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Biorthogonal decomposition: Difference between revisions
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where ''i=1,...,N'' is a temporal index and ''j=1,...,M'' a spatial index (typically). | where ''i=1,...,N'' is a temporal index and ''j=1,...,M'' a spatial index (typically). | ||
The time traces ''Y(i,j)'' for fixed ''j'' are usually sampled at a fixed rate (so ''t(i)'' is equidistant); however the measurement locations ''x(j)'' need not be ordered in any specific way. | The time traces ''Y(i,j)'' for fixed ''j'' are usually sampled at a fixed rate (so ''t(i)'' is equidistant); however the measurement locations ''x(j)'' need not be ordered in any specific way. | ||
The data are decomposed in a small set of linearly independent modes, determined from the structure of the data matrix ''Y'' itself, without prejudice regarding the mode shape. | |||
== Description == | |||
The BOD decomposes the data matrix as follows: | The BOD decomposes the data matrix as follows: | ||