3-D Visualization of Z-Transform

1. Objective:

This is the page that help students to visualize the Z-Transform in 3-D domain. The relationship between Z transform and Fourier Transform will also be illustrated in 3-D form.

2. Draw the Z Transform plot in 3D format

Conventionally, when we draw the 2-D Z transform plot, we assign x-axis as the Real axis and y-axis as the Complex axis. Values on the complex plane will be assigned as numbers or "x"s(when we encounter a pole). Like the figure below:

Figure 1

However, if we made this plot in 3D, the entire transfer function will be clearer and more straightforward. Any point that has no value(zeros) will obtain a height of zero and all poles will expand to infinity.

Take the high pass filter y[n] = 1/2*(x[n]-x[n-1]) as an example.

3. Obtain Fourier Transform from the Z Transform plot