Colors of noise

Summary

In audio engineering, electronics, physics, and many other fields, the color of noise or noise spectrum refers to the power spectrum of a noise signal (a signal produced by a stochastic process). Different colors of noise have significantly different properties. For example, as audio signals they will sound differently to human ears, and as they will have a visibly different texture. Therefore, each application typically requires noise of a specific color. This sense of 'color' for noise signals is similar to the concept of timbre in music (which is also called "tone color"; however, the latter is almost always used for sound, and may consider very detailed features of the spectrum). The practice of naming kinds of noise after colors started with white noise, a signal whose spectrum has equal power within any equal interval of frequencies. That name was given by analogy with white light, which was (incorrectly) assumed to have such a flat power spectrum over the visible range. Othe

Official source

https://en.wikipedia.org/wiki/Colors_of_noise

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An Efficient Signal-to-noise Approximation for Eccentric Inspiraling Binaries

Alexandra Shelest

Eccentricity has emerged as a potentially useful tool for helping to identify the origin of black hole mergers. However, eccentric templates can be computationally very expensive owing to the large number of harmonics, making statistical analyses to distinguish formation channels very challenging. We outline a method for estimating the signal-to-noise ratio (S/N) for inspiraling binaries at lower frequencies such as those proposed for LISA and DECIGO. Our approximation can be useful more generally for any quasi-periodic sources. We argue that surprisingly, the S/N evaluated at or near the peak frequency (of the power) is well approximated by using a constant-noise curve, even if in reality the noise strain has power-law dependence. We furthermore improve this initial estimate over our previous calculation to allow for frequency dependence in the noise to expand the range of eccentricity and frequency over which our approximation applies. We show how to apply this method to get an answer accurate to within a factor of 2 over almost the entire projected observable frequency range. We emphasize this method is not a replacement for detailed signal processing. The utility lies chiefly in identifying theoretically useful discriminators among different populations and providing fairly accurate estimates for how well they should work. This approximation can furthermore be useful for narrowing down parameter ranges in a computationally economical way when events are observed. We furthermore show a distinctive way to identify events with extremely high eccentricity where the signal is enhanced relative to naive expectations on the high-frequency end.

IOP Publishing Ltd2022

Robust speech recognition based on multi-stream processing

Astrid Hagen

Despite sophisticated present day automatic speech recognition (ASR) techniques, a single recognizer is usually incapable of accounting for the varying conditions in a typical natural environment. Higher robustness to a range of noise cases can potentially be achieved by combining the results of several recognizers operating in parallel. One such approach is multi-band processing, mimicking parallel processing of frequency subbands in human speech recognition as had been claimed by Fletcher. However, recent findings in both human and automatic speech recognition have revealed insufficiencies, such as the assumption of independence between frequency subbands, of the original multi-band ASR approach which often leads to reduced performance in the case of clean speech and wide-band noise. To overcome this problem, we propose and investigate a new set of "full combination" rules which integrate acoustic models trained on all possible combinations of subbands, preserving correlation information and leading to higher performance in all noise conditions. In this development, particular attention was given to the theoretical basis for all of the rules developed in terms of statistical theory, so that the assumptions that were necessary in each model become clear. The new combination strategies are developed for both posterior- and likelihood-based systems. These new combination strategies are then also applied to the combination of diverse feature streams, for example derived from multi-time scale analysis, which results in better exploitation of the often used instantaneous and time difference features. While combination may give the same weight to each expert, robustness of a multiple stream system can be further enhanced when each stream expert is assigned a weight reflecting its reliability. The new combination techniques are tested with several fixed and adaptive weighting strategies, including relative frequency of correct classification, least mean squared error, local signal-to-noise ratio, and maximum-likelihood based weights. We will see how the new multi-band approaches, which are consistently trained in clean speech, outperform original multi-band ASR models in both clean and noisy speech. Multi-band processing improves over the baseline fullband recognizer only in the case of narrow-band noise. However, combining multiple data streams from different time scales, using the same "full combination" rules, has also shown to significantly improve over the baseline in wide-band factory noise.

EPFL2002

full combination'' rules which integrate acoustic models trained on all possible combinations of subbands, preserving correlation information and leading to higher performance in all noise conditions. In this development, particular attention was given to the theoretical basis for all of the rules developed in terms of statistical theory, so that the assumptions that were necessary in each model become clear. The new combination strategies are developed for both posterior- and likelihood-based systems. These new combination strategies are then also applied to the combination of diverse feature streams, for example derived from multi-time scale analysis, which results in better exploitation of the often used instantaneous and time difference features. While combination may give the same weight to each expert, robustness of a multiple stream system can be further enhanced when each stream expert is assigned a weight reflecting its reliability. The new combination techniques are tested with several fixed and adaptive weighting strategies, including relative frequency of correct classification, least mean squared error, local signal-to-noise ratio, and maximum-likelihood based weights. We will see how the new multi-band approaches, which are consistently trained in clean speech, outperform original multi-band ASR models in both clean and noisy speech. Multi-band processing improves over the baseline fullband recognizer only in the case of narrow-band noise. However, combining multiple data streams from different time scales, using the same

full combination'' rules, has also shown to significantly improve over the baseline in wide-band factory noise.

École Polytechnique Fédérale de Lausanne2001

full combination'' rules which integrate acoustic models trained on all possible combinations of subbands, preserving correlation information and leading to higher performance in all noise conditions. In this development, particular attention was given to the theoretical basis for all of the rules developed in terms of statistical theory, so that the assumptions that were necessary in each model become clear. The new combination strategies are developed for both posterior- and likelihood-based systems. These new combination strategies are then also applied to the combination of diverse feature streams, for example derived from multi-time scale analysis, which results in better exploitation of the often used instantaneous and time difference features. While combination may give the same weight to each expert, robustness of a multiple stream system can be further enhanced when each stream expert is assigned a weight reflecting its reliability. The new combination techniques are tested with several fixed and adaptive weighting strategies, including relative frequency of correct classification, least mean squared error, local signal-to-noise ratio, and maximum-likelihood based weights. We will see how the new multi-band approaches, which are consistently trained in clean speech, outperform original multi-band ASR models in both clean and noisy speech. Multi-band processing improves over the baseline fullband recognizer only in the case of narrow-band noise. However, combining multiple data streams from different time scales, using the same

full combination'' rules, has also shown to significantly improve over the baseline in wide-band factory noise.

École Polytechnique Fédérale de Lausanne2001

Robust speech recognition based on multi-stream processing

Astrid Hagen

EPFL2002