On the theoretical possibility to apply an acoustic diffraction grating as a complex frequency filter device for electronic signals

In electronics, it is well known that filtering devices can be made that are able to decompose a signal instantaneously into a number of real frequency components. This procedure is equivalent to a numerical real time Fourier transform. However, it is also known that an electronic signal can be decomposed not just in real frequency components, but also in complex frequency components. The current paper shows that it is theoretically possible to create a device, made of a periodically rough surface and a system that transforms the electronic signal into acoustic waves, that can be used to measure the amplitude attributed to considered complex frequency components of an electronic signal, in real time. This 'thought device' is mainly based on the directivity of diffracted sound and the complex frequency dependence of this directivity.