Tukey (tapered cosine) window
w = tukeywin(L,r)
w = tukeywin(L,r) returns an L-point Tukey window in the column vector w. A Tukey window is a rectangular window with the first and last r/2 percent of the samples equal to parts of a cosine. See Definitions for the equation of the Tukey window. r is a real number between 0 and 1. If you input r ≤0, you obtain a rectwin window. If you input r ≥1, you obtain a hann window. r defaults to 0.5.
Compute 128-point Tukey windows with five different values for r and display the results using WVTool.
L=128; t0=tukeywin(L,0); % Equivalent to rectangular window t25=tukeywin(L,0.25); t5=tukeywin(L); % r=0.5 t75=tukeywin(L,0.75); t1=tukeywin(L,1); % Equivalent to Hann window wvtool(t0,t25,t5,t75,t1)
The following equation defines the L–point Tukey window:
where x is a L–point linearly spaced vector generated using linspace. The parameter r is the ratio of cosine-tapered section length to the entire window length with 0 ≤r≤1. For example, setting r =0.5 produces a Tukey window where 1/2 of the entire window length consists of segments of a phase-shifted cosine with period 2r =1. If you specify r≤0, an L-point rectangular window is returned. If you specify r≥1, an L-point von Hann window (hann) is returned.
 Bloomfield P. Fourier Analysis of Time Series: An Introduction, New York: Wiley-Interscience, 2000, p.69.