flattopwin

Flat top weighted window

Syntax

w = flattopwin(L)

w = flattopwin(L,sflag)

w = flattopwin(___,typeName)

Description

w = flattopwin(L) returns an L-point symmetric flat top window

w = flattopwin(L,sflag) returns an L-point symmetric flat top window using the window sampling method specified by sflag.

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

Examples

Flat Top Window

Create a 64-point symmetric flat top window. View the result using wvtool.

N = 64;
w = flattopwin(N);
wvtool(w)

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 — Flat top window

column vector

Flat top window, returned as a column vector.

Algorithms

Flat top windows are summations of cosines. The coefficients of a flat top window are computed from the following equation:

$$w(n)=a_0-a_1\cos \left(\frac{2\pi n}{L-1}\right)+a_2\cos \left(\frac{4\pi n}{L-1}\right)-a_3\cos \left(\frac{6\pi n}{L-1}\right)+a_4\cos \left(\frac{8\pi n}{L-1}\right),$$

where $$0\le n\le L-1$$. The coefficient values are:

Coefficient	Value
a0	0.21557895
a1	0.41663158
a2	0.277263158
a3	0.083578947
a4	0.006947368

Flat top windows have very low passband ripple (< 0.01 dB) and are used primarily for calibration purposes. Their bandwidth is approximately 2.5 times wider than a Hann window.

References

[1] D’Antona, Gabriele, and A. Ferrero. Digital Signal Processing for Measurement Systems. New York: Springer Media, 2006, pp. 70–72.

[2] Gade, Svend, and Henrik Herlufsen. “Use of Weighting Functions in DFT/FFT Analysis (Part I).” Windows to FFT Analysis (Part I): Brüel & Kjær Technical Review. Vol. x, Number 3, 1987, pp. 1–28.

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 flattopwin function supports single-precision outputs.

R2024a: flattopwin supports GPU code generation

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