# 1 Pole Sine, Square and Triangle Response.

Cuthbert Nyack
This applet shows the response of a system with a zero at the origin and a pole at p to a sinusoid at w sampled with sampling time Ts. A continuous system equivalent would be a series RC circuit and would show a decreasing response with frequency.

eg parameters (0.0050, NA, NA, NA, 80, 0.3, 0, 700.0, 0.15, 0.08)
show a peak response of 1.4280. Changing w to 0.3 = p shows a peak response of 0.9510 ie an attenuation of 3.53dB compared with 3dB for a continuous system.

eg parameters (0.03, NA, NA, NA, 80, 0.98, 0, 700.0, 0.15, 0.08)
Pole near +1.0, sharp peak response at low frequencies.

eg parameters (0.03, NA, NA, NA, 80, 1.06, 0, 700.0, 0.15, 0.08)
Pole near +1.0 outside the unit circle, system is unstable.

eg parameters (0.48, NA, NA, NA, 80, -0.95, 0, 700.0, 0.15, 0.08)
Pole near -1.0, sharp peak response at frequencies near half the sampling frequency.

eg parameters (0.48, NA, NA, NA, 80, -1.06, 0, 700.0, 0.15, 0.08)
Pole near -1.0, outside the unit circle, system is unstable.

eg parameters(NA, NA, NA, NA, 100, 0.0, 1, 700.0, 0.1, 0.08)
Here the pole is at zero, the response is a replica of the input delayed by 1 sample time.

eg parameters(NA, NA, NA, NA, 100, 0.8, 1, 700.0, 0.1, 0.08)
Here the pole is at 0.8, the response is that of a first order system.

eg parameters(NA, NA, NA, NA, 100, 1.0, 1, 700.0, 0.1, 0.08)
Here the pole is at 1.0, the response is a triangular wave.

eg parameters(NA, NA, NA, NA, 100, 1.05, 1, 700.0, 0.1, 0.08)
Here the pole is at 1.05, the response is unstable.

eg parameters(NA, NA, NA, NA, 100, -0.7, 1, 700.0, 0.1, 0.08)
Here the pole is at -0.7, the response is stable but has an oscillatory transient.

eg parameters(NA, NA, NA, NA, 100, -1.02, 1, 700.0, 0.1, 0.08)
Here the pole is at -1.02, the response is unstable.

eg parameters (NA, NA, NA, NA, 150, 0.95, 2, 700.0, 0.1, 0.08)
shows a delayed pulse.

eg parameters (NA, NA, NA, NA, 150, 1.03, 2, 700.0, 0.1, 0.08)
shows an unstable system.

eg parameters (NA, NA, NA, NA, 150, -1.04, 2, 700.0, 0.1, 0.08)
shows an unstable system.