sawtooth waveform

Discussion in 'Homework Help' started by theyungwun, May 7, 2005.

  1. theyungwun

    Thread Starter New Member

    May 7, 2005
    2
    0
    hey people:

    im turning to you for help. im a non EE major and im praying that someone out there can help me!

    i have a SAWTOOTH waveform that increases linearly from 0 to A (some amplitude) along a time interval of t=0 to t=T, and then drops straight down to 0 @ t=T. then again it increases linearly to A along t=T to t=2T, and drops straight down to 0 @ t=2T...and this continues on for each time interval (3T, 4T...etc.)

    i am having trouble writing its euqtion in terms of ramp and shifted step functions. i was wondering if ANYBODY could shed some light here. i know that the summation of [sin(nt)]/n] is an infinite equation...but i cannot come up w/ tht ramp and step functions.

    thanks!

    yung
     
  2. Brandon

    Senior Member

    Dec 14, 2004
    306
    0
    Slope of the line = A/T
    Every T we need the signal to reach 0.

    (A/T)*t*[U(t)-U(t+T)] THis makes the 1st Pulse x=0

    (A/T)*(t-T)*[U(t+T)-U(t+2T)] This makes the 2nd Pulse x=1

    (A/T)*(t-2T)*[U(t+2T)-U(t+3T)] This makes the 3rd Pulse x=2

    From this we see a pattern so we have the form

    (A/T)*(t-xT)*[U(t+xT)-U(t+(x+1)T)]

    Therefore we sum based upon various values of X

    so we have

    Summation as x=0 to x=infinity of (A/T)*(t-xT)*[U(t+xT)-U(t+(x+1)T)]
     
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