nuttallwin

Nuttall-defined minimum 4-term Blackman-Harris window

Syntax

w = nuttallwin(L)

w = nuttallwin(L,sflag)

w = nuttallwin(___,typeName)

Description

w = nuttallwin(L) returns a Nuttall defined L-point, four-term symmetric Blackman-Harris window. The coefficients for this window differ from the Blackman-Harris window coefficients computed with blackmanharris and produce slightly lower sidelobes.

w = nuttallwin(L,sflag) uses sflag window sampling.

w = nuttallwin(___,typeName) specifies the option to return the window w with single or double precision for any of the previous syntaxes. (since R2026a)

Examples

Nuttall and Blackman-Harris Windows

Compare 64-point Nuttall and Blackman-Harris windows. Plot them using wvtool.

L = 64;
w = blackmanharris(L);
y = nuttallwin(L);
wvtool(w,y)

Compute the maximum difference between the two windows.

max(abs(y-w))

ans = 
0.0099

Input Arguments

L — Window length

nonnegative integer

Window length, specified as a nonnegative 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, specified as "symmetric" or "periodic". For the equations that define the symmetric and periodic windows, see Algorithms.

typeName — Output data type

"double" (default) | "single"

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 — Nuttall defined Blackman-Harris window

column vector

Nuttall defined Blackman-Harris window, returned as a column vector of length L. The function minimizes the maximum sidelobes of the window.

Algorithms

The equation for the symmetric Nuttall defined four-term Blackman-Harris window is

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

where n= 0,1,2, ... N-1.

The equation for the periodic Nuttall defined four-term Blackman-Harris window is

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

where n= 0,1,2, ... N-1. The periodic window is N-periodic.

The coefficients for this window are

a₀ = 0.3635819

a₁ = 0.4891775

a₂ = 0.1365995

a₃ = 0.0106411

References

[1] Nuttall, Albert H. “Some Windows with Very Good Sidelobe Behavior.” IEEE^® Transactions on Acoustics, Speech, and Signal Processing. Vol. ASSP-29, February 1981, pp. 84–91.

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

R2026a: Enhanced accuracy for window output

The nuttallwin function uses cospi instead of cos to calculate the cosine term that comprises the window. The change results in a more accurate output.

R2026a: Generate single-precision outputs

The nuttallwin function supports single-precision outputs.