Quadratic Phase Array

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

(1)

whence

(2)

where

(3)

with .

Thus  and  are a Fourier pair, and since , it is guaranteed that the sequence  has a flat spectrum. The sequence  is called the "quadratic phase array."

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.