blackmanharris

Minimum four-term Blackman-Harris window

Syntax

w = blackmanharris(L)

w = blackmanharris(L,sflag)

w = blackmanharris(___,typeName)

Description

w = blackmanharris(L) returns an L-point symmetric four-term Blackman-Harris window.

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

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

Examples

Blackman-Harris Window

Create a 32-point symmetric Blackman-Harris window. Display the result using wvtool.

L = 32;
wvtool(blackmanharris(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" — Use this option when using windows for spectral analysis. When you specify "periodic", blackmanharris 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

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-Harris window

column vector

Blackman-Harris window, returned as a column vector.

Algorithms

The equation for the symmetric four-term Blackman-Harris window of length N is

$$w(n)=a_0-a_1\cos \left(\frac{2\pi n}{N-1}\right)+a_2\cos \left(\frac{4\pi n}{N-1}\right)-a_3\cos \left(\frac{6\pi n}{N-1}\right),0\le n\le N-1$$

The equation for the periodic four-term Blackman-Harris window of length N is

$$w(n)=a_0-a_1\cos \frac{2\pi n}{N}+a_2\cos \frac{4\pi n}{N}-a_3\cos \frac{6\pi n}{N},0\le n\le N-1$$

The periodic window is N-periodic.

Coefficient	Value
a0	0.35875
a1	0.48829
a2	0.14128
a3	0.01168

References

[1] harris, fredric j. “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform.” Proceedings of the IEEE^®. Vol. 66, January 1978, pp. 51–83.

Extended Capabilities

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

Version History

Introduced before R2006a

R2024b: Generate Single-Precision Outputs

The blackmanharris function supports single-precision outputs.