Poles and Zeros of Time-Domain Response Functions

response

impulse

step

sin t

t

final

1

This Demonstration displays the response of a system with

s

domain representation

H(s)

to an impulse, step or sinusoidal input.

H(s)

is a transfer function generated by multiplying the poles and zeros together. Poles are at locations

p

i

marked with a red X and have the form

1

s-

p

i

. Zeros are at locations

z

i

marked with a blue O and have the form

s-

z

i

. You can drag the poles and zeros, but because the generating differential equation is assumed to have real coefficients, all complex poles and zeros occur as complex conjugates.

The poles and zeros of a system enable reconstruction of the input/output differential equation.