Computer programs perform statistical spectral analyses of up to seven time series. These programs should have applicability to a variety of engineering systems in the fields of geophysics, physiology, acoustics, and structural analysis

Byars, B. J.

Dubman, M. R.

English

NASA Technical Reports Server

November 1966	 Brief 66-10539 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U. S. space 
program and to encourage their commercial application. Copies are available to the public from 
the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Computer Programs Perform Spectral Analyses of up to Seven Time Series 
The problem: 
To devise computer programs that will describe 
the interrelationships between two or more time 
series in situations where simultaneous measurements 
of the time-varying quantities are recorded in an 
experiment. 
The solution: 
Two computer programs that will perform statistical 
spectral analysis of up to seven time series. One of 
these programs is specifically for cross-spectral analy-
sis of two stationary time series, and the other for 
performing a multidimensional spectral analysis of 
up to seven time series from stationary or nonsta-
tionary processes. These programs are available in 
both Fortran II and Fortran IV versions. 
How it's done: 
The cross-spectral analysis program takes as input 
two stationary time series from simultaneously meas-
ured sample records. Multiple cases are treated 
sequentially, and the time series as well as all the 
other input data may differ in any respect from one 
analysis to another. For data input purposes, the X 
(input time series of the linear model) and Y (ob-
served output) time series sample records are handled 
in an independent manner. Initially, the two sample 
records need not consist of the same number of points, 
nor to have been sampled at the same rate. When 
this is the case, the program will reduce the effective 
sampling rate of the data prior to the cross-spectral 
analysis as indicated by one of the control variables. 
After any desired sampling rate reduction has been 
accomplished, for either time series, the resulting 
sample records are calibrated by the application of
multiplicative calibration factors and trends are de-
rived from the resultant sample records. The pro-
gram then computes estimates of the autocovariance 
and the cross-covariance functions and then obtains 
smoothed estimates of the power spectral densities, 
cospectral density, and quadrature spectral density. 
From these, estimates of the coherence and frequency 
response functions are derived. 
In addition to trend removal and arbitrary pre-
scaling of the time series, the program provides other 
auxiliary features such as tests of significance of 
convex power peaks, corrections for frequency re-
sponse characteristics of the measurement system, 
and corrections for filters employed in the generation 
of the time series input. A variety of modes of data 
input and output are available on a user option basis, 
including CRT plots of the various functions esti-
mated. 
The multidimensional spectral analysis program 
performs the same types of calculations as those 
described above when dealing with stationary time 
series, but, in addition to computing the coherence 
and frequency response pertaining to each pair of 
time series, it also computes multiple coherence func-
tions relating any one of the time series to the 
remaining ones. In addition, if two or more of the 
time series are chosen as inputs and the remaining 
series as outputs in a linear time-invariant system 
model, the program provides estimates of the matrix 
frequency response function of the system and com-
putes related quantities. 
For nonstationary time series, this prof' in com-
putes time-varying estimates of the types lescribed 
in
(continued overicaf) 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19660000537 2020-03-11T17:43:29+00:00Z
by automatically partitioning the total sample record 
into equal-length overlapping subrecords. A complete 
multiple spectral analysis is then carried out for each 
subrecord and each time-varying estimate obtained 
may then be analyzed to obtain estimates of quantities 
such as spectra of power fluctuations or spectra of 
coherence. 
A high degree of flexibility is also available in this 
program because of the modular design and the many 
user-controlled input and output options. 
Notes: 
1. These programs should have applicability to a 
variety of. engineering systems in the fields of 
geophysics, physiology, acoustics, and structural 
analysis. One possible application would be in test-
ing the dynamic response of structures under wind 
loading.
2. Inquiries concerning this innovation may be di-
rected to:
Technology Utilization Officer 
Marshall Space Flight Center 
Huntsville, Alabama 35812 
Reference: B66-10539 
Patent status: 
No patent action is contemplated by NASA. 
Source: M. R. Dubman and B. J. Byars 
of North American Aviation, Inc., 
under contract to 
Marshall Space Flight Center 
(M-FS-1133 & 1134)
. 
. 
Brief 66-10539	 Category 01


Computer programs perform spectral analyses of up to seven time series

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