On the Equivalence Between One-Dimensional Discrete Walsh-Hadamard and Multidimensional Discrete Fourier Transforms

@article{Kunz1979OnTE,
  title={On the Equivalence Between One-Dimensional Discrete Walsh-Hadamard and Multidimensional Discrete Fourier Transforms},
  author={Henry O. Kunz},
  journal={IEEE Transactions on Computers},
  year={1979},
  volume={C-28},
  pages={267-268}
}
  • Henry O. Kunz
  • Published 1 March 1979
  • Mathematics
  • IEEE Transactions on Computers
It is shown that the discrete Walsh–Hadamard transform applied to 2none-dimensional data is equivalent to the discrete n-dimensional Fourier transform applied to the same 2ndata arranged on the binary n-cube. A similar relationship is valid for the generalized discrete Walsh transform suggested by Andrews and Caspari. This relationship explains the theorem concerning the shift invariance of the power spectrum for the Walsh–Hadamard transform and its generalizations. 

Figures from this paper

A hybrid classical-quantum algorithm for solution of nonlinear ordinary differential equations

A hybrid classical-quantum approach for the solution of nonlinear ordinary di ff erential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation

Cryptography and Coding

  • M. Stam
  • Mathematics, Computer Science
    Lecture Notes in Computer Science
  • 2013
TLDR
Olympic polynomials give rise to several new constructions of infinite classes of semi-bent Boolean functions in even dimension, which are useful in constructing significant cryptographic primitives such as plateaued Boolean functions.

Spatial multiplexing using walsh-hadamard transform

This paper proposes a model (WHT-SMX), that combines spatial multiplexing (SMX) with walsh-hadamard transform (WHT). The use of WHT is to convert transmit symbols of SMX to change location of

Nonlinear cryptanalysis of reduced-round Serpent and metaheuristic search for S-box approximations

TLDR
Three variants of a new nonlinear cryptanalytic algorithm are proposed which overcomes the main issues that prevented the use of nonlinear approximations in previous research, and the statistical frameworks for calculating the complexity of each version are presented.

Filtered Nonlinear Cryptanalysis of Reduced-Round Serpent, and the Wrong-Key Randomization Hypothesis

We present a deterministic algorithm to find nonlinear S-box approximations, and a new nonlinear cryptanalytic technique; the "filtered" nonlinear attack, which achieves the lowest data complexity of

Significant Target Detection of Traffic Signs Based on Walsh-Hadamard Transform

TLDR
This method uses the Walsh-Hadamard transform and normalized image binary spectrum to detect the traffic target with significant target and can quickly and effectively detect the significant area of traffic signs compared with other algorithms in the text.

Applications of search techniques to cryptanalysis and the construction of cipher components.

TLDR
The emphasis then shifts from the construction of cryptographic artefacts to the related area of cryptanalysis, in which non-linear approximations to S-boxes more powerful than the existing linear approximation are derived and exploited in cryptanalytic attacks against the ciphers DES and Serpent.

Chapter 4 – LDPC Decoders

The Quantum Condition Space

The fundamental properties of quantum physics are exploited to evaluate event probabilities with projection measurements. Next, to study what events can be specified by quantum methods, the concept

Local Differential Privacy with K-anonymous for Frequency Estimation

TLDR
The numerical experiments demonstrate that SAnonLAP achieves better KL-divergence and estimation error compared to another known privacy model: RAPPOR.

References

SHOWING 1-8 OF 8 REFERENCES

Two-dimensional digital processing of one-dimensional signal

It is of importance to find the necessary and sufficient conditions under which the one-dimensional and two-dimensional processing of any general transform should be equivalent. These conditions are

A Generalized Technique for Spectral Analysis

TLDR
It is shown how the Kronecker product can be mathematically defined and efficiently implemented using a matrix factorization method and a generalized spectral analysis is suggested, and a variety of examples are presented displaying various properties of the decompositions possible.

Orthogonal Transforms for Digital Signal Processing

  • K. R. RaoN. Ahmed
  • Computer Science
    IEEE Transactions on Systems, Man, and Cybernetics
  • 1979
TLDR
The utility and effectiveness of these transforms are evaluated in terms of some standard performance criteria such as computational complexity, variance distribution, mean-square error, correlated rms error, rate distortion, data compression, classification error, and digital hardware realization.

B70-2 Transmission of Information by Orthogonal Functions

  • H. Andrews
  • Economics
    IEEE Transactions on Computers
  • 1970
The book provides a new and interesting approach to the field of information and communication theory and is a welcome and thought- provoking exposition on a subject too often reviewed by

Theory and Application of Digital Signal Processing

TLDR
In this well-written book, Bellman and Wing have indeed accomplished the task of introducing the simplicity of the invariant imbedding method to tackle various problems of interest to engineers, physicists, applied mathematicians, and numerical analysts.