Super Algerbraic Spectral Decay.

CMST Signals Ltd developed the CMST window: a smooth, compactly supported, flat-top window function for spectral analysis where weak signals sit close to strong ones.

How the window works

Sidelobe decay of two window functions Sidelobe level in decibels against frequency offset in bins, on a logarithmic frequency axis. The Hann window falls along a straight line of 18 dB per octave. The C∞ compact-support window curves downward ever more steeply. 0 -40 -80 -120 -160 -200 -240 -280 1 2 5 10 20 50 100 200 400 800 1600 3200 Frequency offset (DFT bins) Sidelobe level (dB) Hann window C∞ compact-support window

Sidelobe envelopes of a Hann window and of a C∞ compactly supported bump window, computed numerically for 8192-sample windows. The Hann window falls at a fixed 18 dB per octave. The smooth window starts higher, crosses near 30 bins and keeps steepening.

Technology

Every classical window has a discontinuity in some derivative at its edges, and that discontinuity fixes how fast its sidelobes decay: as a power of frequency, a straight line on the plot above. A window that is smooth to every order has no such limit.

Smooth
CMST is infinitely differentiable (C∞), including at its edges, so its spectrum decays super-algebraically: faster than any power of frequency.
Compactly supported
It is exactly zero outside a finite interval. It is a finite-length window in the ordinary sense, with no truncation error.
Flat-topped
It equals one across its central region, so the samples there pass through unweighted.

Applications

CMST was developed with gravitational-wave data analysis in mind, where leakage from strong spectral lines can hide much weaker signals nearby.

The same problem appears in any high-dynamic-range spectral measurement: whenever what you are looking for is many tens of decibels below something else in the same record.

Licensing

[CMST is the subject of a UK patent application.]

[It is free to use for non-commercial and open-source work. Commercial use needs a licence from CMST Signals Ltd.]

To discuss a licence, write to info@cmstsignals.com.

Talks

FFT Windows with Superalgebraic Spectral Decay: Why You Might Care
Signal Processing Summit, Milpitas, California, 26–28 January 2027
FFT Windows with Superalgebraic Spectral Decay: Why You Might Care
DSP Online Conference, 9–11 February 2027

Contact

info@cmstsignals.com