Extracting common spectral features by multichannel filtering using circulant matrices

It is well known that the eigenvalue decomposition (EVD) of a circulant matrix returns the discrete Fourier transform (DFT) with the eigenvectors being the transformation vectors and the eigenvalues containing the spectral coefficient in the corresponding frequency band [R.N. Gray, 2006]. For single channel measurements this provides an easy way to calculate the DFT. Going to a multichannel measurement, this method provides a way of calculating the spectra of the different channels by means of one transformation of a block circulant matrix. However, the frequency response of the multichannel measurement is calculated per channel without exchanging information between channels and thus provides no information of common spectral bands. In this abstract, a method is presented to estimate the common spectral content in the different channels based on the circulant matrices of these channels. The spectrum is calculated from an augmented windowed circular matrix for which experiments show they give a better approximation to the common spectral components.