# Frequency distribution not determined by the temporal variation of the pulse?

 PF Gold P: 1,141 Thank you Ctugha, now I understand. To be sure, I plotted the function $$E(t) = \sum_k \sin(k \omega_0 t - \phi_k)$$ for 1) $\varphi_k \in (0,2\pi)$ and 2) for $\varphi_k \in (0,\pi)$. In the first case, the function is completely random without any central peak, while the second one has well-defined peak. So it can be said that the Heisenberg relation gives the width of the pulse made of coherent sine waves, but the wave made of incoherent waves has a peak which is much broader or even unrecognizable.