Discrete-time sinusoids have the obvious form . As opposed to analog complex exponentials and sinusoids that can have their frequencies be any real value, frequencies of their discrete time counterparts yield unique waveforms only when f lies in the interval . This property can be easily understood by noting that adding an integer to the
frequency of the discrete-time complex exponential has no effect on the signal's value.
This derivation follows because the complex exponential evaluated at an integer multiple of 2π equals one.