Sebastian J. Schlecht

Time-varying feedback matrices in feedback delay networks and their application in artificial reverberation

This paper introduces a time-variant reverberation algorithm as an extension of the feedback delay network (FDN). By modulating the feedback matrix nearly continuously over time, a complex pattern of concurrent amplitude modulations of the feedback paths evolves. Due to its complexity, the modulation produces less likely perceivable artifacts and the time-variation helps to increase the liveliness of the reverberation tail. A listening test, which has been conducted, confirms that the perceived quality of the reverberation tail can be enhanced by the feedback matrix modulation. In contrast to the prior art time-varying allpass FDNs, it is shown that unitary feedback matrix modulation is guaranteed to be stable. Analytical constraints on the pole locations of the FDN help to describe the modulation effect in depth. Further, techniques and conditions for continuous feedback matrix modulation are presented.

Feedback Delay Networks: Echo Density and Mixing Time

Feedback delay networks (FDNs) are frequently used to generate artificial reverberation. This paper discusses the temporal features of impulse responses produced by FDNs, i.e., the number of echoes per time unit and its evolution over time. This so-called echo density is related to known measures of mixing time and their psychoacoustic correlates such as auditive perception of the room size. It is shown that the echo density of FDNs follows a polynomial function, whereby the polynomial coefficients can be derived from the lengths of the delays for which an explicit method is given. The mixing time of impulse responses can be predicted from the echo density, and conversely, a desired mixing time can be achieved by a derived mean delay length. A Monte Carlo simulation confirms the accuracy of the derived relation of mixing time and delay lengths.

On Lossless Feedback Delay Networks

Lossless Feedback Delay Networks (FDNs) are commonly used as a design prototype for artificial reverberation algorithms. The lossless property is dependent on the feedback matrix, which connects the output of a set of delays to their inputs, and the lengths of the delays. Both, unitary and triangular feedback matrices are known to constitute lossless FDNs, however, the most general class of lossless feedback matrices has not been identified. In this contribution, it is shown that the FDN is lossless for any set of delays, if all irreducible components of the feedback matrix are diagonally similar to a unitary matrix. The necessity of the generalized class of feedback matrices is demonstrated by examples of FDN designs proposed in literature.

Reverberation enhancement from a feedback delay network perspective

In reverberation enhancement systems (RESs), sound is constantly fed back from multiple microphones to multiple loudspeakers to enhance reverberation artificially in the target room. This contribution shows that such a system can be understood as an extended feedback delay network (FDN). A tuning process, similar to that of the FDN is presented, allowing arbitrary frequency-dependent reverberation elongation. The cross-talk between the loudspeakers and the microphones leads to comb filtering and isolated ringing modes in the RES, which produce undesired metallic and rough sounds. To mitigate these undesired effects, a cross-talk cancellation system is integrated in the RES. In a simulation example, the benefits of cross-talk cancellation is evaluated.

Self-translation induced minimum audible angle

The minimum audible angle has been studied with a stationary listener and a stationary or a moving sound source. The study at hand focuses on a scenario where the angle is induced by listener self-translation in relation to a stationary sound source. First, the classic stationary listener minimum audible angle experiment is replicated using a headphone-based reproduction system. This experiment confirms that the reproduction system is able to produce a localization cue resolution comparable to loudspeaker reproduction. Next, the self-translation minimum audible angle is shown to be 3.3° in the horizontal plane in front of the listener.

The stability of multichannel sound systems with time-varying mixing matrices

Various time-varying algorithms have been applied in multichannel sound systems to improve the systems stability and, among these, frequency shifting has been demonstrated to reach the maximum stability improvement achievable by time-variation in general. However, the modulation artifacts have been found to diminish the gain improvement unusable for a higher number of channels and high-quality applications such as music reproduction. This paper proposes alternatively time-varying mixing matrices, which is an efficient algorithm corresponding to symmetric up and down frequency shifting. It is shown with a statistical approach that time-varying mixing matrices can as well achieve maximum stability improvement for a higher number of channels. A listening test demonstrates the improved quality of time-varying mixing matrices over frequency shifting.