Suddenly Applied Signals in Discrete Time Systems

Thread Starter

leodavinci90

Joined Oct 22, 2014
57
From what I understand that these are input signals produce a transient output at the start & later it becomes a steady-state output when passed through an LTI system or h[n].
  • If that definition is incorrect, then what is a suddenly applied signal in a DT system?
  • Are these signals always sinusoids such as cos(wn) u[n], sin(wn) u[n] and e ^(jwn) u[n]?
 

bogosort

Joined Sep 24, 2011
432
From what I understand that these are input signals produce a transient output at the start & later it becomes a steady-state output when passed through an LTI system or h[n].
  • If that definition is incorrect, then what is a suddenly applied signal in a DT system?
  • Are these signals always sinusoids such as cos(wn) u[n], sin(wn) u[n] and e ^(jwn) u[n]?
The phrase "suddenly applied" is not, as far as I am aware, a technical term. But the meaning seems to be clear: a signal that is identically zero for all time before some time t0. In my EE school, we referred to these as "switched signals".

Most of the math functions we commonly use to represent signals are defined and nonzero for almost all t (such as sinusoids). We can, however, make switched versions by multiplying them with a unit step (Heaviside) signal, which has the convenient properties that it is identically zero for all t < t0, and it is identically one for all t >= t0. Since the product of any number and 0 is 0, and the product of any number and 1 is 1, the unit step lets us switch on (or "suddenly apply") an otherwise infinite signal.

Note that switched signals need not be sinusoids; any well-defined signal x[n] can be switched on with u[n].
 

Thread Starter

leodavinci90

Joined Oct 22, 2014
57
Note that switched signals need not be sinusoids; any well-defined signal x[n] can be switched on with u[n].
What does switched on mean?
 

bogosort

Joined Sep 24, 2011
432
Note that switched signals need not be sinusoids; any well-defined signal x[n] can be switched on with u[n].
What does switched on mean?
By "switched on" I mean what you mean by "suddenly applied".



The image above is of a (continuous-time) cosine being "switched on" at t = 0 by a step function. In other words, the signal x(t) = cos(wt) u(t) is zero for all t < 0.
 

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