Simultaneous measurement of time-invariant linear and nonlinear, and random and extra responses using frequency domain variant of velvet noise (2008.02439v2)

Abstract: We introduce a new acoustic measurement method that can measure the linear time-invariant response, the nonlinear time-invariant response, and random and time-varying responses simultaneously. The method uses a set of orthogonal sequences made from a set of unit FVNs (Frequency domain variant of Velvet Noise), a new member of the TSP (Time Stretched Pulse). FVN has a unique feature that other TSP members do not. It is a high degree of design freedom that makes the proposed method possible without introducing extra equipment. We introduce two useful cases using two and four orthogonal sequences and illustrates their use using simulations and acoustic measurement examples. We developed an interactive and realtime acoustic analysis tool based on the proposed method. We made it available in an open-source repository. The proposed response analysis method is general and applies to other fields, such as auditory-feedback research and assessment of sound recording and coding.

• The paper introduces a novel Frequency domain variant of Velvet Noise (FVN) method for simultaneous acoustic system response measurement, extending Time Stretched Pulse techniques.
• Simulation and real-world measurements validate the FVN method's ability to successfully decompose and separate linear, nonlinear, and random system responses simultaneously.
• This research has substantial implications for theoretical exploration and practical application in acoustic measurement and analysis, including an open-source MATLAB tool for further research.

Simultaneous Measurement of Acoustic System Responses with FVNs

In the paper titled "Simultaneous measurement of time-invariant linear and nonlinear, and random and extra responses using frequency domain variant of velvet noise," the authors introduce a novel method for simultaneous acoustic measurement of system responses. This method is grounded in the use of a Frequency domain variant of Velvet Noise (FVN), expanding the capabilities of Time Stretched Pulse (TSP) techniques. The key innovation of this approach lies in the ability to measure linear time-invariant responses, nonlinear time-invariant responses, and random and time-varying responses simultaneously, without auxiliary hardware or complex post-processing.

Methodology

The authors build upon previous methods of using TSPs such as Swept-Sine and Maximum Length Sequence (MLS) for impulse response measurement. They introduce FVN as a new TSP variant characterized by a high level of design flexibility, which allows for the creation of several orthogonal sequences pivotal for the new measurement approach. By strategically designing these sequences, one can isolate and accurately measure different response components of a system.

They outline a procedure to synthesize two and four orthogonal FVN sequences. The synthesis involves periodic allocation of unit FVN across time axes, where orthogonal sequences are created through varying polarities and weights against time shifts, enabling the extraction of distinct system response characteristics. The authors further detail an orthogonalization process, critical for cancelling out noise-like cross-correlation between different FVN sequences, enhancing measurement fidelity.

Numerical Results

The paper provides both simulation and real-world measurement results to validate the efficacy of the proposed method. Through simulation, they showcase the successful decomposition and power spectrum separation of responses from simulated loudspeakers, including linear, nonlinear, and random components. Real-world acoustic measurements further demonstrate the capability of this approach in practical scenarios, illustrating potential deviations at higher sound pressure levels typically not captured by conventional techniques.

Implications and Future Insights

The implications of this research are substantial, both for theoretical exploration and practical applications. In theoretical terms, this work provides a robust foundation for further exploration into decomposing and understanding system responses in noisy and complex environments. From a practical standpoint, it promises enhancements in acoustic measurement and analysis of various systems, ranging from loudspeakers to broader applications in auditory feedback research and digital audio signal processing.

Furthermore, the authors offer an open-source interactive and real-time tool implemented in MATLAB, encouraging further experimentation and validation by the research community. With access to these tools, researchers can explore the broader applications of these measurement techniques across diverse fields, potentially paving the way for improved signal processing methods and audio system designs in the future.

The paper presents a compelling case for the adoption of FVN-based methods in system analysis and highlights the potential for further advancements through continued research and development. Despite its strengths, areas for optimization such as the design of unit FVNs and exploring additional orthogonal sequence designs are acknowledged, suggesting avenues for future investigation.