Time–frequency analysis

In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform. The mathematical motivation for this study is that functions and their transform representation are tightly connected, and they can be understood better by studying them jointly, as a two-dimensional object, rather than separately. A simple example is that the 4-fold periodicity of the Fourier transform – and the fact that two-fold Fourier transform reverses direction – can be interpreted by conside

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Predictive Hydrology: A Frequency Analysis Approach

Anne-Catherine Favre

The unusual frequency of hydro-meteorological events in recent decades, often with catastrophic consequences for society and the environment, require new methods for designing water management projects and the structures meant to protect us from natural hazards. These methods and techniques are often based on the statistical modeling techniques of frequency analysis. Predictive Hydrology: A Frequency Analysis Approach is the first book to address both the theoretical concepts and the methodological approaches used in frequency hydrology—spelling out the fundamental methods to consider, providing concise instruction on the techniques that are involved, and including examples and critiques based on practical applications. It explores some of the recent research developments in the field. Published originally in French, this English translation targets students in civil engineering, environmental sciences and technology, hydrology, geography, geology and ecology. This book will also serve as a useful reference not only for teachers and researchers, but for engineering practitioners, who are constantly faced with the problems of handling data, but often find themselves without the appropriate analytical tools.

Science Publishers, CRC Press2012

A Robust Method to Count and Locate Audio Sources in a Multichannel Underdetermined Mixture

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We propose a method to count and estimate the mixing directions in an underdetermined multichannel mixture. The approach is based on the hypothesis that in the neighbourhood of some time-frequency points, only one source essentially contributes to the mixture: such time-frequency points can provide robust local estimates of the corresponding source direction. At the core of our contribution is a statistical model to exploit a local confidence measure which detects the timefrequency regions where such robust information is available. A clustering algorithm called DEMIX is proposed to merge the information from all time-frequency regions according to their confidence level. So as to estimate the delays of anechoic mixtures and overcome the intrinsic ambiguities of phase unwrapping as met with DUET, we propose a technique similar to GCC-PHAT which is able to estimate delays that can largely exceed one sample. We propose an extensive experimental study which shows that the resulting method is more robust in conditions where all DUET-like comparable methods fail, that is in particular: a) when time-delays largely exceed one sample; b) when the source directions are very close.

Institute of Electrical and Electronics Engineers2010

A Wideband Doubly-Sparse Approach For MITO Sparse Filter Estimation

Rémi Gribonval

We propose an approach for the estimation of sparse filters from a convolutive mixture of sources, exploiting the time-domain sparsity of the mixing filters and the sparsity of the sources in the time-frequency (TF) domain. The proposed approach is based on a wideband formulation of the cross-relation (CR) in the TF domain and on a framework including two steps: (a) a clustering step, to determine the TF points where the CR is valid; (b) a filter estimation step, to recover the set of filters associated with each source. We propose for the first time a method to blindly perform the clustering step (a) and we show that the proposed approach based on the wideband CR outperforms the narrowband approach and the GCC-PHAT approach by between 5 dB and 20 dB.

IEEE2011

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In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transfo

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The short-time Fourier transform (STFT), is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practi

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In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal,