The discrete implementation of the Fourier transform maps a digital signal into its Fourier series coefficients or harmonics. Unfortunately, neither a time nor a frequency stamp is directly associated with the FFT operation. Modern acquisition systems, whether they use add-on boards or instruments to capture data, allow you to control or specify the sampling interval dt.
Because an acquired array of samples represents a progression of equally spaced samples in time, you can determine the corresponding frequency in Hertz. The sampling frequency fs for dt is
and the frequency interval is
,
where n is the number of samples in the sequence.
Given the sampling interval 1.000E-3, the following block diagram displays a graph with the correct frequency information.
Thus, for the signal x(t), the resulting power spectrum graph with the correct frequency axis and the resulting frequency interval appear as in the following illustration.
The sampling interval is the smallest frequency that the system can resolve through FFT or related routines. One way to increase the resolution is to increase the number of samples or increase the sampling interval.