Z Domain of Time Signal

I have a simple Data Signal like Sine wave or Rectangular Pulse, etc. There are N blocks and each block has delay of 2T sec. t=0:0.01:10 Take for eg Xi=sin(t) I want to get output wave as Xi=a*sin(t)+b*sin(t-2T)+c*sin(t-4T)+....

I have created an arr of [a b c d ...] I want to do it by z domain method. I will create another array in Z domain like [1 z^(-2) z^(-4) ...] I will do convolution of both arrays and multiple with original signal to get output wave. Can anyone suggest a method to do it please.

Do it for X=1-heaviside(t-1) % a rectangular pulse