ON THE BRUUN ALGORITHM AND ITS INVERSE

Bruuns approach for the computation of the DFT is well suited to transform real input signals especially by means of a pipeline architecture. This makes the Bruun algorithm an ideal candidate for convolution applications. Unfortunately Bruuns original derivation of the algorithm rendered the impression of the multiplier coefficients being difficult to evaluate and did not provide any law for the ordering of the output sequence in the frequency domain. In addition there has been no publication yet of an appropriate inverse algorithm which probably lead to Bruuns approach going more or less unnoticed. This paper offers an alternative derivation of the Bruun algorithm which unmasks Bruuns complicated coefficients to be simple cosine values and which presents the law behind the scrambling of the output sequence. Furthermore the corresponding inverse algorithm is presented which will be derived via matrix transposition.