# A Triangular-Matrix-Based Spectral Encoding Method for Broadband Filtering and Reconstruction-Based Spectral Measurement

## TL;DR

This paper introduces a new, simple method for spectral measurement using triangular matrices, which balances efficiency and cost.

## Contribution

A novel triangular-matrix-based encoding method is proposed for efficient and cost-effective spectral measurement.

## Key findings

- The proposed encoding method has a low condition number, ensuring good spectral reconstruction.
- The method performs well under both precise and imprecise measurement conditions.
- It offers a practical trade-off between encoding efficiency and implementation cost.

## Abstract

Broadband filtering and reconstruction-based spectral measurement represent a hot technical route for miniaturized spectral measurement; the measurement encoding scheme has a great effect on the spectral reconstruction fidelity. The existing spectral encoding schemes are usually complex and hard to implement; thus, the applications are severely limited. Considering this, here, a simple spectral encoding method based on a triangular matrix is designed. The condition number of the proposed spectral encoding system is estimated and demonstrated to be relatively low theoretically; then, verification experiments are carried out, and the results show that the proposed encoding can work well under precise or unprecise encoding and measurement conditions; therefore, the proposed scheme is demonstrated to be an effective trade-off of the spectral encoding efficiency and implementation cost.