  The recent breakthrough in metamaterial-based optical computing devices
[Science 343, 160 (2014)] has inspired a quest for similar systems in
acoustics, performing mathematical operations on sound waves. So far, acoustic
analog computing has been demonstrated using thin planar metamaterials,
carrying out the operator of choice in Fourier domain. These so-called
filtering metasurfaces, however, are always accompanied with additional Fourier
transform sub-blocks, enlarging the computing system and preventing its
applicability in miniaturized architectures. Here, employing a simple
high-index acoustic slab waveguide, we demonstrate a highly compact and
potentially integrable acoustic computing system. The system directly performs
mathematical operation in spatial domain and is therefore free of any Fourier
bulk lens. Such compact computing system is highly promising for various
applications including high throughput image processing, ultrafast equation
solving, and real time signal processing.
