o(x,y) = F 0(u,v)} =F-1 I(u,v) H(u,v)} (2.19)


 = f i(xoYo) h(x-xo,y-yo) dxo dyo


 = f(x,y) h(x,y)


 where denotes convolution.

 Consider the effect of an additive noise on the input of the

system. Although the exact form of the noise n(x,y) may not be known,

the noise statistics or power spectral density may be predictable.

Thus, the effect of the system on the input is determined by its

impulse response or frequency response. That is, when there is

knowledge of the input signal and noise, the output signal and noise

characteristics can be predicted. The relationship of the input and

output are expressed in the following diagram and equations. The

letters i and o indicate the input and output terms while the letters

s and n indicate the signal and noise portions.



 Linear System
s(x,y) + n(x,y) h(x -- so(x,y) + no(x,y)
 h(x,y)



 i(x,y) = si(x,y) + ni(x,y) (2.20)


 o(x,y) = So(x,y) + no(x,y) (2.21)


 0(u,v) = I(u,v) H(u,v) (2.22)


 So(u,v) = Si(u,v) H(u,v) (2.23)


No(u,v) = Ni(u,v) H(u,v)


-(2.24)