Sine and Impulse Response Sampled 1st Order Type 1
Cuthbert Nyack
Applet shows the sinusoidal and impulse response for a first order,
type 1 system. The difference equation for the sinusoidal response
is shown below.
Eg parameters (5.0, 2.0, 0.63, 100.0, 0.1). At this low
frequency the output is almost equal to the input and the phase
lag is small.
Eg parameters (5.0, 2.0, 0.03, 100.0, 2.5). Here the input frequency
is the 3db frequency (K/T1 = 2.5), the output lags the input by
45° and the amplitude is down by ~0.7.
Eg parameters (4.0, 2.0, 0.03, 100.0, 4.0). Here the input frequency
is twice the 3db frequency, the amplitude is down by 0.45 and
the phase lag is ~63° .
Eg parameters (4.0, 1.0, 0.5, 100.0, 0.3). Here the pole is at
-1 and the output shows oscillations at half the sampling
frequency.
Eg parameters (4.0, 1.0, 0.51, 100.0, 0.3). Here the pole is outside
the unit circle and the system is unstable.
Eg parameters (2.0, 1.0, 1.0, 30.0, 3.14). Here the pole is at
-1 and the output should show oscillations at half the sampling
frequency. However since the applied frequency is also at half
the sampling frequency, then the result is a linearly increasing
amplitude at half the sampling frequency.
The impulse response is given by the following equation.
eg parameters (1.0, 1.0, 0.1, 50.0). The pole is close to +1 and the
impulse response is similar to the continuous case.
eg parameters (1.0, 1.0, 1.0, 50.0). The pole is at the origin and the
impulse response is zero after the first output.
eg parameters (1.0, 1.0, 2.0, 50.0). The pole is at -1 and the
impulse response is an oscillation at half the sampling
frequency.
eg parameters (1.1, 1.0, 1.83, 50.0). The pole is just
outside the unit circle and the response is unstable.
Gif images below show how the applets should appear.
Return to main page
Return to page index
COPYRIGHT © 2006 Cuthbert Nyack.