Continuous-Time Systems

Signals and Systems
Resume: Lecture 2. Curse 6.003. OCW

Continuous-Time Systems


Differential equations: mathematically compact.

Block diagrams: illustrate signal flow paths
the previous system, it can also be interpreted as: 

where A is the operator:

Unit impulse signal is analogous to the similar discrete d[n]. The unit-impulse signal acts as a pulse with unit area but zero width.

The unit-impulse function is represented by an arrow with the num­ber 1, which represents its area or “weight.”

It has two seemingly contradictory properties:

• it is nonzero only at t = 0, and

• its definite integral (−∞,∞) is one !

Now, if the former system fed with this signal, we obtain what is known as the system impulse response.

Now through simulation in Simulink, we can get that behavior.

Note that we used the unit step to generate the unit impulse, through derivation.

input:

Output:

if you wish, you can check that the response is consistent with the mathematical expression:

where p=1;0. If p<0 converges="converges" system="system" the="the" to="to" zero="zero">

In this case p=-0.5.

The reader can identify that a change in sign of p, it is sufficient for the output signal converge or diverge.

the end.