SPECTRA OF QUANTIZED SIGNALS 



461 



of any linear electrical circuit is obtained by multiplying all impedances by 

 a constant factor. All voltages are multiplied and all currents divided by 

 the same factor. By assuming unit values of resistance we are able to use 



O10-5 

 ^ a 



0.9994 0.9995 0.9996 0.9997 0.9998 0.9999 



CORRELATION FUNCTION OF SIGNAL = a 



Fig. 11 — Correlation function of 7-digit quantizing errors. 



squared values of voltages and currents to represent power.) The theorem 

 states that w/ and yp are related by the equation: 



Wf 



^0 



yj/r COS l-wfr dr 



(2.1) 



Proof may be found in the references cited. When the signal contains peri- 

 odic components, the integral in (2.1) becomes divergent in the ordinary or 

 Riemann sense, but this difficulty may be overcome by either applying the 

 theory of divergent integrals or replacing Riemann by Stieltjes integration. 

 We shall not require these modifications here because we shall base our analy- 

 sis on signals with a continuous spectrum. We note that ^o is the mean 



