Fast computation of the target signal phase in noisy environments

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Abstract

This paper proposes a fast Fourier transform (FFT) based algorithm to compute the desired signal phase in noisy environments for implementing adaptive directionality of dual microphone application systems such as wireless communications, etc. We will show theoretically and by simulation results that the proposed scheme can compute effectively the target signal phase and can further provide an effective reduction of the noise that comes in different direction from the one of the target signal. We will also discuss in more details this proposed scheme from the practical application and real-time implementation points of view. In comparison with other available methods, the proposed scheme has the following advantages: (1) a simple and realizable implementation structure; (2) the elimination of an additional delay processing unit for endfire orientation microphones; (3) an effective solution of microphone mismatch problem and (4) the elimination of the assumption that the target signal must be exactly straight ahead. With these features, this proposed scheme could provide a new tool to compute the target signal phase and to implement adaptive directionality in related application fields.

Introduction

Using the spatial (phase) difference between the target signal and the noise, a system can achieve the goal of noise reduction and enhance the target signal. Such a system usually consists of multi-microphones and is called beamforming system or directional system. If the noise source is moving or time varying, the adaptive directionality of such system is highly desirable so that the system could track the moving or varying noise source, otherwise, the noise reduction performance of such a system will greatly degrade. There have been a lot of available algorithms to deal with adaptive directionality so as to achieve a good compromise between the complexity and performance [1], [2], [4], [6], [7], [8]. In addition, the noise reduction performance of the beamforming system greatly depends on the number of microphones and distance of these microphones. However, in some application fields such as hearing devices, the number of microphones and distance of microphones is strictly limited. For example, behind-the-ear hearing aids can usually have only two microphones and the distance of these two microphones are about 10 mm. In these cases, most available algorithms will deliver a degraded noise reduction performance. Moreover, it would be very difficult to implement in real-time these available algorithms in these application fields mainly because of the limit of hardware size, computation speed, mismatch of microphones, power supply and other practical factors.

Based on these problems, this paper proposes an FFT based algorithm to compute the target signal phase and to implement adaptive directionality for those applications where only two microphones are available. We will show theoretically and by simulation results that the proposed scheme can reduce effectively and adaptively the noise that comes from in different direction from the one of the desired signal. We will also discuss the hardware implementation of this proposed scheme and other related practical factors. Because this proposed method needs only two FFTs and one IFFT, a simple implementation structure can be obtained and can be realizable in real-time.

The rest of this paper is organized as follows. Section 2 will present the proposed algorithm and related theoretical analysis. In Section 3, we will deal with this algorithm in more details from practical application and implementation points of view. Section 4 will present some simulation results.

Section snippets

Proposed algorithm and analysis

For a dual-microphone system, let us denote the received signals at one microphone and the other microphone as X(n) and Y(n), their DFTs as X(ω) and Y(ω), respectively. It will be proven that either of the following two processing methods can provide approximately the noise free signal under certain conditions.Z(ω)=X(ω)-X(ω)Y(ω)X(ω),orZ(ω)=Y(ω)-Y(ω)X(ω)Y(ω),where Z(ω) is the DFT of the system output Z(n). The conditions mainly include:

  • 1.

    The magnitude responses of two microphones should be

Further discussions

Concerning this proposed scheme, we will make the following discussions.

(1) From Algorithms (1), (2), we can know that this scheme can be implemented by performing two FFTs (on the basis of frame by fame) and one IFFT with the size of the frame such as 64, 128, etc. The size of the frame will be determined by the application situations. Also, for the purpose of reducing the time aliasing problem and its artifacts, windowing processing and frame overlap are required. As a matter of fact, at

Simulation results

We have simulated the proposed scheme. Four sets of simulation results are given in this paper. The first curve to the fourth curve in Fig. 1, Fig. 2 are the desired signal, the noise, the signal plus noise and the processed result corresponding to Eq. (1), respectively. The first curve to the fourth curve in Fig. 3, Fig. 4 are the desired signal, the noise, the signal plus noise and the processed result corresponding to Eq. (2), respectively. It is obvious to see that the implemented scheme

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