KaTeX demo
Math formulae to demo LaTeX to MathML rendering
2020-04-15
demo
math
Given two discrete-time systems A and B connected in cascade
to form a new system C = x \mapsto B(A(x)), we examine
the following properties:
## Linearity
If A and B are linear,
i.e. for all signals x_i and scalars a_i,
then C is also linear
## Time Invariance
If A and B are time invariant,
i.e. for all signals x and integers k,
then C is also time invariant
## LTI Ordering
If A and B are linear and time-invariant, there exists
signals g and h such that for all signals x,
A = x \mapsto x * g and B = x \mapsto x * h, thus
or interchanging A and B order does not change C.
## Causality
If A and B are causal,
i.e. for all signals x, y and any choise of integer k,
then C is also causal.
## BIBO Stability
If A and B are stable, i.e. there exists a signal x
and scalars a and b that for all integers n,
then C is also stable, i.e. there exists a signal x
and scalars a, b and c that for all integers n,