Investigation of Frequency Invariance in Automated Event Recognition Using Resonant Atomic Media

Coherent excitation of a resonant medium yields a nonlinear response to the Fourier spectrum of the input signals. This property can be exploited to produce a 1D temporal correlator by applying two signals simultaneously, and subsequently reading out the state of the medium. This intricate process of nonlinear responses generates multiple time-delayed outputs, where we are only interested in the specific segment that pertains to the cross-correlation. To this end, the Schrödinger equation is used as a model to accurately determine the precise time code and location of the desired output. Here, we show via simulations how this may be used for 1D event recognition. By comparing a reference signal to a query signal, we can expect a prominent peak in the cross-correlation if there is a match. Such a system is inherently delay-invariant due to the properties of the Fourier transform but is not invariant to scaling in the time-domain (i.e., frequency shifting). We additionally show how frequency-shift invariant correlation can be achieved by pre-processing the input signals via the Mellin transform. This technique is tested using audio signals to achieve speech recognition, where invariance to frequency shifts means that individual phrases may be recognized independently of the voice of the speaker. This approach can be extended to three-dimensional video recognition systems for real-time event recognition. By utilizing the frequency-shift invariant technique, the system can effectively correlate videos with different time scales, making it applicable to various fields, such as surveillance and copyright plagiarism detection.