Lecture 11 : Differential and Difference Equations
Comparison
between Continuous and Discrete Systems
Let
us first understand what is meant by integer derivative
and integer delay.
1. Integer Derivative: Given x(t)
we find dx(t)/dt.
2. Integer Delay: Given x[t]
we find x[t-N],
where N
is an integer.
Continous
Systems
Discrete
Systems
Integer derivative is exactly
realizable
Integer derivative is not realizable
Integer delay is not exactly
realizable
Integer delay is realizable
Note: Realizability implies giving
a physical structure to the solution with known elements.
We shall see later why integer delay is not exactly
realizable in a continuous system.
