Discrete-Time Systems

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

Multiple Representations of Discrete-Time Systems

Difference equation:

Block Diagram:

but, how is the system behaviour?.

First, define x[n] as a unit sample

Now, we use de Difference equation to approximate the system behaviour.

moreover, also be used computational tools to determine the behavior of the system, in this case we use the block diagram and Simulink.

and the signal x[n] and y[n] respectively

Example 2: Simulation of the accumulator

For this system the difference equation is:

This system has a unique feature, has a feedback. This feedback allows, in this case, that the output signal is maintained even if the input signal does not exist.

In simulink:

and the signal x[n] and y[n] respectively

However, the feedback can also cause the system output to increase indefinitely. The system would then be unstable. In this case the feedback is known as positive feedback. Depending on the sign of the adder. Negative feedback normally base known only as feedback.

Another Example:

The loop gain, causes the output diverge. That is, this grows up indefinitely.

input: 

Output

when the gain is less than one, the system always converges to zero.

Sistem II:

Input

Output

The feedback can be seen as a closed loop around one or more system components.

For more details, visit the following link:

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-003-signals-and-systems-spring-2010/lecture-notes/MIT6_003S10_lec02_handout.pdf