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In mathematics, the Shapiro polynomials are a sequence of polynomials which were first studied by Harold S. Shapiro in 1951 when considering the magnitude of specific trigonometric sums. In signal processing, the Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. The first few members of the sequence are: where the second sequence, indicated by Q, is said to be complementary to the first sequence, indicated by P.

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  • Polynôme de Shapiro (fr)
  • Shapiro polynomials (en)
  • Многочлены Шапиро (ru)
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  • En analyse de Fourier, les polynômes de Shapiro, étudiés par Harold S. Shapiro en 1951, sont des polynômes et définis par la relation de récurrence : Ces polynômes vérifient la propriété : pour z sur le cercle unité. Ces polynômes ont des applications en traitement du signal. (fr)
  • In mathematics, the Shapiro polynomials are a sequence of polynomials which were first studied by Harold S. Shapiro in 1951 when considering the magnitude of specific trigonometric sums. In signal processing, the Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. The first few members of the sequence are: where the second sequence, indicated by Q, is said to be complementary to the first sequence, indicated by P. (en)
  • Многочлены Шапиро — последовательность многочленов, впервые изученная Гарольдом Шапиро в 1951 году при рассмотрении величин некоторых специальных тригонометрических сумм. С точки зрения обработки сигналов, полиномы Шапиро обладают хорошими автокорреляционными свойствами, и их значения в единичном круге малы. Первые члены последовательности: , где вторая последовательность, Q, называется дополнительной к первой последовательности, P. (ru)
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  • http://commons.wikimedia.org/wiki/Special:FilePath/Rudin_shapiro_8_zeros.svg
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  • En analyse de Fourier, les polynômes de Shapiro, étudiés par Harold S. Shapiro en 1951, sont des polynômes et définis par la relation de récurrence : Ces polynômes vérifient la propriété : pour z sur le cercle unité. Ces polynômes ont des applications en traitement du signal. (fr)
  • In mathematics, the Shapiro polynomials are a sequence of polynomials which were first studied by Harold S. Shapiro in 1951 when considering the magnitude of specific trigonometric sums. In signal processing, the Shapiro polynomials have good autocorrelation properties and their values on the unit circle are small. The first few members of the sequence are: where the second sequence, indicated by Q, is said to be complementary to the first sequence, indicated by P. (en)
  • Многочлены Шапиро — последовательность многочленов, впервые изученная Гарольдом Шапиро в 1951 году при рассмотрении величин некоторых специальных тригонометрических сумм. С точки зрения обработки сигналов, полиномы Шапиро обладают хорошими автокорреляционными свойствами, и их значения в единичном круге малы. Первые члены последовательности: , где вторая последовательность, Q, называется дополнительной к первой последовательности, P. (ru)
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