# Autocorrelation function

For what signal applies, that its autocorrelation function at point $0$ is zero, i.e. $R_f(0) = 0\ ?$

I know that autocorrelation is (RootMeanSquare)^2 and for $R_f(0)$ this equals: $$R_f(0) = \frac{1}{T}\int_0^T f(t)^2 dt = \sum_{k=-\infty}^\infty \lvert c_k\rvert^2$$

But I have no idea how to formulate that signal from equation.

Thank you very much for hint that will guide me to the right way of solving this problems.

• So if $R_f(0)$ equals $0$, can you say what that implies for $f(t)$? No? Do you understand the concept of integral as the area the graph of $[f(t)]^2$ and the $t$ axis? Nov 30, 2017 at 19:14
• You really shouldn't ask two different questions in the same question. Imagine someone would like to answer one, but not the other - then they've got no chance to be accepted as answer! So, remove the second question from your question (ask it separately). Nov 30, 2017 at 20:12
• @MarcusMüller done Nov 30, 2017 at 21:08
• @DilipSarwate thank you for your reaction, but I wasn't sure where to fit zeros in the formula, because of 'T' and 't' in the equation. Nov 30, 2017 at 21:12
• $R_f(0) = 0$ is given. $R_f(0) = \sum_{k=-\infty}^\infty |c_k|^2$ is what your book says. Put the two together to get $\sum_{k=-\infty}^\infty |c_k|^2 = 0$. So, the sum of all the terms for which $|c_k|^2$ is positive is cancelled out by sum of all the terms for which $|c_k|^2$ is negative. Can you proceed from here? Dec 1, 2017 at 22:04

You also seem to be prone to using formulas without being sure what the symbols in these mean (your $t$ vs $T$ confusion). So, read the page leading up to that formula.
• The question asked, right up front, is "What signal has an autocorrelation value of $0$ at $t=0$ or $\tau=0$, i.e. $R_f(0) = 0$? Dec 1, 2017 at 0:11