FREQUENCY ANALYSIS OF REVERBERATION 



331 



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*'^*'!'*'^Ngil _• 



k— PING 



|<-ECHO-J 



Figure 5. Periodmeter record of a ping and its echo. 



observed frequency spread in reverberation should be 

 increased by frequency fluctuation in the outgoing 

 ping, is also not surprising. 



The dependence of the frequency spread on the 

 audio output frequency, described by equation (9), 

 seems at first sight rather difficult to understand. In 

 principle, heterodyning simply subtracts a constant 

 frequency from the frequencies of all components of 

 the incoming reverberation signal; thus, if there is no 

 distortion, the average frequency spread should not 

 depend on the audio output frequency.^"'^' However, 

 with a little thought, it can be seen that the difficulty 

 arises because the time intervals between successive 

 zeros of a complex signal are not related in any sim- 

 ple way to the frequency spectrum of that signal. 

 Thus, the assumption that the rms deviation of the 

 instantaneous frequency read from the period- 

 meter should be exactly equal to the true rms fre- 

 quency spread of the reverberation spectrum is cer- 

 tainly not warranted. The complete elucidation of the 

 relation between periodmeter readings and the rever- 

 beration spectrum requires a satisfactory theory of 

 the periodmeter, which has not yet been developed 

 because of mathematical difficulties. A partial anal- 

 ysis of the theory of the periodmeter is given in a 

 report by UCDWR." There it is predicted that the 

 rms spread of the instantaneous frequency should 

 obey the formula 



A/ = X/^^ r-'"^ (11) 



which difTers somewhat from the observational equa- 

 tion (9). However, the mode of derivation of equa- 

 tion (11) has been subjected to some criticism.^" 



This difficulty in relating the response of the 

 periodmeter to the spectrum of the reverberation 



VOLUME REVERBERATION 



Figure 6. Periodmeter records of volume and bottom 

 reverberation. 



illustrates the difficulty which is always experienced 

 in predicting the response to reverberation of any 

 complex circuit, such as the ear or other doppler 

 discriminator. It can be argued that, for the ear, the 

 instantaneous frequencies measured by the period- 

 meter are more significant than the spectrum which 

 gives the intensities in very narrow frequency bands. 

 However, because of the complexity of the ear, this 

 assertion requires proof; for this reason conclusion 

 2 above, and other similar conclusions, cannot be 

 relied on if based on evidence from the periodmeter 

 alone. 



