Direction-Sensitive Fast Measurement of Sub-Sampling-Period Delays

Estimation of the delay between two signals has physical significance in synchronisation problems in, e.g. telecommunications, measurement of motion and vibration, and image registration. Low complexity algorithms can be performed extremely quickly even on limited hardware, and have improved energy consumption over more complex algorithms. We present a partial Fourier analysis of a previously reported algorithm to estimate the magnitude of the delay; the algorithm is the sum of absolute differences. The analysis offers insight into why the algorithm requires the absolute value operation. The algorithm is insensitive to direction of the delay, but the same analysis demonstrates that new approaches are possible to find the signed magnitude of the delay. Arising from that analysis, we propose one such algorithm, and demonstrate its efficacy in simulation, along with its robustness to additive and quantization noise. Our algorithm could be useful in a very wide range of applications, including image stitching, measurement of vibrations in buildings, and synchronisation problems in telecommunications.