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!

Given f(N) as digital signal, find f(2N -1)

  1. Dec 16, 2016 #1
    1. The problem statement, all variables and given/known data
    f(N) is {3, 4, 5, 6, 7}
    It starts at 5 meaning f(o) is 5.
    i have to find f{2N-1}

    2. Relevant equations

    f(N) is given, so first find f(2N) and then delay by 1.

    3. The attempt at a solution
    f(N) is {3, 4, 5, 6, 7}
    finding f(2N)

    f(0) is 5.
    f(2 * 0) is 5

    f(-1) is 4.
    f(2 * -1) is f(-2) is 3.

    f(-2) is 3.
    f(2*-2) is f(-4) is 0

    f(1) is 6
    f(2*1) is f(2) is 7.

    f(2) is 7
    f(2*2) is f(4) is 0

    so f(2N) is {0, 3, 5, 7, 0}
    Starting value at 5.
    So now f(2N-1) is shifting the origin to left by 1 we get f(2N-1) is {3, 5, 7}
    starting at 3.

    But in book they have done:
    f(n) is {3, 4, 5, 6, 7}
    starting at 5
    then f(n-1) is {3, 4, 5, 6, 7
    starting at 4
    then f(2n-1) is {4, 6}
    how can they multiply 2 only to n and not to (-1).
    like shouldnt it be:
    f(n)---->f(2n)---->f(2n-2)...
     
  2. jcsd
  3. Dec 16, 2016 #2

    Mark44

    Staff: Mentor

    This should be f(0) is 5. o is the letter o, not zero.
    No.
    If you know the graph of y = f(n), then the graph of y = f(2n) represents a compression of the graph of y = f(n) toward the vertical axis by a factor of 2.
    Then, f(2n - 1) = f(2(n - 1/2)) represents a shift of the graph of y = f(2n) to the right by 1/2 unit.

    Original function:
    N -2 -1 0 1 2
    f(N) 3 4 5 6 7

    y = f(2N)
    N -1 -1/2 0 1/2 1
    f(2N) 3 4 5 6 7

    For the graph of y = f(2N - 1) = f(2(N - 1/2)), all the points in the table above are shifted to the right by 1/2 unit.
     
  4. Dec 16, 2016 #3
    Yes you are right. The f(2n-1) is actually f(2(n-1/2)). I missed that step as it wasn't in the book.
    Thanks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Given f(N) as digital signal, find f(2N -1)
  1. Find the equation f (Replies: 22)

  2. Find the value of f(2) (Replies: 37)

  3. Finding f(x) given limit (Replies: 35)

Loading...