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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.

Project description:BackgroundInertial measurements (IMUs) facilitate the measurement of human motion outside the motion laboratory. A commonly used open-source software for musculoskeletal simulation and analysis of human motion, OpenSim, includes a tool to enable kinematics analysis of IMU data. However, it only enables offline analysis, i.e., analysis after the data has been collected. Extending OpenSim's functionality to allow real-time kinematics analysis would allow real-time feedback for the subject during the measurement session and has uses in e.g., rehabilitation, robotics, and ergonomics.MethodsWe developed an open-source software library for real-time inverse kinematics (IK) analysis of IMU data using OpenSim. The software library reads data from IMUs and uses multithreading for concurrent calculation of IK. Its operation delays and throughputs were measured with a varying number of IMUs and parallel computing IK threads using two different musculoskeletal models, one a lower-body and torso model and the other a full-body model. We published the code under an open-source license on GitHub.ResultsA standard desktop computer calculated full-body inverse kinematics from treadmill walking at 1.5 m/s with data from 12 IMUs in real-time with a mean delay below 55 ms and reached a throughput of more than 90 samples per second. A laptop computer had similar delays and reached a throughput above 60 samples per second with treadmill walking. Minimal walking kinematics, motion of lower extremities and torso, were calculated from treadmill walking data in real-time with a throughput of 130 samples per second on the laptop and 180 samples per second on the desktop computer, with approximately half the delay of full-body kinematics.ConclusionsThe software library enabled real-time inverse kinematical analysis with different numbers of IMUs and customizable musculoskeletal models. The performance results show that subject-specific full-body motion analysis is feasible in real-time, while a laptop computer and IMUs allowed the use of the method outside the motion laboratory.

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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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