# why human voice is band limited while it's time limited?

According to Wikipedia, time-limited signals can not be band-limited and vice versa. Also we know that human voice is band-limited and has frequencies from $50\textrm{ Hz}$ to $4\textrm{ kHz}$.

So how is the human voice band-limited while it's time-limited ? (consider a man speaking in a period of time to have a time-limited voice signal)

When you say that human speech is band-limited to $4$ kHz, then that's actually not true. We often use that frequency as a cut-off frequency because we know that speech remains intelligible if we filter out frequencies above $4$ kHz. Yet, there is a significant contribution above that frequency, and the harmonics continue indefinitely. But again, their contribution becomes negligible and they disappear in noise.