Applet shows the sinusoidal and impulse response for a first order, type 0 system. The difference equation for the sinusoidal response is shown below.

eg parameters (5.0, 2.0, 0.03, 100.0, 3.0). The applied frequency is equal to the 3dB frequency (1 + K)/T1 = 3.0. The phase lag is 45° and the attenuation is 0.7.

eg parameters (5.0, 0.7, 0.13, 100.0, 0.9). The pole is at zero and the output is a sinusoid from the start. No transient buildup.

eg parameters (4.9, 1.0, 0.42, 100.0, 0.2). The pole is just outside the unit circle and the output shows a growing oscillation at half the sampling frequency.

The impulse response is given by the following equation.

eg parameters (5.0, 1.0, 0.18, 50.0). The pole is close to 0 and the sampled response is the unit impulse.

eg parameters (3.0, 0.4, 0.27, 50.0, 0.25). The pole is close to -1 and the sampled response is a decaying oscillation at half the sampling frequency.

eg parameters (3.0, 0.4, 0.29, 50.0, 0.02). The pole is just outside the unit circle and the output is a growing oscillation at half the sampling frequency.

Gif images below show how the applets should appear.

COPYRIGHT © 2006 Cuthbert Nyack.