blackman

Blackman window

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Syntax

w = blackman(L)
w = blackman(L,sflag)
w = blackman(___,typeName)

Description

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

example

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

w = blackman(___,typeName) specifies the option to return the window w with single or double precision.

Examples

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Open Live Script

Create a 64-point Blackman window. Display the result using wvtool.

L = 64;
wvtool(blackman(L))

Figure Window Visualization Tool contains 2 axes objects and other objects of type uimenu, uitoolbar, uipanel. Axes object 1 with title Time domain, xlabel Samples, ylabel Amplitude contains an object of type line. Axes object 2 with title Frequency domain, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Magnitude (dB) contains an object of type line.

Input Arguments

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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

Window sampling method, specified as:

  • "symmetric" — Use this option when using windows for filter design.

  • "periodic" — Use this option when using windows for spectral analysis. When you specify "periodic", blackman computes a window of length L + 1 and returns the first L points. The missing endpoint is the beginning of the next period of the periodic extension of the sequence. Therefore, the sequence satisfies the periodicity assumption of the discrete Fourier transform.

Data Types: char | string

Since R2024b

Output data type (class), specified as one of these:

  • "double" — Use this option to return a double-precision output w.

  • "single" — Use this option to return a single-precision output w.

Data Types: char | string

Output Arguments

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Blackman window, returned as a column vector.

Algorithms

The following equation defines the Blackman window of length N:

w(n)=0.42−0.5cos(2πnL−1)+0.08cos(4πnL−1), 0≤n≤M−1

where M is N/2 when N is even and (N + 1)/2 when N is 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 to N + 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.

Extended Capabilities

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

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Version History

Introduced before R2006a

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See Also

Apps

Functions