It is Proved that 2n functional vectors DXmi （m =0

1

2

…

n; i =1l

2

…

Cnm）

belonging to the D transformation set{DFn} of the vector space {Fn}of N-ary logical functions

constitute a cpmplete set of orthogonal bases for {DFn}. Some properties of {f（8）} that is the projection of {DFn} onto these orthogonal bases are examined

and the problem of orthogonal expansion of D （Fn⊕CLμ）

the D transformation of （Fn⊕CLu） which is the digital modulation of a sequence CLμ with μtimes clock frequency by Fn

was studied as well. Two approachs to obtain {f（s）} have been given in this paper.As oneapplication of the orthogonal expansion of D transformation

much attention also has been given to the derivation of normalized autocorrelation functions and normalized power spectral density functions of DFn and D（Fn⊕CL）

where Fn is a combined code with n PN codes being prime each other in period and CL is the code clock. By using the expressions derived in this paper

extremely simple arithmetic operations are sufficient to obtain the above mentioned two types of functions of particular PN combined codes f （s）. It’s possible to realize any complicated logical operation by means of the ALU in a general-purpose computer when this method of orthogonal expansion with D transformation is applied.