ARLA/CLUSTER: MIT aumenta o processamento do Algoritmo FFT

[Pedro Ribeiro]

Boa tarde,

A tradução que fez não me parece completamente clara.

Na pratica a inovação introduzida é mais no sentido contrário, de 
necessitar de menos processamento para realizar a mesma tarefa ou de sob 
o ponto de vista inverso encurtar o tempo necessário à operação, 
permitindo mais operações por segundo para o mesmo hardware base.

Creio ter sido este o ponto de vista que quis colocar na tradução, mas 
não ficou muito explicito, trabalhinhos de hora de almoço ...

73!

On 20-01-2012 12:49, João Gonçalves Costa wrote:
>
> The faster-than-fast Fourier transform
>
> MIT researchers have found a way to increase the speed of one of the 
> most important algorithms in signal processing the fast Fourier 
> transform (FFT).
>
> It's a method for representing an irregular signal as a combination of 
> pure frequencies. It's universal in signal processing, but it can also 
> be used to compress image and audio files, solve differential 
> equations and price stock options, among other things.
>
> Ever since the FFT was proposed in the mid-1960's people have wondered 
> whether an even faster algorithm could be found.
>
> At the Association for Computing Machinery's Symposium on Discrete 
> Algorithms (SODA) this week, a group of MIT researchers will present a 
> new algorithm that, in a large range of practically important cases, 
> improves on the fast Fourier transform. Under some circumstances, the 
> improvement can be dramatic --- a tenfold increase in speed. The new 
> algorithm could be particularly useful for image compression, 
> enabling, say, smartphones to wirelessly transmit large video files 
> without draining their batteries or consuming their monthly bandwidth 
> allotments.
>
> The new algorithm --- which associate professor Katabi and professor 
> Piotr Indyk, both of MIT's Computer Science and Artificial 
> Intelligence Laboratory (CSAIL), developed together with their 
> students Eric Price and Haitham Hassanieh --- relies on two key ideas. 
> The first is to divide a signal into narrower slices of bandwidth, 
> sized so that a slice will generally contain only one frequency with a 
> heavy weight.
>
> In signal processing, the basic tool for isolating particular 
> frequencies is a filter. But filters tend to have blurry boundaries:
>
> One range of frequencies will pass through the filter more or less 
> intact; frequencies just outside that range will be somewhat 
> attenuated; frequencies outside that range will be attenuated still 
> more; and so on, until you reach the frequencies that are filtered out 
> almost perfectly.
>
> If it so happens that the one frequency with a heavy weight is at the 
> edge of the filter, however, it could end up so attenuated that it 
> can't be identified. So the researchers' first contribution was to 
> find a computationally efficient way to combine filters so that they 
> overlap, ensuring that no frequencies inside the target range will be 
> unduly attenuated, but that the boundaries between slices of spectrum 
> are still fairly sharp.
>
> Once they've isolated a slice of spectrum, however, the researchers 
> still have to identify the most heavily weighted frequency in that 
> slice. In the SODA paper, they do this by repeatedly cutting the slice 
> of spectrum into smaller pieces and keeping only those in which most 
> of the signal power is concentrated. But in the paper 'Nearly Optimal 
> Sparse Fourier Transform', they describe a much more efficient 
> technique, which borrows a signal-processing strategy from 4G cellular 
> networks. Frequencies are generally represented as up-and-down 
> squiggles, but they can also be though of as oscillations; by sampling 
> the same slice of bandwidth at different times, the researchers can 
> determine where the dominant frequency is in its oscillatory cycle.
>
> Read the full MIT press release at
>
> http://web.mit.edu/newsoffice/2012/faster-fourier-transforms-0118.html
>
> Read the paper Nearly Optimal Sparse Fourier Transform
>
> http://arxiv.org/PS_cache/arxiv/pdf/1201/1201.2501v1.pdf
>
>
>
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