The block sum transformation—A new special discrete fourier transformation method for the analysis of vibrations

Structural Identification Using a Combination of Subspace Analysis and Block Sum Transformation

“…It was shown [5] that the results of the Fourier transformation of the added functions and that of the whole time function is the same, only the frequency discretisation di!er:…”

“…Initially the measured time-discrete, block sum transformed values were processed with the Fourier transformation [5]. The whole measuring interval ¹ is divided into time segments of duration ¹*, where ¹/¹* is an integer number (Fig.…”

“…The block sum transformation [5] is a method to reduce the high amount of incidental measured data considerably, which have to be processed by the identi"cation routine. A combination of the subspace method and the block sum transformation will bring an important progress in structural analysis as will be shown in this article.…”

A note on the block sum transformation

“…In vector notation,x = Fx, where F is the (unitary) n × n Fourier matrix, x is the n-dimensional timedomain vector, andx is the DFT of x. The block sum transformation proposed in [1] allows the computation of a subset of the samplesx i of the DFT, but uses the m-dimensional vector y defined by…”

“…Clearly, this is equivalent to the block sum transformation proposed by Bourchard et al [1]. Using the second Boncelet algorithm, which can be applied whenever n is a multiple of 4, this transformation could be further improved from the computational point of view.…”