What Is Specification Aliasing? How Undersampled Prompts Create Hallucination

By Mario Alexandre
March 21, 2026
sinc-LLM
Prompt Engineering

Aliasing in Signal Processing

In signal processing, aliasing occurs when a signal is sampled below its Nyquist rate. The reconstructed signal contains frequency components that were not in the original, phantom frequencies that are indistinguishable from real ones. This is why poorly digitized audio sounds distorted: the reconstructed waveform includes frequencies the original never had.

x(t) = Σ x(nT) · sinc((t - nT) / T)

The Nyquist-Shannon theorem states the minimum sampling rate to avoid aliasing: 2B samples per unit time, where B is the signal bandwidth.

Specification Aliasing in LLMs

The sinc-LLM paper introduced the concept of specification aliasing: when a prompt fails to sample all specification bands, the LLM reconstructs the missing specifications from its training distribution. These reconstructed specifications were never in your original intent, they are phantom specifications, the prompt engineering equivalent of aliased frequencies.

Example: You write "Summarize this document." You sampled 1 band (TASK) out of 6. The model must invent:

• Who is summarizing (PERSONA), defaults to generic assistant

• For what purpose (CONTEXT), defaults to general audience

• Which parts matter (DATA), defaults to everything equally

• How long, what to include/exclude (CONSTRAINTS), defaults to training distribution

• What format (FORMAT), defaults to paragraph prose

Each invented specification is an aliased component. The output looks reasonable but reflects the model's defaults, not your requirements.

The Mathematics of Specification Aliasing

In classical aliasing, a frequency f sampled at rate f_s Install: pip install sinc-llm | GitHub | Paper

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Originally published at tokencalc.pro

sinc-LLM applies the Nyquist-Shannon sampling theorem to LLM prompts. Read the spec | pip install sinc-prompt | npm install sinc-prompt