Z Domain Transfer Function

Roc is outside the outermost pole.

Z domain transfer function. F g n γ n z f z g z. Likewise in the z domain the transfer function fully describes how the output signal y z responds to an arbitrary input signal x z. X n ast h n ztarrow x z h z.

As we have seen in z transforms the convolution in the time domain transforms to a multiplication in the z domain. With the z transform we can create transfer functions for digital filters and we can plot poles and zeros on a complex plane for stability analysis. Z domain t kt unit impulse.

If roc is the system is causal. If i e unit circle can be included in roc the system is stable. This similarity is explored in the theory of time scale calculus.

H z z2 1 z 0 5 z 0 5. The transfer function of an lti is as shown before without specifying the roc this could be the z transform of one of the two possible time signals. Hence for this problem z transform is possible when a 1.

Causality and stability causality condition for discrete time lti systems is as follows. If i. It can be considered as a discrete time equivalent of the laplace transform.

We choose gamma γ t to avoid confusion and because in the laplace domain γ s it looks a little like a step input. Unit step note u t is more commonly used to represent the step function but u t is also used to represent other things. The inverse z transform allows us to convert a z domain transfer function into a difference equation that can be implemented in code written for a microcontroller or digital signal processor.