Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

Sampling points are $\mathbb{Z}$. Sampling theorem tells us that functions with bandwidth lower than $\frac{1}{2}$ will have no aliases. Take functions with pure frequency $\frac{1}{4}$ as an example.Consider $y=sin(\frac{\pi x}{2})$ and triangle wave $$y=(-1)^k(x-2k),x\in[2k-1,2k+1],k\in\mathbb{Z}$$. Don't they coincide on sampling points? Aren't they aliases? What does sampling theorem say about that situation?

share|cite|improve this question

Your triangle wave is not band limited. It has infinite bandwidth.

share|cite|improve this answer
So there is nothing such as a bandlimited triangle wave? It's really hard to think of sampling theorem in time domain. – user33869 Jun 17 '12 at 15:14
@user33869: it will stop being triangle if you limit bandwidth, I suppose. – Violet Giraffe Jun 17 '12 at 16:11
@user33869: sharp changes means it has arbitrarily large frequency components. The sharpest of all, the Delta function has a no where zero flat frequency spectrum (So its frequency spectrum is the smoothest of all) – bleh Jun 26 '12 at 7:37

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.