RMS of the derivative of the sensor noise. For a harmonic signal with white sensor noise, an effective SNR is derived. Implications of these observations for signal processing are discussed. |
| title | What is a Relevant Signal-to-Noise Ratio for Numerical Differentiation? |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2501.14906 |