Sampling-rate-aware noise generation

TL;DR

This paper addresses the challenge of generating discrete white noise that maintains consistent statistical properties across different sampling rates by proposing a variance scaling approach and analyzing the effects of common signal transformations.

Contribution

It introduces a method for sampling-rate-aware noise generation by defining variance scaling and analyzing transformation effects to ensure consistent noise characteristics.

Findings

Variance of noise should grow proportionally with sampling rate

Transformations like filtering and quantization must be adapted for sampling-rate-aware noise

Proposed approach ensures comparable noise results across sampling rates

Abstract

In this paper we consider the generation of discrete white noise. Despite this seems to be a simple problem, common noise generator implementations do not deliver comparable results at different sampling rates. First we define what we mean with "comparable results". From this we conclude, that the variance of the random variables shall grow proportionally to the sampling rate. Eventually we consider how noise behaves under common signal transformations, such as frequency filters, quantisation and impulse generation and we explore how these signal transformations must be designed in order generate sampling-rate-aware results when applied to white noise.