Discrete Hadamard transform

More commonly, we are faced with the need for mathematical resolution of components, using their different patterns (or spectra) in the various dimensions. That is, literally, mathematical analysis must supplement the chemical or physical analysis. In this case, we very often initially lack sufficient model information for a rigorous analysis, and a number of methods have evolved to "explore the data", such as principal components and "self-modeling analysis (21), cross correlation (22). Fourier and discrete (Hadamard,. . . ) transforms (23) digital filtering (24), rank annihilation (25), factor analysis (26), and data matrix ratioing (27). 

The Hadamard transform is an example of a generalized class of a DFT that performs an orthogonal, symmetric, involuntary linear operation on dyadic (i.e., power of two) numbers. The transform uses a special square matrix the Hadamard matrix, named after French mathematician Jacques Hadamard. Similarly to the DFT, we can express the discrete Hadamard transform (DHT) as... 

HADAMARD AND OTHER DISCRETE TRANSFORMS IN SPECTROSCOPY N. J. A. Sloane... 

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