Adjustable Window with 12 dB/Octave Sidelobes

User-Commanded Mainlobe Width, 12 dB/Octave Roll-Off Instead of 6 dB or 0 dB

Well-known adjustable windows have sidelobe roll-off of either 6 dB/octave (Kaiser, Taylor) or 0 dB/octave (Chebyshev). Win12 provides an adjustable 12 dB/octave window with well-behaved sidelobes.

The adjustment parameter F0 (1 <= F0 <= 3) directly specifies the first null frequency in cycles per window length. The larger F0, the wider the mainlobe and the lower the sidelobes. The thumbnail picture shows win12 with F0 = 2.0, the same first-null frequency as the Hann and Triangle windows. If omitted, F0 is set to 1.5.

Win12 produces unusual-looking windows when F0 < 1.25. These are not erroneous, but this is a region where 6 dB windows are more in their element.

Finally, note that 12 dB windows make good convolutional smoothing filters, compared to a uniform moving average, for example. There’s much less high-frequency content in the result. Win12 can be used as a smoothing filter design function, with F0 controlling the frequency response.

More info on common windows is found in post #46731 “Replacement Window Functions”.