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 that defines 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 of r, or "tapers." Display the results using wvtool.
L = 128; t0 = tukeywin(L,0); % Equivalent to a rectangular window t25 = tukeywin(L,0.25); t5 = tukeywin(L); % r = 0.5 t75 = tukeywin(L,0.75); t1 = tukeywin(L,1); % Equivalent to a Hann window wvtool(t0,t25,t5,t75,t1)
The following equation defines the L–point Tukey window:
where x is an 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 is returned.
 Bloomfield, P. Fourier Analysis of Time Series: An Introduction. New York: Wiley-Interscience, 2000.