Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.
This isn't really a mathematic proof, but does explain.
u(-t) is always 0 for all positive values of t, and 1 for all negative values of t.
-u(t) is always -1 for all positive values of t, and 0 for all negative values of t.
1>in case of u(-t),the independent variable is reversed but in case of -u(t),the function itself reversed.
2> unit step function is not an odd function.so we can not write u(-t)=-u(t)
3>if u plot these functions independtenly then u will see that u(-t) lies in second quadrant and -u(t) lies in fourth quadrant.
Hi,
This relation is not correct.
The proof is very easy:
write u(t)=1 as t>0 ,0 as t<0
put -t instead of t you get:
u(-t)=1 as -t>0 i.e. t<0 and 0 as -t<0 i.e. t>0
So we get that:
u(-t)= 1 as t<0 and 0 as t>0
while -u(t)= -1 as t>0,and 0 as t<0
so it's evident that u(-t) is not equal to -u(t)
Regards,
Consider the four quadrants that we study with reference to trignometry.
For y(t) = u(t) ---> sketch is in the 1st quadrant
y(t) = -u(t) ----> sketch is in the 4th quadrant i.e. reflection of u(t) about the x-axis
y(t) = u(-t) ----> sketch is in the 2nd quadrant
y(t) = -u(-t) ----> sketch is in the 3rd quadrant.
they are not equal because u(-t) is on the left side and has a value 1 throughout but -u(t) is on the right side and a value of -1 throughout
if you mean to say in non signal terms then it is equal only for odd functions
Hi,
If u want a proof. I think the proof given by Tantoun2004 is correct. Otherwise there is no doubt that they r diff. as u can see them from their plot easily.
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.