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The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms
The use of the fast Fourier transform in power spectrum analysis is described. Principal advantages of this method are a reduction in the number of computations and in required core storage, andExpand
Simulation Run Length Control in the Presence of an Initial Transient
A procedure based on Schruben's Brownian bridge model for the detection of nonstationarity and a spectral method for estimating the variance of the sample mean are explored for estimation of the steady state mean of an output sequence from a discrete event simulation. Expand
The Fast Fourier Transform and Its Applications
A description of the alogorithm and its programming is given here and followed by a theorem relating its operands, the finite sample sequences, to the continuous functions they often are intended to approximate. Expand
A spectral method for confidence interval generation and run length control in simulations
A method for placing confidence limits on the steady state mean of an output sequence generated by a discrete event simulation is discussed and a run length control procedure is developed that uses the relative width of the generated confidence interval as a stopping criterion. Expand
On a Generalized M/G/1 Queuing Process in Which the First Customer of Each Busy Period Receives Exceptional Service
Results are obtained that characterize the transient and asymptotic distributions of the queue size, waiting time, and waiting-plus-service time of the M/G/1 queue. Expand
A Perspective on the Use of Control Variables to Increase the Efficiency of Monte Carlo Simulations
The emphasis is on the practical problems and potential of applying the method in the simulation of complex systems and the conditions under which control variables could be profitably applied in practical simulations. Expand
On the relationship between batch means, overlapping means and spectral estimation
  • P. Welch
  • Computer Science, Mathematics
  • WSC '87
  • 1 December 1987
Most of the reduction in the variance of the variance estimate can be achieved with modest amounts of overlapping, which may have practical implications because of the large number of batches required for the statistical test of lack of correlation. Expand
Statistical Results on Control Variables with Application to Queueing Network Simulation
The development and application of control variables for variance reduction in the simulation of a wide class of closed queueing networks is discussed and a result is given which quantifies the loss in variance reduction caused by the estimation of the optimum control coefficients. Expand
The fast Fourier transform algorithm: Programming considerations in the calculation of sine, cosine and Laplace transforms☆
Abstract In the organization of programming packages for computing Fourier and Laplace transforms, it is useful, both for conceptual understanding and for operational efficiency to consider theExpand
What is the fast Fourier transform
The discrete Fourier transform of a time series is defined, some of its properties are discussed, the associated fast method for computing this transform is derived, and some of the computational aspects of the method are presented. Expand