Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In my text book, Digital Signal Processing, Principles, Algorithms, and Applications by John Proakis, it asks the question to show how $\delta(n) = u(n) - u(n-1)$.

I can understand how this is true if "n" is an integer, but sometimes I see the step function as a continuous line instead of a fixed point at an instant. In that case, is it incorrect to think of $u(n)$ as something continuous?

share|improve this question
Does the text in question (who is the author, by the way?) use a very common (but by no means universal) notational convention: $x[n]$ means the $n$-th sample of a continuous-time signal $x(t)$, that is, $x[n] = x(nT)$ where $T$ is the time interval between samples? Or does the author routinely use $x(n)$ to mean either the $n$-th sample or the value of $x(t)$ at time $t = n$, because he, like Humpty Dumpty, scornfully believes that "When I use a word, it means just what I choose it to mean — neither more nor less." ?? – Dilip Sarwate Feb 25 '13 at 2:54
@DilipSarwate That's what I'm confused about. It seems to switch back and forth. – Chris Harris Feb 25 '13 at 5:00
"... it seems to switch back and forth." Well, then, play Follow-my-leader and give the proof that makes sense, prefacing your answer by something like: "In this answer, I use $u$ and $\delta$ to mean sequences with $n$-th elements $u(n)$ and $\delta(n)$ where $n$ is an integer." Then write out your proof (probably just one or two lines) and end with a coda saying that the result to be proved is not correct if $u$ and $\delta$ are interpreted as continuous-time functions. That way you have C-ed YA against TAs eager to knock a few points off. – Dilip Sarwate Feb 25 '13 at 12:17
The question only makes sense if it is referring to discrete sequences and, as Dilip said, the "n" terminology almost always implies discrete sequences, so I would assume that they mean discrete sequences. – Jim Clay Feb 25 '13 at 14:32

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.