Figure. 10.1 shows a delay element so that for an input X(k + 1) it produces an output X(k). Therefore, the element is delayed by one unit.
If z–transform of x(k) be X(z), then z–transform of x (k + 1) is zX (z). Therefore, for an input zX (z) to a delay element, output will be X(z).
Hence the transfer function of delay element
We can also write the letter ‘D’ or z−1 in the block of ‘unit delay’ element.