Misleading documentation

stft docs state hop_length does not affect frequency resolution; this isn’t true. The per-point resolution is unaffected, but that of the time-frequency plane is, and any hop_length greater than 1 guarantees loss of analysis information for most practical signals, and loss of reconstruction information except for certain windows with specific hop_lengths.

[OverLordGoldDragon]

@bmcfee There’s “frequency” in “time-frequency”; methods like synchrosqueezing rely on instantaneous frequency information to accurately extract components per modulation model (AM+FM-decoupled).

Regardless, strictly speaking you’re correct; resolution purely along frequency axis, disregarding its higher order derivatives or other analysis parameters, is unaffected. It’s why I titled “misleading” rather than “wrong”; part of what motivated my post is a few questions I’ve seen on Stack Exchange being surprised or confused about results when using high hop_length.

Experienced users don’t need docs to know said frequency resolution’s unaffected, but it’s those less familiar that might trip on “frequency is captured equally well”. This is more of a design decision - proceed however you see fitting.

[lostanlen]

Hello @OverLordGoldDragon,

The documentation is correct.

The frequency resolution of a windowed Fourier atom is defined as inversely proportional to the energy spread around its center frequency. This energy spread is independent from the choice of discretization, whether orthogonal or redundant. A fortiori, the impact of hop_length on the reconstruction error is an entirely separate question.

In practice, if you wish to estimate empirically the frequency resolution of a time–frequency representation, what you can do is to pass a sine wave of frequency f and measure the energy spread around f. Denoting by Delta(f) this energy spread, the frequency resolution can be defined as 1/Delta(f). Note that Delta(f) is constant for STFT and is proportional to f for CQT.

Conversely:

any hop_length greater than 1 guarantees loss of analysis information for most practical signals

it’s not that simple. I suggest you read on Non-Stationary Gabor Transform (NSGT) to see how the hop_length may be above 1 while still allowing perfect reconstruction.

P. Balazs, M. Dörfler, F. Jaillet, N. Holighaus, and G. A. Velasco. Theory, implementation and applications of nonstationary Gabor frames. J. Comput. Appl. Math., 236(6):1481–1496, 2011 https://www.univie.ac.at/nonstatgab/pdf_files/badohojave11_04042011.pdf