Figure. 10.1 shows a delay element so that for an input **X**(*k* + 1) it produces an output ** X**(

**Fig. 10.1**

If *z*–transform of **x**(*k*) be **X**(*z*), then *z*–transform of **x** (*k* + 1) is *z***X** (*z*). Therefore, for an input *z***X** (*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.

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