We introduce a new member of TSP (Time Stretched Pulse) for acoustic and speech measurement infrastructure, based on a simple all-pass filter and systematic randomization. This new infrastructure fundamentally upgrades our previous measurement procedure, which enables simultaneous measurement of multiple attributes, including non-linear ones without requiring extra filtering nor post-processing. Our new proposal establishes a theoretically solid, flexible, and extensible foundation in acoustic measurement. Moreover, it is general enough to provide versatile research tools for other fields, such as biological signal analysis. We illustrate using acoustic measurements and data augmentation as representative examples among various prospective applications. We open-sourced MATLAB implementation. It consists of an interactive and real-time acoustic tool, MATLAB functions, and supporting materials.