Slices of N dimensions can be extracted from bandlimited data sets of M dimensions. N is any arbitrary value less than N. A value of a slice is defined by an evaluation of an integral of the bandlimited data set weighted by a filter scaling function orientated along the normal of the slice. Due to the properties of the bandlimited data set, the slice is bandlimited in N dimensions as well. The filter scaling function diminishes at substantially the same rate as the aliasing frequency of the bandlimited data set in the normal direction. The convolution of a scaling basis function used to construct the bandlimited data with itself defines the filter scaling function. A scaling basis function widened in the direction of the normal can approximate the filter scaling function in some cases. Quadrature can approximate the value of the integral. Slices may or may not be axis aligned.