= Sampled sinusoid alias
{title2=$f_{\rm alias}=\min_{m\in\mathbb Z}|f-mf_s|\in[0,f_s/2]$}
At uniform sampling times $t_n=n/f_s$, adding an integer multiple of the <sampling rate> to a sinusoid's <frequency> changes its complex phase by an integer multiple of $2\pi n$. The samples therefore agree. Real <cosines> also identify the two signs of frequency, giving the displayed representative below the <Nyquist frequency>. A chosen nonzero sampling-time origin changes the equivalent phase, rather than the alias frequency.
Back to article page
