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Generalizing the inverse FFT off the unit circle.

ABSTRACT: This paper describes the first algorithm for computing the inverse chirp z-transform (ICZT) in O(n?log?n) time. This matches the computational complexity of the chirp z-transform (CZT) algorithm that was discovered 50 years ago. Despite multiple previous attempts, an efficient ICZT algorithm remained elusive until now. Because the ICZT can be viewed as a generalization of the inverse fast Fourier transform (IFFT) off the unit circle in the complex plane, it has numerous practical applications in a wide variety of disciplines. This generalization enables exponentially growing or exponentially decaying frequency components, which cannot be done with the IFFT. The ICZT algorithm was derived using the properties of structured matrices and its numerical accuracy was evaluated using automated tests. A modification of the CZT algorithm, which improves its numerical stability for a subset of the parameter space, is also described and evaluated.

SUBMITTER: Sukhoy V

PROVIDER: S-EPMC6783538 | biostudies-literature | 2019 Oct

REPOSITORIES: biostudies-literature

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Generalizing the inverse FFT off the unit circle.

Sukhoy Vladimir V Stoytchev Alexander A

Scientific reports 20191008 1

This paper describes the first algorithm for computing the inverse chirp z-transform (ICZT) in O(n log n) time. This matches the computational complexity of the chirp z-transform (CZT) algorithm that was discovered 50 years ago. Despite multiple previous attempts, an efficient ICZT algorithm remained elusive until now. Because the ICZT can be viewed as a generalization of the inverse fast Fourier transform (IFFT) off the unit circle in the complex plane, it has numerous practical applications in ...[more]

PMID: 31594961

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Project description:Sedative and analgesic practices in intensive care units (ICUs) are frequently based on anesthesia regimes but do not take account of the important patient related factors. Pharmacologic properties of sedatives and analgesics change when used as continuous infusions in ICU compared to bolus or short-term infusions during anesthesia. In a prospective observational cohort study, we investigated the association between patient related factors and sedatives/analgesics doses in patients on mechanical ventilation (MV) and their association with cessation of sedation/analgesia. We included patients expected to receive MV for at least 24 hours and excluded those with difficulty in assessing the depth of sedation. We collected data for the first 72 hours or until extubation, whichever occurred first. Multivariate analysis of variance, multivariate regression as well as logistic regression were used. The final cohort (N = 576) was predominantly male (64%) with mean (SD) age 61.7 (15.6) years, weight 63.4 (18.2) Kg, Acute Physiology and Chronic Health Evaluation II score 28.2 (8) and 30% hospital mortality. Increasing age was associated with reduced propofol and fentanyl doses requirements, adjusted to the weight (p<0.001). Factors associated with higher propofol and fentanyl doses were vasopressor use (Relative mean difference (RMD) propofol 1.56 (95% confidence interval (CI) 1.28-1.90); fentanyl 1.48 (1.25-1.76) and central venous line placement (CVL, RMD propofol 1.64 (1.15-2.33); fentanyl 1.41 (1.03-1.91). Male gender was also associated with higher propofol dose (RMD 1.27 (1.06-1.49). Sedation cessation was less likely to occur in restrained patients (Odds Ratio, OR 0.48 (CI 0.30-0.78) or those receiving higher sedative/analgesic doses (OR propofol 0.98 (CI 0.97-0.99); fentanyl 0.99 (CI 0.98-0.997), independent of depth of sedation. In conclusion, increasing age is associated with the use of lower doses of sedative/analgesic in ICU, whereas CVL and vasopressor use were associated with higher doses.

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Generalizing the inverse FFT off the unit circle.

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Generalizing the inverse FFT off the unit circle.

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