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We propose Fourier transform algorithms using QTT format for data-sparse approximate representation of one-- and multi-dimensional vectors (
By numerical experiments we demonstrate the examples of problems for which the use of QTT format relaxes the grid size constrains and allows the high-resolution computations of Fourier images and convolutions in higher dimensions without the "curse of dimensionality". We compare the proposed method with Sparse Fourier transform algorithms and show that our approach is competitive for signals with small number of randomly distributed frequencies and signals with limited bandwidth.