# Unit step function symbol

I've been studying communications and i see that the book used the symbol $$u_{-1}(t)$$ for unit step function , why ?

• Can you provide a source where it is used? – Engineer May 4 at 9:34
• Communication systems : an introduction to signals and noise in electrical communication by Bruce Carlson – Elias May 4 at 17:34

The standard notation for the unit step function is $$u(t)$$. I've seen the notation $$u_k(t)$$, with integer $$k$$ in Oppenheim's Signals and Systems, where $$k$$ is the order of the derivative of the Dirac delta impulse. I.e., $$u_1(t)=\delta'(t)$$, etc. Using the same logic, negative values of $$k$$ indicate integrals of the Dirac delta impulse. So $$u_{-2}(t)$$ is the unit ramp: $$u_{-2}(t)=tu(t)$$.
In Signals and Systems, Oppenheim uses $$u_k(t)$$ mainly for $$k\ge 1$$ and $$k\le -2$$, because he prefers to use the standard symbols $$\delta(t)$$ and $$u(t)$$ for the Dirac impulse and the unit step, respectively.
But using the logic explained above, $$u_{-1}(t)$$ is the unit step function, being the integral of the Dirac impulse. The Dirac impulse itself would then be $$u_0(t)$$. I guess that that was the intention of the author of the book you refer to.