Connexions

You are here: Home » Content » Periodic Signals
Content Actions
Lenses

What is a lens?

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

This content is ...
Affiliated with (?)
This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.

  • This module is included inLens: Rice University OpenCourseWare
    By: OpenCourseWare ConsortiumAs a part of collections:"Signals, Systems, and Transforms (under construction)", "Signals and Systems"

    Click the "Rice University OCW" link to see all content affiliated with them.

    Rice University OCW
Also in these lenses

  • This module is included inLens: richb's DSP resources
    By: Richard BaraniukAs a part of collection:"Signals and Systems"

    Comments:

    "My introduction to signal processing course at Rice University."

    Click the "richb's DSP" link to see all content selected in this lens.

    richb's DSP
Tags

(?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Periodic Signals

Module by: Michael Haag, Justin Romberg

Summary: This module defines a periodic function and describes the two common ways of thinking about a periodic signal.

Recall that a periodic function is a function that repeats itself exactly after some given period, or cycle. We represent the definition of a periodic function mathematically as:
ft=ft+mT ∀m:m∈ℤ f t f t m T m m (1)
where T>0 T 0 represents the period. Because of this, you may also see a signal referred to as a T-periodic signal. Any function that satisfies this equation is periodic.
We can think of periodic functions (with period TT) two different ways:
#1) as functions on all of ℝ
per_fxn1.png
Figure 1: Function over all of ℝ where f t 0 =f t 0 +T f t 0 f t 0 T
#2) or, we can cut out all of the redundancy, and think of them as functions on an interval 0T 0 T (or, more generally, aa+T a a T ). If we know the signal is T-periodic then all the information of the signal is captured by the above interval.
per_fxn2.png
Figure 2: Remove the redundancy of the period function so that ft f t is undefined outside 0T 0 T .
An aperiodic CT function ft f t does not repeat for any T∈ℝ T ; i.e. there exists no T T s.t. this equation holds.
Question: DT definitions?

Continuous-Time

Discrete-Time

Note: Circular vs. Line

Comments, questions, feedback, criticisms?

Send feedback