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Analysis of Acoustic Feedback/Echo Cancellation in Multiple-Microphone and Single-Loudspeaker Systems Using a Power Transfer Function Method

機(jī)譯:功率傳遞函數(shù)法分析多麥克風(fēng)和單揚(yáng)聲器系統(tǒng)中的聲學(xué)反饋/回聲消除

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摘要

In this work, we analyze a general multiple-microphone and single-loudspeaker audio processing system, where a multichannel adaptive system is used to cancel the effect of acoustic feedback/echo, and a beamformer processes the feedback/echo canceled signals. We introduce and derive an accurate approximation of a frequency domain measure—the power transfer function—and show how it can be used to predict the convergence rate, system stability bound and the steady-state behavior of the entire cancellation system across frequency and time. We consider three example adaptive algorithms in the cancellation system: the least mean square, normalized least mean square, and the recursive least squares algorithms. Furthermore, we derive expressions to determine the step size parameter in the adaptive algorithms to achieve a desired system behavior, e.g., convergence rate at a specific frequency. Finally, we compare and discuss the performance of all three adaptive algorithms, and we verify the derived expressions through simulation experiments.
機(jī)譯:在這項(xiàng)工作中,我們分析了通用的多麥克風(fēng)和單揚(yáng)聲器音頻處理系統(tǒng),其中多通道自適應(yīng)系統(tǒng)用于消除聲學(xué)反饋/回聲的影響,而波束形成器則處理反饋/回聲消除的信號(hào)。我們介紹并推導(dǎo)了頻域測度(功率傳遞函數(shù))的精確近似值,并展示了如何將其用于預(yù)測整個(gè)消除系統(tǒng)在頻率和時(shí)間范圍內(nèi)的收斂速度,系統(tǒng)穩(wěn)定性邊界和穩(wěn)態(tài)行為。我們考慮抵消系統(tǒng)中的三個(gè)示例自適應(yīng)算法:最小均方,歸一化最小均方和遞歸最小二乘算法。此外,我們導(dǎo)出表達(dá)式以確定自適應(yīng)算法中的步長參數(shù),以實(shí)現(xiàn)所需的系統(tǒng)行為,例如在特定頻率下的收斂速度。最后,我們比較并討論了所有三種自適應(yīng)算法的性能,并通過仿真實(shí)驗(yàn)驗(yàn)證了派生的表達(dá)式。

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