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- En traitement numérique du signal, les méthodes d'échantillonnage non uniforme ou irrégulier visent à contourner les limites imposées par le théorème de l'échantillonnage de Shannon avec des équipements dont la vitesse ou la densité spatiale des capteurs est limitée. (fr)
- Nonuniform sampling is a branch of sampling theory involving results related to the Nyquist–Shannon sampling theorem. Nonuniform sampling is based on Lagrange interpolation and the relationship between itself and the (uniform) sampling theorem. Nonuniform sampling is a generalisation of the Whittaker–Shannon–Kotelnikov (WSK) sampling theorem. The sampling theory of Shannon can be generalized for the case of nonuniform samples, that is, samples not taken equally spaced in time. The Shannon sampling theory for non-uniform sampling states that a band-limited signal can be perfectly reconstructed from its samples if the average sampling rate satisfies the Nyquist condition. Therefore, although uniformly spaced samples may result in easier reconstruction algorithms, it is not a necessary condition for perfect reconstruction. The general theory for non-baseband and nonuniform samples was developed in 1967 by Henry Landau. He proved that the average sampling rate (uniform or otherwise) must be twice the occupied bandwidth of the signal, assuming it is a priori known what portion of the spectrum was occupied.In the late 1990s, this work was partially extended to cover signals for which the amount of occupied bandwidth was known, but the actual occupied portion of the spectrum was unknown. In the 2000s, a complete theory was developed(see the section Beyond Nyquist below) using compressed sensing. In particular, the theory, using signal processing language, is described in this 2009 paper. They show, among other things, that if the frequency locations are unknown, then it is necessary to sample at least at twice the Nyquist criteria; in other words, you must pay at least a factor of 2 for not knowing the location of the spectrum. Note that minimum sampling requirements do not necessarily guarantee numerical stability. (en)
- 非均勻取樣（英語：Nonuniform sampling）是取樣定理下的產物，藉由拉格朗日插值法及均勻取樣理論的關係，來達成滿足取樣定理的概括化型態。取樣定理限制了在對連續訊號取樣時的條件，如奈奎斯特準則，以避免取樣後的重構時產生訊號缺陷。而非均勻取樣則是在不同時間有不同的取樣間隔，但平均下來，整段取樣滿足取樣定理的限制，根據取樣定理的回推，這樣的作法在有限頻寬訊號重構時不會造成缺陷。因此，雖然均勻取樣在訊號重構時較簡單，完整的重構訊號卻不見得一定要用均勻取樣來的訊號才能達到。 1967年藍道提出的對於非均勻取樣及非基頻取樣的泛用理論提到，平均後的取樣率，無論是否均勻取樣，若是知道使用的頻譜為前題下，必須要是訊號占用頻寬的兩倍大。1990年代末期，這個理論推廣到占用頻寬的數量已知，而實際上頻譜位置未知的情形。2000年代，非均勻取樣與壓縮取樣逐漸發展成一套完整的理論，並實際實作在訊號處理上。如果頻譜位置是未知的，取樣率必須至少兩倍大於奈奎斯特準則，也就是說未知頻譜位置的代價是至少多兩倍的頻寬。 (zh)
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- En traitement numérique du signal, les méthodes d'échantillonnage non uniforme ou irrégulier visent à contourner les limites imposées par le théorème de l'échantillonnage de Shannon avec des équipements dont la vitesse ou la densité spatiale des capteurs est limitée. (fr)
- 非均勻取樣（英語：Nonuniform sampling）是取樣定理下的產物，藉由拉格朗日插值法及均勻取樣理論的關係，來達成滿足取樣定理的概括化型態。取樣定理限制了在對連續訊號取樣時的條件，如奈奎斯特準則，以避免取樣後的重構時產生訊號缺陷。而非均勻取樣則是在不同時間有不同的取樣間隔，但平均下來，整段取樣滿足取樣定理的限制，根據取樣定理的回推，這樣的作法在有限頻寬訊號重構時不會造成缺陷。因此，雖然均勻取樣在訊號重構時較簡單，完整的重構訊號卻不見得一定要用均勻取樣來的訊號才能達到。 1967年藍道提出的對於非均勻取樣及非基頻取樣的泛用理論提到，平均後的取樣率，無論是否均勻取樣，若是知道使用的頻譜為前題下，必須要是訊號占用頻寬的兩倍大。1990年代末期，這個理論推廣到占用頻寬的數量已知，而實際上頻譜位置未知的情形。2000年代，非均勻取樣與壓縮取樣逐漸發展成一套完整的理論，並實際實作在訊號處理上。如果頻譜位置是未知的，取樣率必須至少兩倍大於奈奎斯特準則，也就是說未知頻譜位置的代價是至少多兩倍的頻寬。 (zh)
- Nonuniform sampling is a branch of sampling theory involving results related to the Nyquist–Shannon sampling theorem. Nonuniform sampling is based on Lagrange interpolation and the relationship between itself and the (uniform) sampling theorem. Nonuniform sampling is a generalisation of the Whittaker–Shannon–Kotelnikov (WSK) sampling theorem. (en)
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- Échantillonnage non uniforme (fr)
- Nonuniform sampling (en)
- 非均勻採樣 (zh)
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