1. Not finding help here? Sign up for a free 30min 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!

Square wave(Simple Question)

  1. Jul 10, 2008 #1
    Friends,

    While studying Fourier Transforms, i saw that a square wave with amplitude +A and -A can be replaced with a sqaure wave with amplitude 2A.

    Just wondering how it was done? I'm new to Signals and Systems .

    thanks.
     
  2. jcsd
  3. Jul 10, 2008 #2

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It is just a coordinate system shift. Translate by -A.
     
  4. Jul 10, 2008 #3
    If you look at a square wave with amplitude of +/- A on a graph, you will see that it covers a range of 2A (A- -A=2A). This wave has a amplitude that fluctuates between these two values. However, an alternate wave with amplitude 2A has the same range (2A), yet it fluctuates between 0 and 2A. The two are identical in their form, they only differ how values are assigned.
     
  5. Jul 10, 2008 #4
    So that means that an X shift can be done in the same way. For e.g -5 to +5(on the x-axis) can be from 0 to 10 on the positive side.
     
  6. Jul 10, 2008 #5

    NoTime

    User Avatar
    Science Advisor
    Homework Helper

    I think you meant y-axis (the normal up/down designation), but yes.
     
  7. Jul 11, 2008 #6
    NO, i meant X-axis . I assumed that when the coordinate shift can be done on Y-axis, the same can be done on X-axis.

    Also, when x(t) has amplitude of (-A to +A), the book says that we can write it as x1(t) - A, where x1(t) has an amplitude of 2A. Any explainations.

    thanks.
     
  8. Jul 11, 2008 #7

    NoTime

    User Avatar
    Science Advisor
    Homework Helper

    Your statement explicitly says x(t) is an amplitude.
    So t is the location on the x-axis and x(t) is a sample point value on the y-axis.
    Adding a constant to x(t) just shifts the waveform up or down on the y-axis.

    If you want to shift the wave on the x-axis then you would write something like x(t-n).
    This has no overall effect on the y-axis amplitude excursions.
     
  9. Jul 11, 2008 #8

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    I don't see that anywhere.
     
  10. Jul 11, 2008 #9

    NoTime

    User Avatar
    Science Advisor
    Homework Helper

    Do you think the following says something else?
     
  11. Jul 12, 2008 #10

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Missed that, sorry.

    At any rate, if this is just a math exercise in shifting coordinates, a signal can be shifted horizontally by one's choice of zero time. Looking back at message #4, we can say either the signal goes from -5 sec to +5 sec, or 0 to 10 sec.

    This assumes I'm interpreting alextsipkis's statements correctly.
     
  12. Jul 12, 2008 #11

    NoTime

    User Avatar
    Science Advisor
    Homework Helper

    I agree with you about the coordinate shifting part, you can do both.
    Seems to me that the OP defined x to be a square wave generator of amplitude (+A, -A).
    That gives A the definition of amplitude.
    Unless A got redefined somewhere, I don't see how you could get a time shift by adding a voltage value to the square wave.
    Did I miss a redefinition somewhere?
    If so, I'm not seeing it, but I've been known to be blind sometimes.
     
  13. Jul 12, 2008 #12

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    No, adding a voltage can't produce a time shift. It's simply a matter of defining where "zero" is. Whether it's voltage or time, 0V or 0 sec is an arbitrary reference.

    If I have a graph that covers a 10 sec range, from 0 to 10 sec, you might ask "when does t=0". And I might answer that t is zero at 2:00 p.m. today. But we could just as easily say t is zero at 5 seconds past 2:00 p.m., in which case the graph would run from -5 to +5 sec.
     
  14. Jul 12, 2008 #13
    Offsetting the signal on the amplitude axis introduces a 0 Hz component in the frequency domain.

    Shifting the signal on the time axis will introduce a phase change of frequency amplidudes. If you are transforming into sines and cosines the relative amplitudes for at any given frequency will vary inversily. (actually as a^2+b^2=constant, but that may be too much detail)
     
  15. Jul 13, 2008 #14

    NoTime

    User Avatar
    Science Advisor
    Homework Helper

    I admit to being a little rusty on this stuff.
    It has after all been a good 20 years since I've been paid to do any of this.

    Out of curiosity is a 0 Hz component just a fancy way of saying DC offset or is there a deeper implication.

    Rereading this thread it looks like I read "same way" in the following statement to be -5v to +5v, but now notice there is no units specification at all.
    I don't know if the OP is confused or not.
     
  16. Jul 14, 2008 #15

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Yes.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Square wave(Simple Question)
Loading...