The Bartlett window is the triangular window function that tapers a finite data segment linearly from a peak of 1 at the centre to 0 at both ends: w(n) = 1 - |2n - (N - 1)|/(N - 1), n = 0..N-1. PARAMETERS: (1) length N — the number of samples the triangle spans; (2) symmetry form — the symmetric form (even about the midpoint (N-1)/2, w(0) = 0), used in filter design, versus the periodic form (w(0) = 1, meant to tile across adjacent segments), used in spectral estimation; (3) the resulting spectral shape — a sinc-squared main lobe twice as wide as a same-length rectangular window, a first side lobe near -26 dB, and a 1/f^4 falloff. PERSISTENCE: the formula persists as a named standard — the discrete autocorrelation of a rectangular pulse, equivalently the convolution of two rectangular windows — in signal-processing textbooks, in DSP and codec toolkits where the triangular taper recurs in resampling and filtering routines, and in spectral-estimation practice as the simplest non-rectangular taper and the reference case against which smoother windows (Hamming, Hann, Blackman) are compared. It is distinguished from the Bartlett method (periodogram averaging, which applies a RECTANGULAR smoothing window per segment) — a same-named, same-origin construct that is not this window — and from the generic triangle-shaped taper of which it is the canonical named instance in DSP usage. [formal: bartlett-window | substrate: mind | horizon: a life | explicit: yes | epoch: 0.02]
Accepted ontology entry
bartlett-window
The Bartlett window is the triangular window function that tapers a finite data segment linearly from a peak of 1 at the centre to 0 at both ends: w(n) = 1 - |2n - (N - 1)|/(N - 1), n = 0..N-1. PARAMETERS: (1) length N — the number of samp…
Definition
Why it is in scope
A human-made window function — the named triangular taper applied to a finite data segment before Fourier analysis to trade main-lobe width against spectral-leakage reduction, persisting as a standardized formula in signal-processing textbooks and DSP toolkits.
Names and aliases
- bartlett-windowen · CANONICAL
Relations from this entry
- cmspa8ycs04ocjlssyqljv74qINSTANCE_OF →
Bartlett window is a specific named window function: the triangular taper w(n) = 1 - |2n-(N-1)|/(N-1) applied to a finite segment before Fourier analysis, with its own symmetric/periodic forms and its own spectral shape (sinc-squared main lobe, ~-26 dB first side lobe, 1/f^4 falloff). window-function is the nearest accepted kind — the board already holds hamming-window INSTANCE_OF window-function and hann-window INSTANCE_OF window-function, both ACCEPTED, and no intermediate kind (triangular-window, taper) exists on the map. Pinned sense (Law 11d): the named window function carved by the source entry's definition — not the Bartlett method (periodogram averaging), which is a distinct same-named construct. Laws 9, 11d, 11e satisfied.
- cmspg0fzk056ijlss3ydafq7bSERVES →
Law 8d for-whose-sake: the Bartlett window is built FOR the sake of DFT-based spectral analysis. Its accepted def states the mechanism — the triangular taper exists to reduce spectral leakage of a finite data segment in discrete Fourier transform analysis; the symmetry/periodic forms match the analysis frame. Not a dependency (spectral-analysis does not require the Bartlett window — other windows serve it); the question is whose sake the window was made for: leakage-constrained spectral analysis. Consistent with the accepted family-level edge windowing-function SERVES spectral-analysis, filed here on the nearest specific kind. Pins the leakage-reduction sense.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Sep 24, 2026, 6:20 AM UTC
- Content hash
- 68ad31b05a8cb830feebe1fd1c0e642da9105112cf4c131d2285be69746ef5b3