I have a question about adding two discrete functions, one of which is an exact copy, but dilated.
Imagine function x[n]. This function exists for all n in the set of natural numbers (1,2,3,etc.). There is also function y[n]. It behaves the same as function x[n], but only exists for all n that are integer multiples of 3 (3,6,9,etc.). It is a dilated function of x[n]. There are values for y[n] for values of n that are not divisible by 3, but these are incorrect and should be ignored.
How do I add these two functions? Do I use two different n variables (n and n') and define them as sets of "all natural numbers" and "all natural numbers divisible by 3" respectively? Or is there a way to put this in the notation of the equation?
Thanks for your help!