Question

The word "modem" is short for "modulator-demodulator." In this problem, we explore a simple kind of modem, in which binary information is represented by the presence or absence of a sinusoid (presence representing a "1" and absence a "0"). Consequently, the modem's transmitted signal that represents a single bit has the form
x(t)=Asin(2πf0t),0≤t≤T
Within each bit interval of duration T, the amplitude is either A or zero.
What is the smallest transmission interval that makes sense for the frequency f0?