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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. | 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 | + | == 2. Draw the Z Transform plot in 3D format == |
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| + | 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: | ||
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| + | 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. | ||
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| + | Take the high pass filter y[n] = 1/2*(x[n]-x[n-1]) as an example. | ||
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| + | == 3. Obtain Fourier Transform from the Z Transform plot == | ||
Revision as of 23:40, 29 November 2017
Contents
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:
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.
