Prom equations (2) and (3) 



= B L if) 



^ (t) 5 exp0"2iyt) 



The frequency response function may also be written 



*' x if) = I*- Cf)| expO-000) 



where | J* 1 (/)| , the absolute value of R x (f), me;i ures the 

 amplitude response of the system to the input frequency /, 

 and &(/) represents the corresponding phase response. 



Since V 1 (t) vanishes for t< , equation (k) may be written 



*\ if) = J_ V t (t) exp(-j2nfT)dr (5) 



The integral (5) exists for stable filters; hence the fre- 

 quency-response function of a stable filter is the Fourier 

 transform of its weighting function. Let W ( T ) be symmet- 

 rical about some point t a and define a new variable t such 

 that T=t+ Ta . Then W x (t) = W x (t + t ) =w{t) . The fre- 

 quency R{j), expressed in terms ofV(t), is 



00 

 *(/) = f "it) exp(-J2xft)dt (6) 



U -OB 



The weighting function V(t) is given by the inverse Fourier 

 transform: 



V{t) = f B(f) exp(j2jtft)0f (7) 



. <_/ -co 



The integrals (6) and (7) exist for stable filters, and their 

 application will be basic to the discussions which follow in 

 this report. 



An experimental function known only by a set of data sampled 



1 



J 



