A Scaling Law for Bandwidth Under Quantization
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910034211897344 |
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| author | Kalcher, Maximilian Dubcek, Tena |
| author_facet | Kalcher, Maximilian Dubcek, Tena |
| contents | We derive a scaling law relating ADC bit depth to effective bandwidth for signals with $1/f^α$ power spectra. Quantization introduces a flat noise floor whose intersection with the declining signal spectrum defines an effective cutoff frequency $f_c$. We show that each additional bit extends this cutoff by a factor of $2^{2/α}$, approximately doubling bandwidth per bit for $α= 2$. The law requires that quantization noise be approximately white, a condition whose minimum bit depth $N_{\min}$ we show to be $α$-dependent. Validation on synthetic $1/f^α$ signals for $α\in \{1.5, 2.0, 2.5\}$ yields prediction errors below 3\% using the theoretical noise floor $Δ^2/(6f_s)$, and approximately 14\% when the noise floor is estimated empirically from the quantized signal's spectrum. We illustrate practical implications on real EEG data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23252 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Scaling Law for Bandwidth Under Quantization Kalcher, Maximilian Dubcek, Tena Signal Processing Information Theory We derive a scaling law relating ADC bit depth to effective bandwidth for signals with $1/f^α$ power spectra. Quantization introduces a flat noise floor whose intersection with the declining signal spectrum defines an effective cutoff frequency $f_c$. We show that each additional bit extends this cutoff by a factor of $2^{2/α}$, approximately doubling bandwidth per bit for $α= 2$. The law requires that quantization noise be approximately white, a condition whose minimum bit depth $N_{\min}$ we show to be $α$-dependent. Validation on synthetic $1/f^α$ signals for $α\in \{1.5, 2.0, 2.5\}$ yields prediction errors below 3\% using the theoretical noise floor $Δ^2/(6f_s)$, and approximately 14\% when the noise floor is estimated empirically from the quantized signal's spectrum. We illustrate practical implications on real EEG data. |
| title | A Scaling Law for Bandwidth Under Quantization |
| topic | Signal Processing Information Theory |
| url | https://arxiv.org/abs/2602.23252 |