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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 Algorithms 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.


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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


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.


[1] Bloomfield, P. Fourier Analysis of Time Series: An Introduction. New York: Wiley-Interscience, 2000.

Extended Capabilities

See Also



Introduced before R2006a

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