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Quadratic Phase Array


A method to obtain a signal C_l(z) with a flat spectrum c(theta;z) (such as a pulse), but having a smaller amplitude than the pulse.

 c(theta;z)=e^(izphi(theta))=sum_(l=-infty)^inftye^(iltheta)C_l(z),
(1)

whence

 C_l(z)=1/(2pi)int_(-pi)^pie^(i(zphi(theta)-ltheta))dtheta,
(2)

where

 phi(theta)=(1-|theta|/pi)theta/pi,
(3)

with |theta|<=pi.

Thus c(theta;z) and C_l(z) are a Fourier pair, and since |c(theta;z)|=1, it is guaranteed that the sequence C_l has a flat spectrum. The sequence C_l is called the "quadratic phase array."


See also

Quadratic

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References

Aarts, R. M. and Janssen, A. J. E. M. "On Analytic Design of Loudspeaker Arrays with Uniform Radiation Characteristics." J. Acoust. Soc. Amer. 107, 287-292, 2000.

Referenced on Wolfram|Alpha

Quadratic Phase Array

Cite this as:

Weisstein, Eric W. "Quadratic Phase Array." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/QuadraticPhaseArray.html

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