Hi Folks, I am teaching myself DSP and have got a problem with checking if a system is linear. The system is linear if and only if the rules of homogeneity and superposition apply. They are both the necessary and sufficient conditions for linearity. I am stuck on the following y[n]=x[n] to check whether this is linear I can apply the homegneity rule that is multiply the system by a constant. y[n]=αx[n]. if by making that constant 0 the output also goes to 0. The system obeys homegeneity, this is however only necassary not sufficent for linearity. The system must also obey superposition. My understanding of it as that 2 seperate functions X1[n] + X2[n] should equal if: y1[n]=x1[n] y2[n]=x2[n] How does a response of the system become: y3[n]= [α1x1[n]+β2x2[n]] Surely this can not be looked at from the POV of numbers as: 3+4 (3+4) I can only assume I have to look at it in terms of a digital system but can not visulaise it. Any help will be appreciated.