# Mathematical expression for a system

I have a system that delays the input with k samples and concatenates the new input with delayed one so that y = [x(n) x(n-k)] so if the input comes with n samples the output should be k+n samples. How to express that in a clear mathematical expression.

• Are you sure you mean "concatenate", not just accumulate, i.e., sum up? I would think that the system you're talking about is just $y[n]=x[n]+x[n-k]$, so for each input sample there's an output sample, not an output vector (of 2 samples). – Matt L. May 9 '19 at 9:26
• @MattL. No, it is not summing up it delays and concatenate the incoming samples with the old one it has a buffer and the output is indeed a vector. – King May 10 '19 at 1:58