Why LLMs Hallucinate: The Signal Processing Explanation

Why LLMs Hallucinate: The Signal Processing Explanation By Mario Alexandre March 21, 2026 sinc-LLM Prompt Engineering The Real Cause of LLM Hallucination Every week, another headline declares that LLMs "make things up." The standard explanations range from "stochastic parrots" to "training data gaps." But there is a more precise explanation rooted in signal processing: hallucination is aliasing caused by undersampled prompts . When you send a raw, unstructured prompt to an LLM, you are transmitting a complex specification signal through a single sample. The Nyquist-Shannon sampling theorem tells us exactly what happens next: the model reconstructs a signal, but not your signal. It reconstructs whatever fits the insufficient data you provided. That is aliasing. That is hallucination. What the Nyquist-Shannon Theorem Says The theorem is precise: to faithfully reconstruct a signal with bandwidth B, you need at least 2B samples per unit time. Below that rate, the reconstructed signal conta