rectwin -Rectangular window

Syntax

w=rectwin(L)

Description

w = rectwin(L) returns a rectangular window of length L in the column vector w. This function is provided for completeness; a rectangular window is equivalent to no window at all.

Algorithm

w = ones(L,1);

References

[1] Oppenheim, A.V., and R.W. Schafer. Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice-Hall, 1999, pp. 468-471.

 

taylorwin -Taylor window

Syntax

w = taylorwin(n)
w = taylorwin(n,nbar)
w = taylorwin(n,nbar,sll)

Description

Taylor windows are similar to Chebyshev windows. While a Chebyshev window has the narrowest possible mainlobe for a specified sidelobe level, a Taylor window allows you to make tradeoffs between the mainlobe width and 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 aperature radar images and antenna design.

w = taylorwin(n) returns an n-point Taylor window in a column vector w. The values in this vector are the window weights or coefficients. n must be a positive integer. The default value for the number of approximately equal height sidelobes (nbar) is 4 and for the maximum sidelobe level (sll) is -30.

w = taylorwin(n,nbar) returns an n-point Taylor window with nbar nearly constant-level sidelobes adjacent to the mainlobe. These sidelobes are "nearly constant-level" because some decay occurs in the transition region.nbar must be a positive integer.

w = taylorwin(n,nbar,sll) returns an n-point Taylor window with a maximum sidelobe level of sll dB relative to the mainlobe peak.sll must be a negative value, such as -30, which produces sidelobes with peaks 30 dB down from the mainlobe peak.

Example

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.

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

http://www.mathworks.com/help/toolbox/signal/taylorwin.gif

References

[1] Carrara, W.G., R.M. Majewski and R.S. Goodman, Spotlight Synthetic Aperature Radar: Signal Processing Algorithms, Artech House Publishers, Boston, 1995, Appendix D.2.

[2] Brookner, Eli, Practical Phased Array Antenna Systems, Lex Book, Lexington, MA, 1991.

 

triang -Triangular window

Syntax

triang(L)

Description

triang(L) returns an L-point triangular window in the column vector w. The coefficients of a triangular window are:

For L odd:

http://www.mathworks.com/help/toolbox/signal/eqn1142451893.gif

For L even:

http://www.mathworks.com/help/toolbox/signal/eqn1142452057.gif

The triangular window is very similar to a Bartlett window. The Bartlett window always ends with zeros at samples 1 and L, while the triangular window is nonzero at those points. For L odd, the center L-2 points oftriang(L-2) are equivalent to bartlett(L).

Examples

Create a 200-point triangular window and plot the result using WVTool.

L=200;
wvtool(triang(L)) 

http://www.mathworks.com/help/toolbox/signal/triang.gif

References

[1] Oppenheim, A.V., and R.W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1989, pp. 447-448.

 

tukeywin -Tukey (tapered cosine) window

Syntax

w=tukeywin(L,r)

Description

w = tukeywin(L,r) returns an L-point, Tukey window in column vector w. Tukey windows are cosine-tapered windows. r is the ratio of taper to constant sections and is between 0 and 1. r ≤ 0 is a rectwin window and r≥ 1 is a hann window. The default value for r is 0.5.

Examples

Compute 128-point Tukey windows with five different tapers and display the results using WVTool:

L=128;
t0=tukeywin(L,0);        % Equivalent to rectangular window
t25=tukeywin(L,0.25);
t5=tukeywin(L);          % r=0.5
t75=tukeywin(L,0.75);
t1=tukeywin(L,1);        % Equivalent to Hann window
wvtool(t0,t25,t5,t75,t1)

http://www.mathworks.com/help/toolbox/signal/tukeywin.gif

Algorithm

The following equation defines the N–point Tukey window:

http://www.mathworks.com/help/toolbox/signal/eqn1244142224.gif

where x is a N–point linearly spaced vector generated using linspace. The parameter α denotes the ratio of tapered section to constant section with 0 ≤α≤1. If you specify α≤0, an N-point rectangular window is returned. If you specify α≥1, a von Hann window (sigwin.hann) is returned.

References

[1] Harris, F. J. "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform." Proceedings of the IEEE. Vol. 66 (January 1978). pp. 66-67.

 

parzenwin -Parzen (de la Valle-Poussin) window

Syntax

w=parzenwin(L)

Description

w = parzenwin(L) returns the L-point Parzen (de la Valle-Poussin) window in column vector w. Parzen windows are piecewise cubic approximations of Gaussian windows. Parzen window sidelobes fall off as 1/ω⁴.

Examples

Compare 64-point Parzen and Gaussian windows and display the result using sigwin window objects andwintool:

wintool(sigwin.parzenwin(64),sigwin.gausswin(64))

http://www.mathworks.com/help/toolbox/signal/parzenwin_ex.gif

Algorithm

The following equation defines the N–point Parzen window over the interval http://www.mathworks.com/help/toolbox/signal/eqn1244646625.gif:

http://www.mathworks.com/help/toolbox/signal/eqn1244645527.gif

References

[1] Harris, F.J. "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform." Proceedings of the IEEE. Vol. 66, No. 1 (January 1978).