Recursive Gabor filtering

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 operations. Further, the complexity is and coefficients of the recursive equation have a simple independent of the values of σ and ω in the Gabor kernel closed-form solution given σ and ω. Our implementation admits not only a forward Gabor transform from t→ω but an inverse transform from ω→t that is also O(N) complexity