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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Perceiving Loudness, Pitch, and Location01:21

Perceiving Loudness, Pitch, and Location

The human brain perceives pitch through two primary mechanisms reflected in place theory and frequency theory. Each mechanism describes how sound waves are interpreted as specific pitches by the brain, offering insights into the intricate processes of auditory perception.
Place theory, or place coding, suggests that different pitches are heard because various sound waves activate specific locations along the cochlea's basilar membrane. The brain determines the pitch of a sound by identifying...
Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
Aliasing01:18

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...

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A Tactile Automated Passive-Finger Stimulator (TAPS)
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Speech Enhancement, Gain, and Noise Spectrum Adaptation Using Approximate Bayesian Estimation.

Jiucang Hao1, Hagai Attias, Srikantan Nagarajan

  • 1Institute for Neural Computation, University of California, San Diego, CA 92093-0523 USA.

IEEE Transactions on Audio, Speech, and Language Processing
|April 30, 2010
PubMed
Summary

This study introduces a new Bayesian estimator for speech enhancement, improving noisy audio quality. The novel method offers better signal-to-noise ratio and lower word error rates for clearer speech.

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Area of Science:

  • Signal Processing
  • Audio Engineering
  • Machine Learning

Background:

  • Speech enhancement is crucial for improving audio clarity in noisy environments.
  • Traditional methods often face computational intractability for exact signal estimation.
  • Gaussian Mixture Models (GMMs) are typically used in the frequency domain, but this work explores the log-spectral domain.

Purpose of the Study:

  • To develop a computationally efficient approximate Bayesian estimator for speech enhancement.
  • To model speech signals using Gaussian Mixture Models (GMMs) in the log-spectral domain.
  • To improve signal-to-noise ratio (SNR) and reduce word recognition error rates in noisy speech.

Main Methods:

  • Developed three approximations for efficient signal estimation, including Gaussian approximation and Laplace methods (frequency and log-spectral domains).
  • Transformed log-spectral domain GMMs to the frequency domain using Kullback-Leibler (KL)-divergence.
  • Employed the Expectation-Maximization (EM) algorithm for gain and noise spectrum adaptation within the GMM framework.

Main Results:

  • The proposed algorithms significantly improved the signal-to-noise ratio (SNR) of enhanced speech.
  • A notable reduction in word recognition error rate was observed compared to existing methods.
  • Experimental results showed decreased spectral distortion, indicating higher fidelity of the enhanced speech signal.

Conclusions:

  • The approximate Bayesian estimator provides an efficient and effective solution for speech enhancement.
  • The log-spectral domain GMM approach with proposed approximations outperforms traditional frequency domain methods.
  • The method demonstrates practical utility in enhancing speech corrupted by speech-shaped noise (SSN).