taylorwin

Taylor window

Syntax

w = taylorwin(L)

w = taylorwin(L,nbar)

w = taylorwin(L,nbar,sll)

w = taylorwin(___,typeName)

Description

w = taylorwin(L) returns an L-point Taylor window.

w = taylorwin(L,nbar) returns an L-point Taylor window with a number (nbar) of nearly constant-level sidelobes adjacent to the mainlobe.

w = taylorwin(L,nbar,sll) returns an L-point Taylor window with a maximum sidelobe level of sll dB relative to the mainlobe peak.

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

Examples

Taylor Window

Generate a 64-point Taylor window with four nearly constant-level sidelobes and a peak sidelobe level of -35 dB relative to the mainlobe peak. Visualize the result with wvtool.

w = taylorwin(64,4,-35);
wvtool(w)

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

nbar — Number of constant level sidelobes

4 (default) | positive integer

Number of nearly constant-level sidelobes adjacent to the mainlobe, specified as a positive integer. These sidelobes are “nearly constant-level” because some decay occurs in the transition region.

sll — Maximum sidelobe level relative to mainlobe peak

-30 (default) | real negative scalar

Maximum sidelobe level relative to mainlobe peak, specified as a real negative scalar in dB. It produces sidelobes with peaks sll dB down below the mainlobe peak.

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 — Taylor window

column vector

Taylor window, returned as a column vector.

Algorithms

Taylor windows are similar to Chebyshev windows. A Chebyshev window has the narrowest possible mainlobe for a specified sidelobe level, but a Taylor window allows you to make tradeoffs between the mainlobe width and the sidelobe level. The Taylor distribution avoids edge discontinuities, so Taylor window sidelobes decrease monotonically. Taylor window coefficients are not normalized. Taylor windows are typically used in radar applications, such as weighting synthetic aperture radar images and antenna design.

The following equation defines the L-point Taylor window w with parameter $$\overline{n}$$ and maximum sidelobe level of SLL dB relative to the mainlobe peak (SLL<0):

$$\begin{array}{l}w(x)=1+2{\displaystyle \sum _{m=1}^{\overline{n}-1}{F}_{\text{m}}(m)\cos \left(\pi mx\right)},x=\frac{2\times \left(1,2,\cdots ,L\right)-1-L}{L}\\ F_{\text{m}}(m)=\frac{{(-1)}^{m+1}}{2}\frac{{\displaystyle \prod _{n=1}^{\overline{n}-1}\left(1-\frac{m^2}{S(A^2+{(n-0.5)}^2)}\right)}}{{\displaystyle \prod _{\begin{array}{l}n=1\\ n\ne m\end{array}}^{\overline{n}-1}\left(1-\frac{m^2}{n^2}\right)}},m=1,2,\cdots ,\overline{n}-1\\ A=\frac{1}{\pi }{\cosh }^{-1}\left({10}^{SLL/20}\right)\\ S=\frac{{\overline{n}}^2}{A^2+{(\overline{n}-0.5)}^2}.\end{array}$$

References

[1] Brookner, Eli. Practical Phased Array Antenna Systems. Boston: Artech House, 1991.

[2] Carrara, Walter G., Ronald M. Majewski, and Ron S. Goodman. Spotlight Synthetic Aperture Radar: Signal Processing Algorithms. Boston: Artech House, 1995, Appendix D.2.

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 in R2006a

R2026a: Enhanced accuracy for window output

The taylorwin 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 taylorwin function supports single-precision outputs.