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Digital Signal Processing. The Z Transform has a strong relationship to the DTFT, and is incredibly useful in transforming, analyzing, and manipulating discrete calculus equations. The Z transform is named such because the letter 'z' (a lower-case Z) is used as the transformation variable.he Z transform is named such because the letter 'z' (a lower-case Z) is used as the transformation variable.
1 In sampled systems, inputs and outputs are related by difference equations and Z-transform techniques are used to solve those differential equations. 2  An analog signal is converted to a digital form in an A/D. 3  The digital signal is processed somehow. There are tools that you have available from work with Laplace transforms. 2  For example, with two real poles you should be able to divide the transform into two parts, each with one real pole, using partial fractions.