# Computation of the spectrum of $\text{dc}^2$-balanced codes

## TL;DR

This paper develops an approximation method for analyzing the spectrum of dc2-balanced codes using the central limit theorem, achieving high accuracy for codeword length 256.

## Contribution

It introduces a cubic approximation for the auto-correlation function of dc2-balanced codes and quantifies the spectral approximation error.

## Key findings

- Auto-correlation function approximated by a cubic function
- Spectrum approximation error less than 0.04 dB for n=256
- Method provides accurate spectral analysis of dc2-balanced codes

## Abstract

We apply the central limit theorem for deriving approximations to the auto-correlation function and power density function (spectrum) of second-order spectral null (dc2-balanced) codes.We show that the auto-correlation function of dc2-balanced codes can be accurately approximated by a cubic function. We show that the difference between the approximate and exact spectrum is less than 0.04 dB for codeword length n = 256.