WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Analog-to-Discrete System Conversion Using Impulse Invariance

​
second-order system specification
′′
y
(t) + 2 ξ
Ω
n
′
y
(t) +
2
Ω
n
y(t) = δ(t)
ξ
0.07
Ω
n
(rad/sec)
1
T (sec)
1
′′
y
(t) + 0.140
′
y
(t) + 1y(t) = δ(t)
y(t)
scale
time scale
50
use automatic scale
use automatic scale
This Demonstration illustrates the impulse invariance method used to convert an analog to a discrete system representation. The analog system consisting of the Laplace transfer function
H(s)
is converted to the discrete system
H(z)
, the
Z
transfer function. This analog system is the response of a standard second-order system (with damping and stiffness) to a given impulse with zero initial conditions. The functions
H(s)
and
H(z)
are displayed with their pole locations.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.