Application de la transformée en nombres entiers à la conception d'algorithmes de faible complexité pour l'annulation d'échos acoustiques

The principal objective of our study is to evaluate the posibility of an acoustic canceler system development in real time. To reduce the computational cost of this system, we looked further into the mathematical bases of the Number Theoretic Transform (NTT) which is meant to find more and more various applications in signal processing. We introduced more particularly the Fermat Number Transform (FNT), which, compared to the Fast Fourier Transform (FFT), allows reduction of several multiplications which are necessary to achieve certain functions such as convolution products. To highlight this transformation, we proposed and studied new algorithms for echo cancelers of low complexity, which we treated by blocks and made robust before implanting them using the FNT. The result of this implementation, compared to an implemetation by the FFT, has shown a strong reduction in the number of multiplications along with an increase in the number of classical operations. To reduce this rise, we proposed a new technique of the transform, entitled Generalized Sliding FNT (GSFNT), which consists in calculating the FNT of a succession of sequences that differ from a certain number of samples from one to another. The numerical simulations show that a GSFNT-based echo canceler helps to remedy the increase in the number of classical operations observed by FNT-based echo canceler. Finally, the implementation of algorithms for echo canceler and through a new procedure of Multi-Delay Filter (MDF) algorithm associated with the new method for the step-size adaptation coefficient, has permitted a significant reduction in the computational complexity.Le principal objectif de notre étude est d'évaluer la possibilité d'un développement en temps réel d'un système d'annulation d'écho acoustique. Pour réduire le coût de calcul de ce système, nous avons approfondi les bases mathématiques de la transformée en nombres entiers (NTT : Number Theoretic Transform) qui est amenée à trouver des applications de plus en plus diverses en traitement du signal. Nous avons introduit plus particulièrement la transformée en nombres de Fermat (FNT : Fermat Number Transform) qui permet une réduction, par rapport à la FFT (Fast Fourier Transform), des nombres de multiplications nécessaires à la réalisation de certaines fonctions telles que les produits de convolution. Pour mettre en évidence cette transformée, nous avons proposé et étudié de nouveaux algorithmes d'annulation d'écho de faible complexité que nous avons traités par blocs et rendus robustes avant de les implanter au moyen de la FNT. Le résultat de cette implantation, comparée à une implantation par la FFT, a montré une forte réduction du nombre de multiplications accompagnée d'une augmentation du nombre d'opérations classiques. Pour réduire cette augmentation, nous avons proposé une nouvelle technique de la transformée, intitulée Generalized Sliding FNT (GSFNT). Celle-ci consiste à calculer la FNT d'une succession de séquences qui diffèrent d'un certain nombre d'échantillons l'une de l'autre. Le résultat des simulations des performances de ces algorithmes d'annulation d'écho, traités au moyen de cette technique, a montré que celle-ci permet de pallier à l'augmentation du nombre d'opérations classiques observée lors d'une implantation en FNT. Enfin, l'implantation des algorithmes d'annulation d'écho en FNT et par une nouvelle procédure de l'algorithme MDF (Multi-Delay Filter ) associée à la nouvelle méthode de calcul du pas d'adaptation, a permis une réduction significative de la complexité de calcul

Fast Convolution Using Generalized Sliding Fermat Number Transform with Application to Digital Filtering

International audienceThis paper is about a new efficient method for the implementation of a Block Proportionate Normalized Least Mean Square (BPNLMS++) adaptive filter using the Fermat Number Transform (FNT). An efficient state space method for implementing the FNT over rectangular windows is used in the cases where there is a large overlap between the consecutive input signals. This is called Generalised Sliding Fermat Number Transform (GSFNT) and is useful for reducing the computational complexity of finite ring convolvers and correlators. In this contribution, we propose, as a first objective, an efficient state algorithm with the purpose of reducing the complexity of inverse FNT. This algorithm, called Inverse Generalised Sliding Fermat Number Transform (IGSFNT) uses the technique of Generalised Sliding, associated to matricial calculations in the Galois Field. The second objective is to realize an implementation of the BPNLMS++ adaptive filter using GSFNT and IGSFNT, which can significantly reduce the computation complexity of the filter implantation on digital processors

Inverse of Fermat Number Transform Using the Sliding Technique

International audienceThis paper is about a new efficient method for the implementation of convolvers and correlators using the Fermat Number Transform (FNT) and the inverse (IFNT). The latter present advantages compared to Inverse Fast Fourier Transform (IFFT). An efficient state space method for implementing the Inverse FNT (IFNT) over rectangular windows is proposed for the cases where there is a large overlap between the consecutive input signals. This is called Inverse Generalized Sliding Fermat Number Transform (IGSFNT) and is useful for reducing the computational complexity of finite ring convolvers and correlators. This algorithm uses the technique of Generalized Sliding associated to matricial calculation in the Galois Field. The computational complexity of this method is compared with that of standard IFNT

Block Robust Algorithm for Network Echo Cancellation

http://www.praiseworthyprize.com/IRECAP.htmInternational audienceThis paper is about an efficient implementation of adaptive filtering for echo cancelers. Recently a fast converging algorithm called Robust Proportionate Normalized Least Mean Squares (RPNLMS++) against double-talk has been proposed. This paper presents a realization of an improved version of the previous RPNLMS++ adaptive filter using block structure in which the filter coefficients are adjusted one per each output block. Then, an efficient implementation of the block filtering process is proposed using Number Theoretic Transforms (NTT) which can significantly reduce the computation complexity of filter implantation on Digital Signal Processor (DSP). Analyses of convergence properties, during single and double-talk, and complexity show that the new block adaptive filter permits fast implementations while maintaining performance equivalent to that of the widely used RPNLMS++ adaptive filter

Realization of Multi-Delay Filter using Fermat Number Transforms

International audienceThis paper is about an efficient implementation of adaptive filtering for echo cancelers. The first objective of this paper is to propose a simplified method of the flexible block Multi-Delay Filter (MDF) algorithm in the time-domain. Then, we will derive a new method for the step-size adaptation coefficient. The second objective is about the realization of a Block Proportionate Normalized Least Mean Squares (BPNLMS++) with the simplified MDF (SMDF) implementation. Using the new step-size method and the smaller block dimension proposed by SMDF, we achieve a faster convergence of the adaptive process with a limited computational cost. Then, an efficient implementation of the new procedure (SMDF-BPNLMS++) block filtering is proposed using Fermat Number Transform, which can significantly reduce the computation complexity of filter implantation on Digital Signal Processor

Realization of block adaptive filters using Fermat number transforms

International audienceThis paper is about an efficient implementation of adaptive filtering for echo cancelers. First, a realization of an improved Proportionate Normalized Least Mean Squares (PNLMS+ +) adaptive filter using block structure is presented. Then, an efficient implementation of the block filtering process is proposed using Number Theoretic Transforms (NTT) which can significantly reduce the computation complexity of filter implantation on Digital Signal Processor (DSP)

Realization of Block Robust Adaptive Filters using Generalized Sliding Fermat Number Transform

International audienceThis paper is about an efficient implementation of adaptive filtering for echo cancelers. First, a realization of an improved Block Proportionate Normalized Least Mean Squares (BPNLMS++) using Generalized Sliding Fermat Number Transform (GSFNT) is presented. Unfortunately, during the double-talk mode, the echo cancelers often diverge. We can cope with this problem by employing a double-talk detector formed by two Voice Activity Detectors (VAD's) . We propose a general system based on the Robust-Block-PNLMS ++ (RBPNLMS++) adaptive filter combined with a post-filter. The general system was implemented with GSFNT which can significantly reduce the computation complexity of the filter implantation on Digital Signal Processing (DSP)

Adaptively Modulated Optical OFDM Transmission using two cascaded SOAs for optical access networks

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Significantly Improved Optical OFDM Transmission Performances with 10dB Reduced Optical Input Powers by Quantum Dot SOA Intensity Modulators

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Two cascaded SOAs used as intensity modulators for adaptively modulated optical OFDM signals in optical access networks

International audienceDetailed theoretical and numerical investigations of the transmission performance of adaptively modulated optical orthogonal frequency division multiplexed (AMOOFDM) signals are undertaken, for the first time, in optical amplification and chromatic dispersion (CD) compensation free single mode fiber (SMF) intensity-modulated and directdetection (IMDD) systems using two cascaded semiconductor optical amplifiers in a counterpropagating configuration as an intensity modulator (TC-SOA-CC-IM). A theoretical model describing the characteristics ofthis configuration is developed. Extensive performance comparisons are also made between the TC-SOA-CC and the single SOA intensitymodulators. It is shown that, the TC-SOA-CC reaches its strongly saturated region using a lower input optical power much faster than the single SOAresulting in significantly reduced effective carrier lifetime and thus wide TC-SOA-CC bandwidths. It is shown that at low input optical power, wecan increase the signal line rate almost 115% which will be more than twice the transmission performance offered by single SOA. In addition, the TCSOA-CC-IM is capable of supporting signal line rates higher than corresponding to the SOA-IM by using 10dB lower input optical powers.For long transmission distance, the TC-SOA-CC-IM has much stronger CD compensation capability compared to the SOA-IM. In addition the use ofTC-SOA-CC-IM is more effective regarding the capability to benefit from the CD compensation for shorter distances starting at 60km SMF, whilst forthe SOA-IM starting at 90km