Angular decompositions for the discrete fractional signal transforms
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Design of a high performance FFT processor based on FPGA
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
Journal of VLSI Signal Processing Systems
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16-point reversible integer discrete Fourier transform with 12 control bits
IEEE Transactions on Signal Processing
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Improved reversible integer-to-integer color transforms
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Quaternion multiplier inspired by the lifting implementation of plane rotations
IEEE Transactions on Circuits and Systems Part I: Regular Papers
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A concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has the properties that it is an integer-to-integer mapping, is power adaptable and is reversible. The lifting scheme is used to approximate complex multiplications appearing in the FFT lattice structures where the dynamic range of the lifting coefficients can be controlled by proper choices of lifting factorizations. Split-radix FFT is used to illustrate the approach for the case of 2N-point FFT, in which case, an upper bound of the minimal dynamic range of the internal nodes, which is required by the reversibility of the transform, is presented and confirmed by a simulation. The transform can be implemented by using only bit shifts and additions but no multiplication. A method for minimizing the number of additions required is presented. While preserving the reversibility, the IntFFT is shown experimentally to yield the same accuracy as the FxpFFT when their coefficients are quantized to a certain number of bits. Complexity of the IntFFT is shown to be much lower than that of the FxpFFT in terms of the numbers of additions and shifts. Finally, they are applied to noise reduction applications, where the IntFFT provides significantly improvement over the FxpFFT at low power and maintains similar results at high power