Fast Convolution Algorithms

Nussbaumer, Henri J.

doi:10.1007/978-3-642-81897-4_3

Cited by 45 publications

(59 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Obviously, Yn,,k is equal to Y,,,k2 since k can be taken modulo N2 in this case (see (12) and (15)). Thus, we rewrite (16) as (18) n 1 =0 which can be reduced, using (12), to…”

Section: The Cooley-tukey Mappingmentioning

confidence: 99%

“…For comparison purposes, we will count the number of real operations that are required, provided that the multiplication of a complex number x by W~ is done using 3 real multiplications and 3 real additions [12]. …”

Section: Radix-2 and Radix-4 Algorithmsmentioning

confidence: 99%

“…Actually, a detailed operation count using the simplifications indicated above gives the following result [12]:…”

Section: Radix-2 and Radix-4 Algorithmsmentioning

confidence: 99%

“…This limits the degree of the polynomials whose products can be computed by this method. Other suboptimal methods exist [ 12], but are nevertheless based on the same kind of approach (the 'dot products' (50) become polynomial products of lower degree, but the overall structure remains identical).…”

Section: X~(z) = X'~(z) Wq(2)mentioning

confidence: 99%

“…Note that the number of additions in the WFTA was reduced later by Nussbaumer with a scheme called 'split nesting' [12], leading to the algorithm with the least known number of operations (multiplications + additions). [38] PFA and WFTA are seen to be both described by the following equation: Nevertheless, these are not the only ways of obtaining X: C and B can be factorized as two matrices each, to fully describe the way the algorithms are implemented.…”

Section: P Duhamel M Vetterli / a Tutorial On Fast Fourier Transformsmentioning

confidence: 99%

See 4 more Smart Citations

Fast fourier transforms: A tutorial review and a state of the art

Duhamel¹,

1990

View full text Add to dashboard Cite

Rrsum4. La publication de l'algorithme de Cooley-Tukey pour la transformation de Fourier rapide a ouvert une nouvelle ~re dans le traitement num6rique des signaux, en r4duisant l'ordre de complexit6 de probl~mes cruciaux, comme la transformation de Fourier ou la convolution, de N 2 ~ N log2 N (oh N est la taille du probl~me). Le drvelopment des algorithmes principaux (Cooley-Tukey, split-radix FFT, algorithmes des facteurs premiers, et transform6e rapide de Winograd) est drcrit. Ensuite, l'&at de l'art est donn4, et on parle des probl~mes ouverts et des implantations.

show abstract

“…Obviously, Yn,,k is equal to Y,,,k2 since k can be taken modulo N2 in this case (see (12) and (15)). Thus, we rewrite (16) as (18) n 1 =0 which can be reduced, using (12), to…”

Section: The Cooley-tukey Mappingmentioning

confidence: 99%

Section: Radix-2 and Radix-4 Algorithmsmentioning

confidence: 99%

“…Actually, a detailed operation count using the simplifications indicated above gives the following result [12]:…”

Section: Radix-2 and Radix-4 Algorithmsmentioning

confidence: 99%

Section: X~(z) = X'~(z) Wq(2)mentioning

confidence: 99%

Section: P Duhamel M Vetterli / a Tutorial On Fast Fourier Transformsmentioning

confidence: 99%

See 3 more Smart Citations

Fast fourier transforms: A tutorial review and a state of the art

Duhamel¹,

1990

View full text Add to dashboard Cite

show abstract

A new superfast bit reversal algorithm

Rubio

Gómez-Vilda

Drouiche

2002

Adaptive Control & Signal

View full text Add to dashboard Cite

In this paper we present a new bit reversal algorithm which outperforms the existing ones. The bit reversal technique is involved in the fast Fourier transform technique (FFT), which is widely used in computerbased numerical techniques for solving numerous problems. The new approach for computing the bit reversal is based upon a pseudo-semi-group homomorphism property. The surprise is that this property is almost trivial to prove but at the same time it also leads to a very efficient algorithm which we believe to be the best with only OðN Þ operations and optimal constant, i.e. unity.

show abstract

A Miniaturized, Battery‐Free, Wireless Wound Monitor That Predicts Wound Closure Rate Early

Garland,

Song,

et al. 2023

Adv Healthcare Materials

View full text Add to dashboard Cite

Diabetic foot ulcers are chronic wounds that affect millions and increase the risk of amputation and mortality, highlighting the critical need for their early detection. Recent demonstrations of wearable sensors enable real‐time wound assessment, but they rely on bulky electronics, making them difficult to interface with wounds. Herein, a miniaturized, wireless, battery‐free wound monitor that measures lactate in real‐time and seamlessly integrates with bandages for conformal attachment to the wound bed is introduced. Lactate is selected due to its multifaceted role in initiating healing. Studies in healthy and diabetic mice reveal distinct lactate profiles for normal and impaired healing wounds. A mathematical model based on the sensor data predicts wound closure rate within the first 3 days post‐injury with ≈76% accuracy, which increases to ≈83% when pH is included. These studies underscore the significance of monitoring biomarkers during the inflammation phase, which can offer several benefits, including short‐term use of wound monitors and their easy removal, resulting in lower risks of injury and infection at the wound site. Improvements in prediction accuracy can be achieved by designing mathematical models that build on multiple wound parameters such as pro‐inflammatory and metabolic markers. Achieving this goal will require designing multi‐analyte wound monitors.

show abstract

Fast Convolution Algorithms

Cited by 45 publications

References 1 publication

Fast fourier transforms: A tutorial review and a state of the art

Fast fourier transforms: A tutorial review and a state of the art

A new superfast bit reversal algorithm

A Miniaturized, Battery‐Free, Wireless Wound Monitor That Predicts Wound Closure Rate Early

Contact Info

Product

Resources

About