The Arithmetic Fourier Transform (AFT): Iterative Computation and Image Processing Applications,
RHODE ISLAND UNIV KINGSTON DEPT OF ELECTRICAL ENGINEERING
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A Fourier analysis method using an iterative Arithmetic Fourier Transform AFT is presented. It overcomes the difficulty of dense, Farey-fraction sampling which is inherent in the original AFT algorithm. This disadvantage of the AFT is turned into an advantage and dense frequency-domain samples are obtained without any additional interpolation or zero-padding. The implementation of the iterative computations is designed to preserve the advantage of the AFT for VLSI implementation by using a permuted difference coefficient structure. This iterative AFT is intended for cases in which a the function to be analyzed can only be sampled uniformly and at a rate close to the Nyquist rate or b dense frequency-domain samples are needed. The one and two dimensional versions of the discrete cosine transform 1-D DCT and 2-D DCT can be simply computed using the 1-D and 2-D AFT, but dense, Farey-fraction sampling in the image domain is then required. And it also requires special computations for the marginal DCT values. These difficulties can be overcome by the iterative 1-D or 2-D AFT. Dense samples then occur in the transform domain where they can be advantageously used for parameter estimation or the determination of a few principal components.
- Numerical Mathematics