1. Welcome to our site! Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.
    Dismiss Notice

SINC X

Discussion in 'Mathematics and Physics' started by derick007, Feb 23, 2017.

  1. derick007

    derick007 Member

    Joined:
    Feb 5, 2013
    Messages:
    89
    Likes:
    1
    Location:
    NORTHERN IRELAND, UK



    If the normalised sinc (πx) = ∫ sin^2 (πx) / (πx)^2 dx = 0.5


    0



    Then does the Absolute Spectral power in the Band for additive white Gaussian noise with power spectral density N0 / 2 and a filter transfer function of sin (πx) / x = H(x) :




    = N0 ∫ sin^2 (πx) / (πx)^2 dx = 0.5 N0

    0


    If so then if x = 219, was considered the half power point i.e. – 3 dB

    Then does the Absolute Spectral power in the Band

    219


    = N0 ∫ sin^2 (πx) / (πx)^2 dx = 0.5 N0 (0.5) = N0 / 4


    0


    ALSO IF



    If the normalised sinc (πx) = ∫ sin^2 (πx) / (πx)^2 dx = 0.5

    0
    THEN DOES



    the normalised sinc (Kπx) = ∫ sin^2 (Kπx) / (πx)^2 dx = 0.5 WERE K = CONSTANT

    0


     
    Last edited by a moderator: Feb 23, 2017
  2. DerStrom8

    DerStrom8 Super Moderator Most Helpful Member

    Joined:
    Aug 9, 2010
    Messages:
    5,500
    Likes:
    503
    Location:
    Vermont (GMT-5:00)
    Please clean up the formatting of your question. It is a mess right now and difficult to read. I have already reduced the font size as it made the post much too large and unreadable.
     
  3. derick007

    derick007 Member

    Joined:
    Feb 5, 2013
    Messages:
    89
    Likes:
    1
    Location:
    NORTHERN IRELAND, UK
    ∞​
    If the normalised sinc (πx) = sin^2 (πx) / (πx)^2 dx = 0.5
    0​

    Then does the Absolute Spectral power in the Band for additive white Gaussian noise with power spectral density N0 / 2 and a filter transfer function of sin (πx) / πx = H(x) :

    ∞​
    =N0sin^2 (πx) / (πx)^2 dx = 0.5 N0
    0​

    If so then if x = 219, was considered the half power point i.e. – 3 dB. Then does the Absolute Spectral power in the Band

    219​
    = N0sin^2 (πx) / (πx)^2 dx = 0.5 N0 (0.5) = N0 / 4
    0

    ∞​
    Also if the normalised sinc (πx)= sin^2 (πx) / (πx)^2 dx = 0.5
    0

    ∞​
    does the normalised sinc (Kπx)= sin^2 (Kπx) / (πx)^2 dx = 0.5 WERE K = CONSTANT
    0​
     
    Last edited: Feb 23, 2017

Share This Page