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" — Use this option when using windows for spectral analysis. When you specify "periodic", flattopwin 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 — 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.