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
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)]