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We investigate the binary phase filters of finite support that have a Fourier transform magnitude that is the broadest and flattest. We call this behavior maximally flat, after the electrical filters devised by Butterworth. Solutions are obtained by direct algebraic manipulation, and numerical results are given for filters of up to five elements. Their application for increasing depth of focus is described.
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Colin J. R. Sheppard (2011) studied this question.
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