Author
Peter D. Welch
Bio: Peter D. Welch is an academic researcher from IBM. The author has contributed to research in topics: Discrete-time Fourier transform & Non-uniform discrete Fourier transform. The author has an hindex of 22, co-authored 37 publications receiving 13323 citations.
Papers
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IBM1
TL;DR: In this article, the use of the fast Fourier transform in power spectrum analysis is described, and the method involves sectioning the record and averaging modified periodograms of the sections.
Abstract: 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, and convenient application in nonstationarity tests. The method involves sectioning the record and averaging modified periodograms of the sections.
9,705 citations
IBM1
TL;DR: 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.
Abstract: This paper studies the estimation of the steady state mean of an output sequence from a discrete event simulation. It considers the problem of the automatic generation of a confidence interval of prespecified width when there is an initial transient present. It explores 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. The procedure is evaluated empirically for a variety of output sequences. The performance measures considered are bias, confidence interval coverage, mean confidence interval width, mean run length, and mean amount of deleted data. If the output sequence contains a strong transient, then inclusion of a test for stationarity in the run length control procedure results in point estimates with lower bias, narrower confidence intervals, and shorter run lengths than when no check for stationarity is performed. If the output sequence contains no initial transient, then the performance measures of the procedure with a stationarity test are only slightly degraded from those of the procedure without such a test. If the run length is short relative to the extent of the initial transient, the stationarity tests may not be powerful enough to detect the transient, resulting in a procedure with unreliable point and interval estimates.
1,237 citations
IBM1
TL;DR: 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.
Abstract: The advent of the fast Fourier transform method has greatly extended our ability to implement Fourier methods on digital computers 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 An analysis of the error due to discrete sampling over finite ranges is given in terms of aliasing Procedures for computing Fourier integrals, convolutions and lagged products are outlined
833 citations
TL;DR: 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.
Abstract: The fast Fourier transform is a computational tool which facilitates signal analysis such as power spectrum analysis and filter simulation by means of digital computers. It is a method for efficiently computing the discrete Fourier transform of a series of data samples (referred to as a time series). In this paper, the discrete Fourier transform of a time series is defined, some of its properties are discussed, the associated fast method (fast Fourier transform) for computing this transform is derived, and some of the computational aspects of the method are presented. Examples are included to demonstrate the concepts involved.
471 citations
IBM1
TL;DR: 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.
Abstract: This paper discusses a method for placing confidence limits on the steady state mean of an output sequence generated by a discrete event simulation. An estimate of the variance is obtained by estimating the spectral density at zero frequency. This estimation is accomplished through a regression analysis of the logarithm of the averaged periodogram. By batching the output sequence the storage and computational requirements of the method remain low. A run length control procedure is developed that uses the relative width of the generated confidence interval as a stopping criterion. Experimental results for several queueing models of an interactive computer system are reported.
442 citations
Cited by
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TL;DR: Following the discussion of interference temperature as a new metric for the quantification and management of interference, the paper addresses three fundamental cognitive tasks: radio-scene analysis, channel-state estimation and predictive modeling, and the emergent behavior of cognitive radio.
Abstract: Cognitive radio is viewed as a novel approach for improving the utilization of a precious natural resource: the radio electromagnetic spectrum. The cognitive radio, built on a software-defined radio, is defined as an intelligent wireless communication system that is aware of its environment and uses the methodology of understanding-by-building to learn from the environment and adapt to statistical variations in the input stimuli, with two primary objectives in mind: /spl middot/ highly reliable communication whenever and wherever needed; /spl middot/ efficient utilization of the radio spectrum. Following the discussion of interference temperature as a new metric for the quantification and management of interference, the paper addresses three fundamental cognitive tasks. 1) Radio-scene analysis. 2) Channel-state estimation and predictive modeling. 3) Transmit-power control and dynamic spectrum management. This work also discusses the emergent behavior of cognitive radio.
12,172 citations
IBM1
TL;DR: In this article, the use of the fast Fourier transform in power spectrum analysis is described, and the method involves sectioning the record and averaging modified periodograms of the sections.
Abstract: 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, and convenient application in nonstationarity tests. The method involves sectioning the record and averaging modified periodograms of the sections.
9,705 citations
01 Jan 1978
TL;DR: A comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared is included, and an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.
Abstract: This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared. Finally, an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.
7,130 citations
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.
5,689 citations
01 Apr 1975
TL;DR: This paper gives an exposition of linear prediction in the analysis of discrete signals as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal.
Abstract: This paper gives an exposition of linear prediction in the analysis of discrete signals The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum The major part of the paper is devoted to all-pole models The model parameters are obtained by a least squares analysis in the time domain Two methods result, depending on whether the signal is assumed to be stationary or nonstationary The same results are then derived in the frequency domain The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra This also leads to a discussion of the advantages and disadvantages of the least squares error criterion A spectral interpretation is given to the normalized minimum prediction error Applications of the normalized error are given, including the determination of an "optimal" number of poles The use of linear prediction in data compression is reviewed For purposes of transmission, particular attention is given to the quantization and encoding of the reflection (or partial correlation) coefficients Finally, a brief introduction to pole-zero modeling is given
4,206 citations