The Blind RT60 Estimation module is a Python implementation based on the paper "Blind estimation of reverberation time" by Ratnam et al. [1]. It aims to estimate the reverberation time (RT60) of an input audio signal.

[1] Ratnam, Rama & Jones, Douglas & Wheeler, Bruce & O'Brien, William & Lansing, Charissa & Feng, Albert. (2003). Blind estimation of reverberation time. The Journal of the Acoustical Society of America. 114. 2877-92. 10.1121/1.1616578.

For the evaluation, a speech utterance was taken from the NOIZEUS database [3], a repository of noisy speech corpus.

pip install blind_rt60

from blind_rt60 import BlindRT60
from scipy.io import wavfile

# Create an instance of the BlindRT60 estimator
estimator = BlindRT60()

# Load your audio signal (x) and its sampling frequency (fs)
# Example: fs, x = wavfile.read("path/to/audio/file.wav")

# Estimate the RT60
rt60_estimate = estimator(x, fs)

# Visualize the results
fig = estimator.visualize(x, fs)
plt.show()

The BlindRT60 class accepts various parameters that allow customization of the estimation process. Here are the key parameters:

• fs: Sample rate of the audio signal.
• framelen: Length of each analysis frame in seconds.
• hop: Hop size between analysis frames in seconds.
• percentile: Pre-specified percentile value for RT60 estimation.
• a_init: Initial value for the decay rate parameter.
• sigma2_init: Initial value for the signal variance parameter.
• max_itr: Maximum number of iterations for convergence.
• max_err: Maximum error for convergence.
• a_range: Range of valid values for the decay rate parameter.
• bisected_itr: Number of iterations for the bisection method.
• sigma2_range: Range of valid values for the signal variance parameter.
• verbose: Enable verbose output for each iteration.

Contributions are welcome! If you find any issues or have suggestions for improvement, please open an issue or submit a pull request on the GitHub repository.

This project is licensed under the MIT License. See the LICENSE file for more information.

For any inquiries or questions, please contact zoreasaf@gmail.com.

We assume that the reverberant tail of a decaying sound y is the product of a fine structure x that is random process, and an envelope a that is deterministic. $x\left[ n \right]$ is independent and identically random variables drawn from the normal distribution $N\left( {0,\sigma } \right)$.
The model for room decay then suggests that the observations y are specified by $y\left( n \right) = x\left( n \right) \cdot a\left( n \right)$. Due to the time-varying term $a\left( n \right)$, $y\left( n \right)$ independent but not identically distributed, and their probability density function is $N\left( {0,\sigma \cdot a\left( n \right)} \right)$.
For each estimation interval the likelihood function of y is, $$L\left( {y;a,\sigma } \right) = \frac{1}{{\prod\limits_{n = 0}^{N - 1} {a\left( n \right)} }} \cdot {\left( {\frac{1}{{2\pi {\sigma ^2}}}} \right)^{N/2}} \cdot \exp \left( { - \frac{{\sum\limits_{n = 0}^{N - 1} {{{\left( {\frac{{y\left( n \right)}}{{a\left( n \right)}}} \right)}^2}} }}{{2{\sigma ^2}}}} \right)$$ N+1 parameters of the model: $a[0,...N], \sigma$.
Describe $a[n]$ by damped free decay $a\left[ n \right] = \exp \left( { - \frac{n}{\tau }} \right) \buildrel \Delta \over = {a^n}$, $$L\left( {y;a,\sigma } \right) = {\left( {\frac{1}{{2\pi {a^{N - 1}}{\sigma ^2}}}} \right)^{N/2}} \cdot \exp \left( { - \frac{{\sum\limits_{n = 0}^{N - 1} {{a^{ - 2n}}y{{\left( n \right)}^2}} }}{{2{\sigma ^2}}}} \right)$$

Given the likelihood function, the parameters $a$ and $\sigma$ can be estimated using a maximum-likelihood approach, $$\frac{{\partial \ln L\left( {y;a,\sigma } \right)}}{{\partial a}} = {a^{ - 1}}\left( {\frac{1}{{{\sigma ^2}}}\sum\limits_{n = 0}^{N - 1} {n \cdot {a^{ - 2n}}y{{\left( n \right)}^2} - \frac{{N\left( {N - 1} \right)}}{2}} } \right)$$ $$\frac{{{\partial ^2}\ln L\left( {y;a,\sigma } \right)}}{{\partial {a^2}}} = \frac{{N\left( {N - 1} \right)}}{2}{a^{ - 2}} + \frac{1}{{{\sigma ^2}}}\sum\limits_{n = 0}^{N - 1} {n\left( {1 - 2n} \right) \cdot {a^{ - 2n}}y{{\left( n \right)}^2}} $$ $$\frac{{\partial \ln L\left( {y;a,\sigma } \right)}}{{\partial \sigma }} = - \frac{N}{\sigma } + \frac{1}{{{\sigma ^3}}}\sum\limits_{n = 0}^{N - 1} {{a^{ - 2n}}y{{\left( n \right)}^2}} $$

• The geometric ratio is notably compressive, and in actual scenarios, the values of a are expected to be proximate to 1. Conversely, $\sigma$ exhibits a broad range.
• Examining the gradient of $\frac{{\partial \ln L\left( {y;a,\sigma } \right)}}{{\partial a}}$, initiating the process with an initial value smaller than a requires the root-solving strategy to descend the gradient fast enough.

• Solved using numerical and iterative approach $\frac{{\partial \ln L\left( {y;a,\sigma } \right)}}{{\partial a}} = 0$; $\frac{{\partial \ln L\left( {y;a,\sigma } \right)}}{{\partial \sigma }} = 0$.
• Estimating $a*$:
  1. The root was bisected until the zero was bracketed.
  2. The Newton–Raphson method was applied to accurate the root, ${a_{n = 1}} = {a_n} - \frac{{\frac{{\partial \ln L\left( {y;{a_n},\sigma } \right)}}{{\partial a}}}}{{\frac{{{\partial ^2}\ln L\left( {y;{a_n},\sigma } \right)}}{{\partial {a^2}}}}}$.
• Estimating $\sigma$: $${\sigma ^2} = \frac{1}{N}\sum\limits_{n = 0}^{N - 1} {{a^{ - 2n}}y{{\left( n \right)}^2}}$$

The model will fail during (1) estimation Frames Do Not Fall Within a Region of Free Decay, and (2) sound with a gradual rather than rapid offset.

• In the first case, the damping of sound in a room cannot occur at a rate faster than the free decay. A robust strategy would be to select a threshold value such that the left tail of the probability density function of $a*$.
• In the second case, $p(a^*)$ is likely to be multimodal. the strategy then is to select the first dominant peak.
• For a unimodal symmetric distribution with $\gamma = 0.5$ the filter will track the peak value, i.e., the median. In connected speech, where peaks cannot be clearly discriminated or the distribution is multi-modal, $\gamma$ should peaked based on the statistics of gap durations.