Communication in the Presence of Noise.¶
Shannon, C. E. (1949). Communication in the Presence of Noise. Proceedings of the IRE, 37(1), 10-21.
Cited by¶
7 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Aliasing
- The folding is lawful, not random — a 45 kHz tone sampled at 44 kHz does not become noise; it becomes a clean, convincing 1 kHz tone — and that lawfulness is exactly what makes it dangerous: the fabricated structure passes the credibility checks that random error would fail, so an analyst trusts a measurement that is systematically lying.
This sourceStates and proves the sampling theorem, formalizing the bandlimit/sampling-rate condition for perfect reconstruction.
- The folding is lawful, not random — a 45 kHz tone sampled at 44 kHz does not become noise; it becomes a clean, convincing 1 kHz tone — and that lawfulness is exactly what makes it dangerous: the fabricated structure passes the credibility checks that random error would fail, so an analyst trusts a measurement that is systematically lying.
- Cadence
- The matching relation is the load-bearing structural fact, and here it has an exact mathematical form: the Nyquist criterion requires the sampling cadence to be at least twice the highest frequency present in the signal it must track, so the cadence must be matched to the tempo of the thing observed — too slow (sub-Nyquist) and the loop misses or aliases the signal's variation (the sluggishness failure, made precise as aliasing), too fast and it wastes bandwidth and computation on redundant samples (the overhead failure).
This sourceStates the sampling theorem: the sampling rate must be at least twice the highest signal frequency — the matching-of-rate criterion in exact form.
- The matching relation is the load-bearing structural fact, and here it has an exact mathematical form: the Nyquist criterion requires the sampling cadence to be at least twice the highest frequency present in the signal it must track, so the cadence must be matched to the tempo of the thing observed — too slow (sub-Nyquist) and the loop misses or aliases the signal's variation (the sluggishness failure, made precise as aliasing), too fast and it wastes bandwidth and computation on redundant samples (the overhead failure).
- Channel Capacity
- The capacity ceiling is then the bandwidth multiplied by the base-two logarithm of one plus the signal-to-noise ratio, in bits per second — a definite number once the band and noise are fixed.
This sourceDerives the band-limited Gaussian-channel capacity C = B·log2(1 + S/N), the Shannon–Hartley theorem.
- The capacity ceiling is then the bandwidth multiplied by the base-two logarithm of one plus the signal-to-noise ratio, in bits per second — a definite number once the band and noise are fixed.
- Compression
This sourceThe sampling theorem and geometric (signal-space) view of communication. Tier C (bibliography only). DOI verified.
- Reference Cadence Exceeds Tracking Bandwidth
- The pattern also has a cousin in aliasing — when reference content above the sampling or response rate folds into a spurious low-frequency signal the system mistakes for real — both arising from a rate inadequate to the reference spectrum.
This sourceStates the sampling theorem; reference content above the sampling/response rate folds (aliases) into a spurious low-frequency signal.
- The pattern also has a cousin in aliasing — when reference content above the sampling or response rate folds into a spurious low-frequency signal the system mistakes for real — both arising from a rate inadequate to the reference spectrum.
- Tempo Mismatch
- The matching condition is the Nyquist criterion: faithful response requires \(f_s > 2 f_{\max}\).
This sourceThe sampling theorem (Nyquist criterion): faithful reconstruction requires a sample rate above twice the highest signal frequency, below which aliasing folds high frequencies into spurious low ones.
- The matching condition is the Nyquist criterion: faithful response requires \(f_s > 2 f_{\max}\).
Domain-specific¶
Verification¶
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