Multi-Channel System Identification
High quality videoconferencing systems or multi-media applications increasingly require multi-channel signal processing. Knowledge about the nature of these channels is needed for the research, design, and development of relevant algorithms.
Owing to its simplicity and generality, an approach based on the least mean square algorithm (LMS) with a special excitation signal [Antweiler 2008] has been used routinely for a couple of years. This technique has a wide range of possible applications in mobile communications, acoustics, digital speech processing, and in the medical community, especially for the identification and tracking of time-variant linear systems. Two example are the dynamic sonotubometric assessment of the Eustachian tube function for ontological diagnostics (see more details) or the acquisition of continuous-azimuth head-related impulse responses (HRIRs).
Head-related transfer functions (HRTFs) or in the time domain head-related impulse responses (HRIRs), respectively, are usually obtained from measurements on human subjects or dummy heads taken from systematic measurements over a discrete set of angles, at discrete frequencies and time instants. To produce a realistic illusion of moving sound sources and changes in listener position with real-time virtual auditory spaces, a very dense grid of HRIRs is required. Typically, practical systems interpolate the necessary functions between measured HRIRs.
In [Enzner 2008] an alternative concept has been proposed which is based on a rotating, dynamical measurement setup. The quasi-continuous HRIR acquisition at any azimuth was treated as a time-varying system identification problem on the basis of dynamical measurements. As the system identification is handled by LMS-type adaptive filters, we have the freedom to choose the excitation signal in this application.
In [Antweiler 1995], [Antweiler 2008] it has been shown that so called perfect sequences represent a favorable stimulus signal for this application. Perfect sequences guarantee a rapid convergence speed as they represent — due to their specific correlation properties — the optimal excitation signal of the LMS-algorithm. These characteristics can be exploited also for the acquisition of continuous-azimuth HRIRs [Antweiler 2009], [Antweiler 20011], [Antweiler 2012], [Enzner 2013]. Mainly two different types of perfect sequences have been accomplished in previous work, the perfect sweeps and the odd-perfect sequences. To enable easy access to perfect sequences, the software we use to generate them, is published here as open source under a BSD-style license.
With an appropriate choice of the system components, such as rotational speed, sampling rate and filter length, algorithms of this kind are capable to continuously track the dynamic changes and to provide in each time instant with the identified filter coefficients a relevant reconstruction of the actual HRIRs. As a result, HRIRs are obtained at quasi all angular positions along the horizontal plane (with respect to the sampling rate) avoiding the need of interpolation. The low effort for the actual measurement procedure in combination with the resulting high resolution and quality of these HRIRs makes this approach especially attractive for binaural rendering systems.
Binaural Rendering Engine
As an example of successful usage of continuous HRIR measurements, we implemented a binaural rendering engine for multiple moving sound sources. With this real-time demonstrator six rotating audio objects (singer, guitar, etc.) and a stereo virtual-loudspeaker arrangement can be rendered. The demonstrator is based on RTProc, a rapid real-time prototyping system for audio signal processing [Krüger 2009], and a sampled version of continuous-HRIR data in combination with simple and uncritical cross-fading techniques.
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