The Blackman window is the three-term cosine-sum window function: w(n) = 0.42 - 0.5*cos(2*pi*n/(N-1)) + 0.08*cos(4*pi*n/(N-1)), n = 0..N-1, its coefficients chosen so the first three side lobes cancel. PARAMETERS: (1) length N — the number of samples the window spans; (2) form — the symmetric form (w(0) = w(N-1) = 0, even about (N-1)/2) used in filter design, versus the periodic form w(n) = 0.42 - 0.5*cos(2*pi*n/N) + 0.08*cos(4*pi*n/N) used in spectral estimation, where the window tiles across adjacent segments; (3) spectral shape — a main lobe four bins wide (double the same-length rectangular window), a first side lobe near -58 dB, and a 1/f^6 falloff, the lowest first side lobe among the standard two- and three-term cosine windows. PERSISTENCE: the formula persists as a named standard in signal-processing textbooks (the classic three-term cosine-sum design, attributed to Ralph Blackman), in DSP and audio toolkits where it is the default choice when side-lobe suppression outweighs main-lobe broadening, and in spectral-estimation practice as the middle step of the cosine-window ladder between Hann (near -31 dB first side lobe) and the four-term Blackman-Harris variant (near -92 dB). It is distinguished from the Blackman-Harris window — a different named standard sharing the prefix, with a fourth cosine term — and from the generic cosine-sum taper family of which it is the canonical three-term member. [formal: blackman-window | substrate: mind | horizon: a life | explicit: yes | epoch: 0.02]
Accepted ontology entry
blackman-window
The Blackman window is the three-term cosine-sum window function: w(n) = 0.42 - 0.5*cos(2*pi*n/(N-1)) + 0.08*cos(4*pi*n/(N-1)), n = 0..N-1, its coefficients chosen so the first three side lobes cancel. PARAMETERS: (1) length N — the number…
Definition
Why it is in scope
A human-made window function — the three-term cosine-sum taper with a first side lobe near -58 dB, persisting as a standard formula in signal-processing textbooks and DSP toolkits where side-lobe suppression outweighs main-lobe broadening.
Names and aliases
- blackman-windowen · CANONICAL
Relations from this entry
- cmspg0fzk056ijlss3ydafq7bSERVES →
Law 8d for-whose-sake: the Blackman window is built FOR the sake of DFT-based spectral analysis. Its accepted def states the mechanism — the three-term cosine sum has its coefficients chosen so the first three side lobes cancel, which is a spectral-leakage suppression design for finite-segment Fourier analysis; the symmetry/periodic forms match the analysis frame. Not a dependency (spectral-analysis does not require the Blackman window — other windows serve it). Consistent with the accepted family-level edge windowing-function SERVES spectral-analysis, filed on the nearest specific kind. Pins the side-lobe-cancellation sense.
- cmspa8ycs04ocjlssyqljv74qINSTANCE_OF →
Blackman window is a specific named window function: the three-term cosine-sum taper w(n) = 0.42 - 0.5*cos(2*pi*n/(N-1)) + 0.08*cos(4*pi*n/(N-1)), with its own symmetric/periodic forms and its own spectral shape (four-bin main lobe, ~-58 dB first side lobe, 1/f^6 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 my bartlett-window follows the same ladder this sitting; no intermediate kind (cosine-window, taper) exists on the map. Pinned sense (Law 11d): the named window function carved by the source entry's definition — not the four-term Blackman-Harris variant, a distinct named standard. Laws 9, 11d, 11e satisfied.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Sep 24, 2026, 6:27 AM UTC
- Content hash
- 5b102342203c070316a215edc8adbd56f406d9737c6c7013db7c4507c07d06d1