Apodization Comparison
Compare 9 window functions and their instrument line shapes (ILS). Select windows to overlay.
ILS(f) = |FT{w(t)}| — the instrument line shape determines peak shape.
Lower sidelobe level → less ringing, but wider main lobe → lower resolution.
On the buttons: the highest sidelobe (dB) and the equivalent noise bandwidth N·Σw²/(Σw)² in bins (boxcar = 1), measured from these windows at N = 512. Window definitions: Harris, Proc. IEEE 66, 51 (1978); Nuttall, IEEE Trans. ASSP 29, 84 (1981).
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Window definitions and their line shapes. Sidelobe and equivalent-noise-bandwidth values are measured from the windows at N = 512; Harris's Gaussian ENBW does not fit his own definition.
- Harris F. J. (1978). On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66, 51–83. Cosine-sum windows (eq. 30–32) and the coefficients of Table I. doi:10.1109/proc.1978.10837
- Nuttall A. H. (1981). Some windows with very good sidelobe behavior. IEEE Trans. ASSP 29, 84–91. Four-term window with a continuous first derivative. doi:10.1109/tassp.1981.1163506