# On Lossless Feedback Delay Networks

arXiv: https://arxiv.org/abs/1606.07729 · HTML: https://mlsanity.com/paper/1606.07729/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2016.

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

- [Data-Driven Room Acoustic Modeling Via Differentiable Feedback Delay Networks With Learnable Delay Lines](https://mlsanity.com/paper/2404.00082/) (2024)

## Abstract (arXiv)

Lossless Feedback Delay Networks (FDNs) are commonly used as a design prototype for artificial reverberation algorithms. The lossless property is dependent on the feedback matrix, which connects the output of a set of delays to their inputs, and the lengths of the delays. Both, unitary and triangular feedback matrices are known to constitute lossless FDNs, however, the most general class of lossless feedback matrices has not been identified. In this contribution, it is shown that the FDN is lossless for any set of delays, if all irreducible components of the feedback matrix are diagonally similar to a unitary matrix. The necessity of the generalized class of feedback matrices is demonstrated by examples of FDN designs proposed in literature.