NAPI TR-lU^O 



Aside from the factor of ^, We is the ratio of the area under 

 the autocorrelation (autoconvolution) function of N(f ) to the value of 

 the autocorrelation function evaluated at zero shift- Thus, We can be 

 referred to as the equivalent autocorrelation width of N(f ); Bracewell 

 (17, pp 152-155) presents a discussion as to why such a "width measure" 

 can be advantageous under certain conditions, although his measure does 

 not include the factor of 2. 



The concept of an equivalent autocorrelation width has been 

 freely used in the 'time domain, i.e. for F^ (t) (9, pp 2'i6-248) ; there, the 

 width is referred to as the correlation time, t^ ^ for the process x(t). 

 The actual correlation function, Rx('^)j is replaced by a rectangular 

 function of width Te and height Rx(0). It can readily be seen that an 

 analagous interpretation is valid for the frequency domain; We is one of 

 the many possible though perhaps least used — definitions of band- 

 width. 



The factor of 2 may be bothersome, but it is basically just fall- 

 out from the mathematics. It could, of course, be arbitrarily left out 

 of the definition in eqn. (b1), and a factor of ^ would then appear in eqn 

 (B2). It is more convenient and intuitively satisfying to leave it in 

 the definition of bandwidth. As defined in (B1), both ideal low pass 

 and ideal band pass (reactangular functions) white noise of bandwidth W 

 have We = W. Similarly, a triangular spectrum of total extent W has 

 We = 0.75 W. Other examples are provided in both Blackraan and Tukey 

 (16) and Bracewell (17). 



B-3 



