1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Frequency of a constant function

  1. Apr 11, 2016 #1
    Just a quick question that I feel should be simple, but I'm unable to come up with a satisfactory answer.

    A constant signal has an arbitrarily small period (rather, it has no fundamental period), and so it seems to me that this means the frequency of a constant signal grows without bound. However, in Fourier analysis, for instance, we treat constant signals as having a frequency component only at ##f = 0##. Why, mathematically, can we not say that a constant signal has (approaching) infinite frequency since ##f = 1/T## and a constant function has arbitrarily small ##T##? I mean, certainly from an experimental basis (i.e. Designing a high pass filter to get rid of a constant component of a signal), ##f=0## corresponds to a constant signal, but I'd like a mathematical reason for this.
     
  2. jcsd
  3. Apr 11, 2016 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You get a constant signal from ##\cos (\omega t)## if you let ##\omega \downarrow 0##, definitely not if you let ##\omega \rightarrow \infty##
     
  4. Apr 11, 2016 #3
    Ah yes, of course. Then what's the issue with looking at it in terms of ##f=1/T##?
     
  5. Apr 11, 2016 #4

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You can look at it from the perspective of ##T\rightarrow\infty##: the signal never crosses the zero...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted