Abstract
Jul 26, 2019 Thus, gives side-lobes which are dB below the main-lobe peak. Since the side lobes of the Dolph-Chebyshev window transform are equal height, they are often called ``ripple in the stop-band' (thinking now of the window transform as a lowpass filter frequency response).The smaller the ripple specification, the larger has to become to satisfy it, for a given window length.
We present a synthesis technique for circular arrays of antennas that allows to determine an array pattern having side lobes of assigned level and one main beam whose width does not exceed a prescribed threshold. The method develops in two steps. At first it generates, by means of a suitable Chebyshev polynomial, a reference pattern satisfying the conditions imposed by the synthesis problem. Subsequently, it determines the solution as the array pattern minimizing the mean-square distance from the reference pattern. Numerical examples show the effectiveness of the method.
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References
- [1]N. Goto and Y. Tsunoda, 'Sidelobe Reduction of Circular Arrays with a Constant Excitation Amplitude', IEEE Trans. Antennas Propagat., vol. AP-25,no. 6, pp. 896–898, Nov. 1977.
- [2]F. Watanabe, N. Goto, A. Nagayama, and G. Yoshida, 'A Pattern Synthesis of Circular Arrays by Phase Adjustment,' IEEE Trans. Antennas Propagat., vol. AP-28,no. 6, pp. 896–898, Nov. 1980.
- [3]S. Prasad and R. Charan, 'On the Constrained Synthesis of Array Patterns With Applications to Circular and Arc Arrays,' IEEE Trans. Antennas Propagat., vol. AP-32,no. 6, pp. 725–730, July 1984.
- [4]C. L. Dolph, 'A current Distribution for Broadside Arrays Which Optimizes the Relationship Between Beamwidth and Side-Lobe Level,' Proc. IRE and Waves and Electrons, June 1946.
- [5]R. S. Elliott, Antenna theory and design. Englewood Cliffs, N. J.: Prentice-Hall, 1981, Ch. II.
- [6]R. Vescovo, 'Constrained and Unconstrained Synthesis of Array Factor for Circular Arrays,' IEEE Trans. Antennas Propagat., vol. AP-43,no. 12, pp. 1405–1410, Dec. 1995.
- [7]T. Rahim and D.E.N. Davies, 'Effect of directional eleménts on the directional response of circular antenna arrays,' IEE Proc. H, vol. 129,no. 1, pp. 18–22, 1982.
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Vescovo, R. An Extension of the Dolph-Chebyshev Synthesis Technique to Circular Arrays of Antennas. International Journal of Infrared and Millimeter Waves20, 1957–1976 (1999) doi:10.1023/A:1022941416515
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- DOI: https://doi.org/10.1023/A:1022941416515
- Synthesis
- Circular arrays
- Chebyshev polynomials
Package: sigwin
Construct Dolph-Chebyshev window object
Description
Note
The use of
sigwin.chebwin
is not recommended.Use chebwin
instead.sigwin.chebwin
creates a handle to a Dolph-Chebyshevwindow object for use in spectral analysis and FIR filtering by thewindow method. Object methods enable workspace import and ASCII fileexport of the window values.The Dolph-Chebyshev window is constructed in the frequency domainby taking samples of the window's Fourier transform:
where
determines the level of thesidelobe attenuation. The level of the sidelobe attenuation is equalto . For example, 100 dB of attenuationresults from setting
The discrete-time Dolph-Chebyshev window is obtained by takingthe inverse DFT of and scaling theresult to have a peak value of 1.
Construction
H = sigwin.chebwin
returns a Dolph-Chebyshevwindow object H
of length 64 with relative sidelobeattenuation of 100 dB.H = sigwin.chebwin(Length
)
returnsa Dolph-Chebyshev window object H
of length Length
withrelative sidelobe attenuation of 100 dB. Length
requiresa positive integer. Entering a positive noninteger value for Length
roundsthe length to the nearest integer. A window length of 1 results ina window with a single value equal to 1.H = sigwin.chebwin(Length
,SidelobeAtten
)
returnsa Dolph-Chebyshev window object with relative sidelobe attenuationof atten_param
dB.Properties
Length | Dolph-Chebyshev window length. |
SidelobeAtten | The attenuation parameter in dB. The attenuation parameter isa positive real number that determines the relative sidelobe attenuationof the window. |
Methods
generate | Generates Dolph-Chebyshev window |
info | Display information about Dolph–Chebyshev windowobject |
winwrite | Save Dolph-Chebyshev window object values in ASCII file |
Copy Semantics
Handle. To learn how copy semantics affect your use of the class,see CopyingObjects (MATLAB) in the MATLAB® Programming Fundamentals documentation.
Examples
Generate a Dolph-Chebyshev window of length N = 16. Specify a relative sidelobe attenuation of 40 dB. Return the window values as a column vector. Show information about the window object. Display the window.
References
harris, fredric j. “On the Use of Windows for HarmonicAnalysis with the Discrete Fourier Transform.” Proceedingsof the IEEE®. Vol. 66, January 1978, pp. 51–83.
See Also
chebwin
| window
| wvtool
Topics
- ClassAttributes (MATLAB)
- PropertyAttributes (MATLAB)