# Amplitude response and square wave describing functions

arXiv: https://arxiv.org/abs/2412.01579 · HTML: https://mlsanity.com/paper/2412.01579/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2024.

## Built on by (most cited first, 1 of 1)

- [Dimensionless Controls of Plasticity Under Alternating Tasks: From Evolutionary Biology to Continual Learning](https://mlsanity.com/paper/2608.23889/) (2026)

## Abstract (arXiv)

An analog of the describing function method is developed using square waves rather than sinusoids. Static nonlinearities map square waves to square waves, and their behavior is characterized by their response to square waves of varying amplitude - their amplitude response. The output of an LTI system to a square wave input is approximated by a square wave, to give an analog of the describing function. The classical describing function method for predicting oscillations in feedback interconnections is generalized to this square wave setting, and gives accurate predictions when oscillations are approximately square.