Abstract: Systems and methods for structuring information include determining information quantity (IQ) and information value (IV) in an original digital information file (ODIF). An initial manipulation process applied to the ODIF forms a first resulting DIF (FRDIF), and a subsequent manipulation process applied to the FRDIF forms a second resulting DIF, wherein each manipulation process removes at least one element of the processed DIF and/or represents an element combination with a representative element and a first indicia of an interrelationship between the representative element and one or more elements in the combination, to reduce the IQ of the processed DIF, while retaining the IV thereof within a threshold. Manipulation processes are successively applied to the previously resulting DIF until successive applications do not achieve a threshold reduction in IQ. The last resulting DIF has a primary structure with a reduced IQ and an IV within the threshold of the original IV.

Abstract: Systems and methods for structuring information include determining information quantity (IQ) and information value (IV) in an original digital information file (ODIF). An initial manipulation process applied to the ODIF forms a first resulting DIF (FRDIF), and a subsequent manipulation process applied to the FRDIF forms a second resulting DIF, wherein each manipulation process removes at least one element of the processed DIF and/or represents an element combination with a representative element and a first indicia of an interrelationship between the representative element and one or more elements in the combination, to reduce the IQ of the processed DIF, while retaining the IV thereof within a threshold. Manipulation processes are successively applied to the previously resulting DIF until successive applications do not achieve a threshold reduction in IQ. The last resulting DIF has a primary structure with a reduced IQ and an IV within the threshold of the original IV.

Abstract: A method, apparatus, and computer program product for calculating a sampled signal are disclosed. A method in accordance with the disclosure may include determining discrete samples of a continuous signal having a finite spectrum and using a function series expansion to calculate at least a portion of the continuous signal over the discrete samples. In accordance with some embodiments, an original signal may be calculated over discrete samples with arbitrary accuracy. Polyphase filtering is not used in some embodiments. Some embodiments can be used for arbitrary, including irrational, variation of the sampling rate of the signal with a bounded spectrum. Some embodiments provide for much faster calculation than direct application of the Kotelnikov (Nyquist-Shannon) theorem. In some embodiments, the calculation may be performed according to the disclosed theorem but, instead of discrete signal convolutions with kernels having different phases, a function series expansion may be used.