tukeywin

Tukey (tapered cosine) window

Syntax

w = tukeywin(L,r)

Description

w = tukeywin(L,r) returns an L-point Tukey window with cosine fraction r.

Examples

Tukey Windows

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)

Input Arguments

L — Window length

positive integer

Window length, specified as a positive integer.

Note

If you specify L as noninteger, the function rounds it to the nearest integer value.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

r — Cosine fraction

0.5 (default) | real scalar

Cosine fraction, specified as a real scalar. The Tukey window is a rectangular window with the first and last r/2 percent of the samples equal to parts of a cosine. 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.

Data Types: single | double

Output Arguments

w — Tukey window

column vector

Tukey window, returned as a column vector.

Algorithms

The following equation defines the L-point Tukey window:

$$w(x)=\{\begin{array}{ll}\frac{1}{2}\{1+\cos (\frac{2\pi }{r}[x-r/2])\},\hfill & 0\le x<\frac{r}{2}\hfill \\ 1,\hfill & \frac{r}{2}\le x<1-\frac{r}{2}\hfill \\ \frac{1}{2}\{1+\cos (\frac{2\pi }{r}[x-1+r/2])\},\hfill & 1-\frac{r}{2}\le x\le 1\hfill \end{array}$$

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.

References

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a