Abstract
In this paper we present a recursive algorithm for the Gabor filter that achieves-to within a multiplicative constant-the fastest possible implementation. For a signal consisting of N samples, our implementation requires O(N) multiply-and-add (MADD) operations. Further, the complexity is independent of the values of ? and ? in the Gabor kernel and coefficients of the recursive equation have a simple, closed-form solution given ? and ?. Our implementation admits not only a forward Gabor transform from t ? ? but an inverse transform from ? ? t that is also O(N) complexity.