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Useful Definitions for ECE301: signals and systems

Periodic CT Signal:

  • A CT signal $ x(t)\ $ is called periodic if there exists $ T>0\ $ period such that $ x(t+T)=x(t)\ $, for all values of t. The fundamental period is the smallest period of all periods of a signal (denoted by $ T_0\ $).

In Mathspeak:

  • $ x(t) periodic \iff \exists T>0 \ni x(t+T)=x(t), \forall t \in \mathbb{R} $

Periodic DT Signal:

  • A DT signal $ x[n]\ $ is called periodic if there exists $ N>0\ $ period such that $ x[n+N]=x[n]\ $, for all values of n. the fundamental period is the smallest period of all periods of a signal (denoted by $ N_0\ $).

In Mathspeak:

  • $ x[n] periodic \iff \exists N>0 \ni x[n+N]=x[n], \forall n \in \mathbb{N} $

Comment:

  • The difference between CT and DT:

Note that the period N must be an integer in DT, but that the period T in CT can be any positive real number.

-Mimi (Wed, 26 Sep 2007 16:29:43)

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva