The Number Theoretic Hilbert Transform
نویسندگان
چکیده
منابع مشابه
The Number Theoretic Hilbert Transform
Abstract This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being zero and non-zero. Specific examples for 4point, 6-point, and 8-point NHT are provided. The NHT transformation can be used as a primitive to create cry...
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This paper presents an approach for the development of a number theoretic discrete Hilbert transform. The forward transformation has been applied by taking the odd reciprocals that occur in the DHT matrix with respect to a power of 2. Specifically, the expression for a 16-point transform is provided and results of a few representative signals are provided. The inverse transform is the inverse o...
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This paper presents new results in the theory of number theoretic Hilbert (NHT) transforms. New polymorphic solutions have been found for the 14-point and 16-point transforms. Several transform pairs are computed and solutions found for which the sequence and the transform have the same shape. The multiplicity of solutions for the same moduli increases their applicability to cryptography.
متن کاملRandom Residue Sequences and the Number Theoretic Hilbert Transform
This paper presents random residue sequences derived from the number theoretic Hilbert (NHT) transform and their correlation properties. The autocorrelation of a NHT derived sequence is zero for all non-zero shifts which illustrates that these are self-orthogonal sequences. The cross correlation function between two sequences may be computed with respect to the moduli of the either sequence. Th...
متن کاملThe 10-point and 12-point Number Theoretic Hilbert Transform
This paper presents 10-point and 12-point versions of the recently introduced number theoretic Hilbert (NHT) transforms. Such transforms have applications in signal processing and scrambling. Polymorphic solutions with respect to different moduli for each of the two cases have been found. The multiplicity of solutions for the same moduli increases their applicability to cryptography.
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ژورنال
عنوان ژورنال: Circuits, Systems, and Signal Processing
سال: 2014
ISSN: 0278-081X,1531-5878
DOI: 10.1007/s00034-014-9759-8