Frequency Resolution

In an FFT, the sampled signal is represented by a fixed number of evenly spaced frequency bins across the available frequency range. The bin spacing is the sampling rate divided by the FFT length, so increasing N makes the frequency grid finer while increasing f_s spreads the same number of bins over a wider range. This is why a longer FFT gives better ability to distinguish nearby tones in the spectrum.

Use this when you want to know how close two spectral peaks can be before they appear in separate FFT bins. It is especially useful in audio analysis, vibration monitoring, communications, and any system where you need to choose an FFT size for a desired frequency detail.

• Confusing FFT size with the number of visible peaks instead of the number of points used in the transform
• Using the Nyquist frequency f_s/2 in the formula instead of the full sampling rate f_s
• Assuming smaller bin spacing alone guarantees perfect ability to separate two close frequencies