512 research outputs found
Generic Feasibility of Perfect Reconstruction with Short FIR Filters in Multi-channel Systems
We study the feasibility of short finite impulse response (FIR) synthesis for
perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis
banks, we focus on the one with the minimum filter length. For filter banks
with oversampling factors of at least two, we provide prescriptions for the
shortest filter length of the synthesis bank that would guarantee PR almost
surely. The prescribed length is as short or shorter than the analysis filters
and has an approximate inverse relationship with the oversampling factor. Our
results are in form of necessary and sufficient statements that hold
generically, hence only fail for elaborately-designed nongeneric examples. We
provide extensive numerical verification of the theoretical results and
demonstrate that the gap between the derived filter length prescriptions and
the true minimum is small. The results have potential applications in synthesis
FB design problems, where the analysis bank is given, and for analysis of
fundamental limitations in blind signals reconstruction from data collected by
unknown subsampled multi-channel systems.Comment: Manuscript submitted to IEEE Transactions on Signal Processin
Convolutive Blind Source Separation Methods
In this chapter, we provide an overview of existing algorithms for blind source separation of convolutive audio mixtures. We provide a taxonomy, wherein many of the existing algorithms can be organized, and we present published results from those algorithms that have been applied to real-world audio separation tasks
Blind Separation of Independent Sources from Convolutive Mixtures
International audienceThe problem of separating blindly independent sources from a convolutive mixture cannot be addressed in its widest generality without resorting to statistics of order higher than two. The core of the problem is in fact to identify the para-unitary part of the mixture, which is addressed in this paper. With this goal, a family of statistical contrast is first defined. Then it is shown that the problem reduces to a Partial Approximate Joint Diagonalization (PAJOD) of several cumulant matrices. Then, a numerical algorithm is devised, which works block-wise, and sweeps all the output pairs. Computer simulations show the good behavior of the algorithm in terms of Symbol Error Rates, even on very short data blocks
Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings
We tackle the multi-party speech recovery problem through modeling the
acoustic of the reverberant chambers. Our approach exploits structured sparsity
models to perform room modeling and speech recovery. We propose a scheme for
characterizing the room acoustic from the unknown competing speech sources
relying on localization of the early images of the speakers by sparse
approximation of the spatial spectra of the virtual sources in a free-space
model. The images are then clustered exploiting the low-rank structure of the
spectro-temporal components belonging to each source. This enables us to
identify the early support of the room impulse response function and its unique
map to the room geometry. To further tackle the ambiguity of the reflection
ratios, we propose a novel formulation of the reverberation model and estimate
the absorption coefficients through a convex optimization exploiting joint
sparsity model formulated upon spatio-spectral sparsity of concurrent speech
representation. The acoustic parameters are then incorporated for separating
individual speech signals through either structured sparse recovery or inverse
filtering the acoustic channels. The experiments conducted on real data
recordings demonstrate the effectiveness of the proposed approach for
multi-party speech recovery and recognition.Comment: 31 page
Groebner Basis Methods for Multichannel Sampling with Unknown Offsets
In multichannel sampling, several sets of sub-Nyquist sampled signal values are acquired. The offsets between the sets are unknown, and have to be resolved, just like the parameters of the signal itself. This problem is nonlinear in the offsets, but linear in the signal parameters. We show that when the basis functions for the signal space are related to polynomials, we can express the joint offset and signal parameter estimation as a set of polynomial equations. This is the case for example with polynomial signals or Fourier series. The unknown offsets and signal parameters can be computed exactly from such a set of polynomials using Gröbner bases and Buchbergerâs algorithm. This solution method is developed in detail after a short and tutorial overview of Gröbner basis methods. We then address the case of noisy samples, and consider the computational complexity, exploring simplifications due to the special structure of the problem
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