blackman

Blackman window

Syntax

w = blackman(L)

w = blackman(L,sflag)

w = blackman(___,typeName)

Description

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

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

Blackman Window

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

L = 64;
wvtool(blackman(L))

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

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 length L + 1 and returns the first L points.

Data Types: char | string

typeName — Output data type

"double" (default) | "single"

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

w — Blackman window

column vector

Blackman window, returned as a column vector.

Algorithms

The following equation defines the Blackman window of length N:

$$w(n)=0.42-0.5\cos \left(\frac{2\pi n}{L-1}\right)+0.08\cos \left(\frac{4\pi n}{L-1}\right),0\le n\le M-1$$

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

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

R2024b: Generate Single-Precision Outputs

The blackman function supports single-precision outputs.

R2024a: blackman supports GPU code generation

The blackman function supports code generation for graphical processing units (GPUs). You must have MATLAB^® Coder™ and GPU Coder™ to generate CUDA^® code.