# sawtooth waveform

#### theyungwun

Joined May 7, 2005
2
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

#### Brandon

Joined Dec 14, 2004
306
Originally posted by theyungwun@May 7 2005, 07:21 PM
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
[post=7524]Quoted post[/post]​
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)]