Measurement of Matrix Frequency Response Functions and Multiple Coherence Functions

Item

Title
Measurement of Matrix Frequency Response Functions and Multiple Coherence Functions
Date
1965
Index Abstract
Coming Soon
Photo Quality
Not Needed
Report Number
AFFDL TR 65-56
Creator
Goodman, N. R.
Corporate Author
Measurement Analysis Corporation
Laboratory
Air Force Flight Dynamics Laboratory
Extent
36
NTRL Accession Number
AD619993
Identifier
AD0619993
Access Rights
Notice(s)
Distribution Classification
1
Contract
AF 33(615)-1418
DoD Project
1370
DoD Task
137005
DTIC Record Exists
No
Distribution Change Authority Correspondence
None
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.
Report Availability
Full text available
Date Issued
1965-06
Provenance
AFRL/VACA
Type
report
Format
1 online resource
Media
AFFDLTR65-056.pdf