Let us go back to the example of the unit circle.

See the unit circle at the left of Figure 2.

Another simple example is the unit circle, S (see picture above).

In fact we see that the image of h is the unit circle.

The transformation of all complex numbers on the unit circle is a special case.

If it so happens that then the point is within the unit circle and should be accepted.

The region of convergence must therefore include the unit circle.

The following figure shows unit circles with various values of p:

This means the unit circle must be the continuous spectrum of "T".

Also note that if we consider this as a function from the unit circle to the real numbers, then it is neither open nor closed.

Thus the construction of a pi-length from a unit circle is impossible.

Consider the unit circle circumscribed by a square of side length 2.

The diagram alongside shows values of atan2 at selected points on the unit circle.

Let T denote the unit circle in the complex plane.

For instance, rotation can be represented by elements of the unit circle in the complex plane.

One day he casually asked me, "What's the average length of a chord in a unit circle?"

For instance, on the unit circle, let S be the set of points for which is a rational number.

A system is minimum-phase if all its zeros are also inside the unit circle.

The zeros of the discrete-time system are outside the unit circle.

In one dimension, a wrapped distribution will consist of points on the unit circle.

A similar definition can be made in the case of laws supported on the unit circle .

An average vector is calculated based on the distribution of phase points around the unit circle.

The complex roots can be shown to be located on or close to the unit circle.

If you need both, stability and causality, all the poles of the system function must be inside the unit circle.

This is the case at least for all t on the unit circle , see characteristic function.