Communication in the Presence of Noise.

Shannon, C. E. (1949). Communication in the Presence of Noise. Proceedings of the IRE, 37(1), 10-21.

Type

Journal article

Intellectual base

Primary research

Year

1949

Volume

37

Issue

1

Pages

10-21

DOI

10.1109/jrproc.1949.232969

DOI registrant

Institute of Electrical and Electronics Engineers

Link

https://doi.org/10.1109/JRPROC.1949.232969

Cited from

engineering_design, information_theory, music_musicology, systems_cybernetics

Cited by

11 citations across 11 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.

• 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.

• 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.

• Compression

  • This sourceThe sampling theorem and geometric (signal-space) view of communication. 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.

• 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.

Domain-specific

• Additive White Gaussian Noise
  • Shannon's continuous-channel work established the signal-space and noise setting underlying the Gaussian channel capacity result.

Mechanisms

• Anti-Aliasing Bin Selection
  • Its failure mode is that the whole method rests on knowing the source's fastest dynamics, and if that top speed is underestimated the bin is sized too coarse and aliasing slips through looking perfectly stable.

    This sourceProves that reconstructing a signal requires sampling at a rate set by its highest frequency, so understating the bandwidth makes the sampling interval too coarse.

• Rolling Planning Cycle
  • Too slow, and the cadence aliases the target — you plan against a reference that has already drifted, and the sampled picture misleads.

    This sourceEstablishes that sampling too slowly makes distinct underlying signals indistinguishable and yields a misleading sampled representation.

• Sampling Interval Choice
  • The Nyquist–Shannon result

    This sourceEstablishes the twice-bandwidth sampling boundary, which makes a rate above 400 Hz appropriate for a signal band extending to 200 Hz.

• Temporal Rollup
  • Its signature failure is aliasing: choosing a grain coarser than the events being tracked makes short spikes vanish or, worse, masquerade as a phantom trend — the sampling problem behind the Nyquist limit.

    This sourceStates the sampling theorem underlying the Nyquist sampling limit.

Verification

Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Not recorded. Neither this nor any other of the 11 citations of this work carries a recorded support check.

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