Davis and Zarnick 



Fourier Analysis of Recorded Transients 



The Fourier transform of a transient record is defined by the mathematical 

 relation 



F(ja;) 



dt f(t) cos cot - j 



CC 



I 



dt f(t) sin cot 



(21) 



and is readily accomplished by digital computation or by special- purpose de- 

 vices designed for this application. 



For this exploratory investigation, it was decided to use a particular analog 

 computer configuration which has interesting properties. A single channel is 

 shown in Fig. 5 where conventional analog computer symbols are used. As de- 

 scribed in Ref. 5, this undamped resonant circuit is driven by a transient input 

 and oscillates as t ^ co at an amplitude corresponding to the magnitude of the 

 transform of the input transient at the particular frequency co and with a phase 

 corresponding to the phase of the transform. A number of similar computer 

 configurations all adjusted to the same frequency, were driven simultaneously 

 by the tape-recorded transients resulting from a particular experiment in order 

 to maintain a common time base for phase measurements. 



TRANSIENT 



STEADY STATE 

 ~~* OSCILLATION 

 AMPLITUDE = I F(jw)| 

 PHASE=ZF(jw) 



Fig. 5 - Transient analyzer configuration 

 on analog computer 



The use of this scheme for transient analysis was motivated by considera- 

 tions of accessibility and operator control of the computations. However, for 

 mass handling of transient records on an assembly- line basis, other techniques 

 will be employed. 



TEST RESULTS 



Tests of three different models are described in this report. Emphasis is 

 placed on a correlation of transient wave results with regular wave results 

 rather than on a complete description of the characteristics of any particular 

 hull form. A chronological description is used to indicate the problems encoun- 

 tered and the progress obtained to date. 



516 



