Weighted Least Squares Fit of a Real Tone to Discrete Data, by Means of an Efficient Fast Fourier Transform Search

1986 ◽  
Author(s):  
Albert H. Nuttall
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Discrete Data ◽  
Least Squares Fit

The transfer function of a short-period vertical seismograph

1961 ◽  
Vol 51 (4) ◽  
pp. 503-513
Author(s):  
B. P. Bogert
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Least Squares ◽  
Damping Ratio ◽  
Weighted Least Squares ◽  
Measured Frequency ◽  
Least Squares Fit ◽  
Short Period ◽  
Measured Frequency Response ◽  
Poles And Zeros

Abstract We locate the poles and zeros of the transfer function of a seismograph which consists of the Geotech Model 1051 Benioff vertical seismometer and the Geotech Model 4500 galvanometer-phototube amplifier with a 5 cps galvanometer. A weighted least squares fit to the measured frequency response of the seismometer, assuming a damping ratio of 17 to 1, gives for the pole locations of the seismometer transfer function: - 10 . 539 ; - 5 . 787 + i 7 . 407 ; - 5 . 787 - i 7 . 407 There is a triple zero at the origin. The overall seismograph transfer function has additional poles at - 22 . 21 + i 22 . 21 ; - 22 . 21 - i 22 . 21 ; - 0 . 06283 ; - 29 . 62 + i 29 . 62 ; - 29 . 62 - i 29 . 62 ; an additional zero at the origin, and a quadruple zero at infinity. an additional zero at the origin, and a quadruple zero at infinity.

A Weighted Least-Squares Parametric Method of Reducing Nuclear-Reactor Gamma Spectral Data

1961 ◽  
Vol 5 ◽  
pp. 306-323
Author(s):  
J. C. Whiton ◽  
R. L. Gamble ◽  
R. M. Thornton
Keyword(s):  
Least Squares ◽  
Spectral Data ◽  
High Speed ◽  
Nuclear Reactor ◽  
Weighted Least Squares ◽  
Parametric Method ◽  
Pulse Height ◽  
Least Squares Fit ◽  
Pure Matrix ◽  
Program Error

AbstractA mathematical method has been developed which reduces nuclear-reactor gamma pulse-height spectral data to the form of differential energy spectra through the use of a high-speed computer machine. In essence, the method consists of a least-squares fit of weighted multichannel analyzer data and the utilization of curve-smoothing parametrization. The least-squares approach tends to reduce the magnitude of data that must be handled, i.e., reduces the order of matrix involved. Weighting is used to obtain fractional deviations for minimization by lease squares and thus obtain a satisfactory fit throughout the entire channel range. The parametrization smoothes the reduced data by making use of the fact that reactor gamma spectra can be represented by the product of an exponential and a polynomial. Difficulties that arise when pure matrix inversion is applied have been obviated, and the advantage of high-speed data reduction is gained through the use of an IBM 704-7090 computer program. Error analyses have been undertaken, and data have been reduced for comparative purposes. Results are included in the presentation of the investigation.

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