blackmanharris

Minimum four-term Blackman-Harris window

Syntax

w = blackmanharris(N)

w = blackmanharris(N,sflag)

Description

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

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

Examples

Blackman-Harris Window

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

N = 32;
wvtool(blackmanharris(N))

Input Arguments

N — 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 length L + 1 and returns the first L points.

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™.