blackman

Blackman window

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Syntax

w = blackman(L)

w = blackman(L,sflag)

Description

example

w= blackman(L)returns anL-point symmetric Blackman window.

w= blackman(L,sflag)returns a Blackman window using the window sampling method specified bysflag.

Examples

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Blackman Window

Open Live Script

Create a 64-point Blackman window. Display the result usingwvtool.

L = 64; wvtool(blackman(L))

Input Arguments

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`L`—Window length
positive integer

Window length, specified as a positive integer.

Data Types:single|double

`sflag`—Window sampling
`'symmetric'`(default) |`'periodic'`

Window sampling method, specified as:

'symmetric'— Use this option when using windows for filter design.
'periodic'— This option is useful for spectral analysis because it enables a windowed signal to have the perfect periodic extension implicit in the discrete Fourier transform. When'periodic'is specified, the function computes a window of lengthL+ 1 and returns the firstLpoints.

Output Arguments

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`w`— Blackman window
column vector

Blackman window, returned as a column vector.

Algorithms

The following equation defines the Blackman window of lengthN:

$w (n) = 0.42 - 0.5 \cos (\frac{2 π n}{L - 1}) + 0.08 \cos (\frac{4 π n}{L - 1}), 0 \leq n \leq M - 1$

whereMisN/2 whenNis even and (N+ 1)/2 whenNis odd.

In the symmetric case, the second half of the Blackman window,M≤n≤N– 1, is obtained by reflecting the first half around the midpoint. The symmetric option is the preferred method when using a Blackman window in FIR filter design.

The periodic Blackman window is constructed by extending the desired window length by one sample toN+ 1, constructing a symmetric window, and removing the last sample. The periodic version is the preferred method when using a Blackman window in spectral analysis because the discrete Fourier transform assumes periodic extension of the input vector.

References

[1] Oppenheim, Alan V., Ronald W. Schafer, and John R. Buck.Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, 1999, pp. 468–471.

blackman

Syntax

Description