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For any triple of positive integers (m, N, q), the matrix F (m, N, q), called the (m, N, q)-regular Fourier matrix, is defined. The regular Fourier matrices F (m, N, q) are then applied to set up new algorithms for nonuniform fast Fourier transforms. Numerical results show that the accuracies obtained by our algorithms are much better than previously reported results with the same computation complexity. The algorithms require O(N · log 2 N ) arithmetic operations, where N is the number of data points.

Abstract. We prove that any iterated function system of finite type possesses the weak separation property.

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