Error bound for multi-stage synthesis of narrow bandwidth Gabor filters

This paper develops an error bound for narrow bandwidth Gabor filters synthesized using multiple stages. It is shown that the error introduced by approximating narrow bandwidth Gabor (1946) kernels by a weighted sum of spatially offset, separable kernels is a function of the frequency offset and the reduction in bandwidth of the desired kernel compared to the basis values, as well as the spatial subsampling rate between filter stages. This error bound should prove useful in the design of a general basis filter set for multi-stage filtering because the maximum frequency offset is largely determined by the spacing of the basis filters.