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Measurement of Matrix Frequency Response Functions and Multiple Coherence Functions.

AD619993

Publication Date	1965
Personal Author	Goodman, N. R.
Page Count	36
Abstract	Fundamental concepts involved in the statistical analysis of multiple-input single-output time-invariant linear systems are described. The definitions of a matrix frequency response function and a multiple coherence function are presented. Formulas for computing simultaneous confidence bands for all elements of the matrix frequency response function are obtained, using the standard 'F' distribution. Expressions for the confidence bands are given both as a function of the various types of coherences and of the elements of the spectral density matrix. The effect of the various quantities on the width of the confidence bands is discussed in detail. Confidence bands for the gains and phases of the frequency response functions are also developed. The interpretation of linear system computational results in terms of a time invariant nonlinear system model is described. It is shown how the linear system results provide what may be thought of as a 'best' linear fit to the nonlinear model. The multiple coherence function then gives a quantitative measure of goodness of this fit. In this sense the coherence function may be used to provide a test for system linearity. (Author)
Keywords	Matrix algebra Statistical analysis Functions Linear systems Analysis of variance Statistical distributions Frequency response functions Coherence functions
Corporate Authors	Measurement Analysis Corp Los Angeles Calif
Document Type	Technical Report
Title Note	Final rept. for Mar 64-Jan 65.
NTIS Issue Number	196519
Contract Number	AF33 615 1418

Measurement of Matrix Frequency Response Functions and Multiple Coherence Functions.

Measurement of Matrix Frequency Response Functions and Multiple Coherence Functions.
AD619993

Publication Date	1965
Personal Author	Goodman, N. R.
Page Count	36
Abstract	Fundamental concepts involved in the statistical analysis of multiple-input single-output time-invariant linear systems are described. The definitions of a matrix frequency response function and a multiple coherence function are presented. Formulas for computing simultaneous confidence bands for all elements of the matrix frequency response function are obtained, using the standard 'F' distribution. Expressions for the confidence bands are given both as a function of the various types of coherences and of the elements of the spectral density matrix. The effect of the various quantities on the width of the confidence bands is discussed in detail. Confidence bands for the gains and phases of the frequency response functions are also developed. The interpretation of linear system computational results in terms of a time invariant nonlinear system model is described. It is shown how the linear system results provide what may be thought of as a 'best' linear fit to the nonlinear model. The multiple coherence function then gives a quantitative measure of goodness of this fit. In this sense the coherence function may be used to provide a test for system linearity. (Author)
Keywords	Matrix algebra Statistical analysis Functions Linear systems Analysis of variance Statistical distributions Frequency response functions Coherence functions
Corporate Authors	Measurement Analysis Corp Los Angeles Calif
Document Type	Technical Report
Title Note	Final rept. for Mar 64-Jan 65.
NTIS Issue Number	196519
Contract Number	AF33 615 1418