Zero-aliasing correlation filters

Abstract

Traditional correlation filters are designed and implemented via the frequency domain, where the correlation of two signals may be computed efficiently. However, when the discrete Fourier transform (DFT) of length N is used, multiplication in the frequency domain results in an N-point circular correlation, rather than a linear correlation. The resulting correlation filter output is therefore corrupted by the aliasing effects of circular correlation. One solution is to design and implement the correlation filter directly in the space domain. However, this is more computationally intense. Recent literature has discussed ways in which to minimize circular correlation effects, but the effects are not completely removed. We propose a new frequency domain method for completely eliminating circular correlation effects when designing correlation filters. We demonstrate this idea with the well-known minimum average correlation energy (MACE) filter and show how the reformulated MACE filter in the frequency domain outperforms the original formulation of the MACE filter.