2 Linear Diff. Eqns.

2.3 Frequency ResponseAll Activities

The following figure illustrates how the output, $Y(z)$, phase and magnitude vary with the input frequency, $\omega$, and pole location.

frequency response
$Y(z)$ =
z
z + 0.23
$U(z)$
where: $u_k = sin$ 123$kT$
$\omega$:
frequency response
Figure 1: Frequency response of a 1st order system.
Lines connecting discrete points are not part of the response. They are provided to improve visualization.

In Figure 1, drag the pole (x) on the z-plane to change the transfer function. Use the slider to change the input frequency. The input to, and output from, the transfer function are shown on the bottom graph.

Adjust the input frequency, $\omega$, and notice how the output amplitude and phase change. Then change the transfer fuctnion pole and repeat the process. Again, notice how the output amplitude and phase change as you change in input frequency.

  1. Using a pole of 0.5, change the frequency input. Notice how the amplitude of the output, $y_k$ changes. How does this response change for different pole locations.
  2. How does the phase difference between in input and output change as frequency increases? What is the maximum phase shift you can achieve using the graph? This is related to the order of the transfer function, just as in continuous time systems.