An FFT of block length N at sample rate fs produces spectral lines spaced
and needs a time block of duration
Finer frequency resolution therefore always costs proportionally more measurement time - there is no way around (2), only ways to spend the time well (averaging, overlap). Frequencies are only observable up to the Nyquist limit fs/2.
The FFT silently assumes the analysed block repeats forever. A tone whose frequency falls between two spectral lines violates that assumption at the block edges, and its energy smears ("leaks")[3] across neighbouring lines - the level reads low and the skirt reads high. Multiplying the block by a window[2] that tapers to zero at the edges suppresses the discontinuity. Every window trades main-lobe width (frequency selectivity) against side-lobe height (dynamic range); the guide's practical rules[1]:
| Signal | Window |
|---|---|
| Periodic tones, harmonics | Hann or Blackman-family |
| Broadband random noise | Hann, with density scaling |
| Transients fully inside the block | Rectangular (no window) |
(Phonalyser.web's FFT pane offers these and several flat-top / HFT windows; coherent averaging changes the trade-offs - that will be covered in the FFT chapter of this help.)
The same spectrum can be displayed against different references: linear amplitude (same unit as the input - right for discrete tones), power (amplitude squared), or spectral density (power or amplitude normalised per Hz of bandwidth - right for noise, because a noise floor in density units does not move when the FFT length changes). Phonalyser.web's V/√Hz unit is exactly this density scaling.
Averaging n spectra reduces the variance of the noise estimate - the fluctuation of an RMS-averaged spectrum falls as 1/√n. Overlapping successive blocks (typically by 2/3 or 3/4 with a Hann window) re-uses samples the window's taper would otherwise waste and raises the update rate without extra capture time.
With a reference channel, cross-spectra give the frequency-response function of a system and the coherence - a 0...1 figure telling how much of the output is linearly caused by the input. These are the foundations of the frequency-response measurement described in the generator chapter.