A new matrix approach to real FFTs and convolutions of length 2 k

Lundy, Thomas; Buskirk, James Van

doi:10.1007/s00607-007-0222-6

Cited by 37 publications

(26 citation statements)

References 17 publications

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“…Furthermore, we note also that the existing theory may be modified to handle lossy systems (nonsymplectic ABCD matrices). As 40 years of research in digital signal processing and computer science has not exhausted the potential for further refinement of FFT algorithms, e.g., [51][52][53], it appears to be simply a matter of whether the FLCT can now attract the attention the FFT continues to receive.…”

Section: Resultsmentioning

confidence: 99%

Fast linear canonical transforms

Healy

Sheridan

2009

J. Opt. Soc. Am. A

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Section: Resultsmentioning

confidence: 99%

Fast linear canonical transforms

Healy

Sheridan

2009

J. Opt. Soc. Am. A

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“…This count was recently surpassed by new algorithms achieving a flop count 34 9 N log 2 N + O(N ) [1], [17]. Similarly, the lowest-known flop count for the DCT-II of size N = 2 m > 1 was previously 2N log 2 N − N + 2 for a unitary normalization (with the additive constant depending on normalization) [6], [7], [12], [13], [18]- [26], and could be achieved by starting with the split-radix FFT and discarding redundant operations [6], [7].…”

Section: Introductionmentioning

confidence: 99%

Type-II/III DCT/DST algorithms with reduced number of arithmetic operations

Shao

Johnson

2008

Signal Processing

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“…(28). We will then use Ω l ≡ −Φ(t * l ) as the oscillation frequency of the IIR filter assigned for this constantfrequency interval, and prescribe a complex amplitude of…”

Section: A the Newtonian Chirp Waveformmentioning

confidence: 99%

Towards low-latency real-time detection of gravitational waves from compact binary coalescences in the era of advanced detectors

et al. 2012

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Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation before the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method.PACS numbers: 04.80. Nn, 97.60.Gb

show abstract

A new matrix approach to real FFTs and convolutions of length 2 k

Cited by 37 publications

References 17 publications

Fast linear canonical transforms

Fast linear canonical transforms

Type-II/III DCT/DST algorithms with reduced number of arithmetic operations

Towards low-latency real-time detection of gravitational waves from compact binary coalescences in the era of advanced detectors

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