# A modulation property of time-frequency derivatives of filtered phase and its application to aperiodicity and fo estimation

## TL;DR

This paper presents a linear SNR estimator for speech aperiodicity that estimates background noise levels indirectly, applicable across various window functions, and can replace existing periodicity detection modules in vocoders.

## Contribution

It introduces a novel, simple, and linear SNR estimator based on time-frequency derivatives that reliably estimates aperiodicity without direct noise extraction.

## Key findings

- Effective SNR estimation from 0dB to 80dB without calibration
- Applicable to various window functions with low sidelobe levels
- Can replace existing aperiodicity estimation modules in vocoders

## Abstract

We introduce a simple and linear SNR (strictly speaking, periodic to random power ratio) estimator (0dB to 80dB without additional calibration/linearization) for providing reliable descriptions of aperiodicity in speech corpus. The main idea of this method is to estimate the background random noise level without directly extracting the background noise. The proposed method is applicable to a wide variety of time windowing functions with very low sidelobe levels. The estimate combines the frequency derivative and the time-frequency derivative of the mapping from filter center frequency to the output instantaneous frequency. This procedure can replace the periodicity detection and aperiodicity estimation subsystems of recently introduced open source vocoder, YANG vocoder. Source code of MATLAB implementation of this method will also be open sourced.