Spectral filtering using the fast Walsh transform

Zarowski, C.J.; Yunik, M.

doi:10.1109/tassp.1985.1164689

Cited by 21 publications

(5 citation statements)

References 7 publications

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“…Where W W W 2N is the symmetric matrix that applies a 2N -DWT. Since χ χ χ j is circulant, it has been shown in [30] that X X X j is diagonal by part and antisymmetric. The structure of X X X j is shown in Fig.…”

Section: B the Walsh Block Lms (Wlms)mentioning

confidence: 99%

A Block-Based LMS Using the Walsh Transform for Digital Predistortion of Power Amplifiers

Fellmann

Rivet

Deltimple

et al. 2023

IEEE Trans. Commun.

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A novel non-linear adaptive filter for the linearization of Radio Frequency (RF) Power Amplifiers (PAs) is presented. In this study, we aim at reducing the Digital Predistortion (DPD) complexity and enhancing its convergence speed for reduced computation time. The Walsh Transform is used as a computational basis for evaluating a predistorter (PD) model. The mathematical properties of the Walsh theory are exploited to adapt a memory polynomial (MP) in the sequency domain. A block-based Walsh LMS is introduced to seek the optimal PD coefficients. Simulations and results of linearization of class-AB PAs are exhibited. The comparison with conventional DPD algorithms shows that the proposed method converges 10 times faster with a reduction of 12% of the complexity for similar accuracy. Finally, a complete DPD architecture based on the Walsh Transform is proposed.

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Section: B the Walsh Block Lms (Wlms)mentioning

confidence: 99%

A Block-Based LMS Using the Walsh Transform for Digital Predistortion of Power Amplifiers

Fellmann

Rivet

Deltimple

et al. 2023

IEEE Trans. Commun.

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“…sequences have also been built [78]. analysis and synthesis, sequency filtering, multiplexing and, encoding and decoding [51], [64], [69], [78] and [120].…”

Section: Example Villamentioning

confidence: 99%

“…These general properties of Walsh and related orthogonal transforms have made them of interest to scientists in many fields: image processing [56], [77], [82], [117] and [118], signal coding [24], [64], [69] and [88], filter design [120], imaging in spectroscopy and astronomy [116] and [117]- [119], telecommunication [24] and [69], statistical analysis [76J, digital control systems [115], associative memory systems [121], and many other areas.…”

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confidence: 99%

Spectral Methods for Boolean and Multiple-Valued Input Logic Functions

Falkowski¹

2000

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Spectral techniques in digital logic design have been known for more than thirty years. They have been used for Boolean function classification, disjoint decomposition, parallel and serial linear decomposition, spectral translation synthesis (extraction of 2 linear pre-and post-filters), multiplexer synthesis, prime implicant extraction by spectral summation, threshold logic synthesis, estimation of logic complexity, testing, and state assignment.This dissertation resolves many important issues concerning the efficient application of spectral methods used in the computer-aided design of digital circuits. The main obstacles in these applications were, up to now, memory requirements for computer systems and lack of the possibility of calculating spectra direcdy from Boolean equations.By using the algorithms presented here these obstacles have been overcome. Moreover, the methods presented in this dissertation can be regarded as representatives of a whole family of methods and the approach presented can 1Y: easily adapted to other orthogonal transforms used in digital logic design. Algorithms are shown for Adding, Arithmetic, and Reed-Muller transforms. However, the main focus of this dissertation is on the efficient computer calculation of Rademacher-Walsh spectra of Boolean functions, since this particular ordering of Walsh transforms is most frequendy used in digital logic design.A theory has been developed to calculate the Rademacher-Walsh transform from a cube array specification of incompletely specified Boolean functions. The importance of representing Boolean functions as arrays of disjoint ON-and DC-cubes has been pointed out, and an efficient new algorithm to generate disjoint cubes from non-disjoint ones has been designed. The transform algorithm makes use of the properties of an array of disjoint cubes and allows the determination of the spectral coefficients in an independent way. By such an approach each spectral coefficient can be calculated separately or all the coefficients can be calculated in parallel. These advantages are absent in the existing methods. The possibility of calculating only some coefficients is very important since there are many spectral methods in digital logic design for which the values of only a few selected coefficients are needed.Most of the current methods used in the spectral domain deal only with completely specified Boolean functions. On the other hand, all of the algorithms introduced here are valid, not only for completely specified Boolean functions, but for functions with don't cares. Don't care minterms are simply represented in the form of disjoint cubes.The links between spectral and classical methods used for designing digital cir- A new algorithm is shown that converts the disjoint cube representation of Boolean functions into fixed-polarity Generalized Reed-Muller Expansions (GRME).Since the known fast algorithm that generates the GR..\1E, based on the factorization of 4 the Reed-Muller transform matrix, always starts from the truth table (mintenns) of a Boole...

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“…First, two-stage factorization of DFT where the preprocess is the Walsh-Hadamard Transform (WHT) was given in [18,19]. However, in that approach the postprocess does not consist of circular correlations, and there is no simple way to compute them.…”

Section: Computational Complexitymentioning

confidence: 99%

A novel correlation‐based FFT algorithm

Chin

1992

Journal of the Chinese Institute of Engineers

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Since the discovery of the fast Fourier transform (FFT), many new FFT algorithms have been developed. Conventionally, the convolution-based approach deals commonly with the prime length discrete Fourier transforms. In this paper, based on some theorems of Number Theory, a new algorithm for computing the FFT (with power of two length) is proposed. This novel recursive algorithm contains three stages, the first and the last stages contian only additions and substractions, and the second stage is of block diagonal form, with each block being a circular correlation/convolution matrix.The newly proposed convolution-based FFT algorithm has the following advantages:(1) In terms of computational counts, this algorithm can achieve the multiplicative lower bound derived by Winograd.(2) The proposed algorithm can easily be implemented in a parallel computing environment. (3) The proposed algorithm is recursive in nature, and thus the computation structure is rather regular.

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Spectral filtering using the fast Walsh transform

Cited by 21 publications

References 7 publications

A Block-Based LMS Using the Walsh Transform for Digital Predistortion of Power Amplifiers

A Block-Based LMS Using the Walsh Transform for Digital Predistortion of Power Amplifiers

Spectral Methods for Boolean and Multiple-Valued Input Logic Functions

A novel correlation‐based FFT algorithm

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