An audio signal downmixing apparatus for processing an input audio signal into an output audio signal, the input audio signal comprising a plurality of input channels recorded at a plurality of spatial positions and the output audio signal comprising a plurality of primary output channels, the audio signal downmixing apparatus comprising: a downmix matrix determiner configured to determine for each frequency bin j of a plurality of frequency bins a downmix matrix (D U) with j being an integer in the range from 1 to N, wherein for a given frequency bin j the downmix matrix (Du) maps a plurality of Fourier coefficients associated with the plurality of input channels of the input audio signal into a plurality of Fourier coefficients of the primary output channels of the output audio signal, wherein for frequency bins with j being smaller than or equal to a cutoff frequency bin k the downmix matrix (D U) is determined by determining eigenvectors of a discrete Laplace-Beltrami operator defined by the plurality of spatial positions where the plurality of input channels are recorded, and wherein for frequency bins with j being larger than the cutoff frequency bin k the downmix matrix (D U) is determined by determining a first subset of eigenvectors of a covariance matrix defined by the plurality of input channels of the input audio signal; and a processor configured to process the input audio signal using the downmix matrix (Du) into the output audio signal; wherein the downmix matrix determiner is configured to determine the cutoff frequency bin k by determining the frequency bin of the plurality of frequency bins which has the smallest compactness measure θ C of all frequency bins having a compactness measure θ C greater than a predefined threshold T, wherein the compactness measure θ C of a frequency bin is determined using the following equation: θ C ⁢ ​ = ‖ diag U ^ H COV U ^ ‖ F ‖ off U ^ H C OV U ^ ‖ F wherein Û denotes a unitary matrix containing the selected eigenvectors of the discrete Laplace-Beltrami operator, Û H denotes the hermitian transpose of Û, diag (...) denotes a matrix diagonalization operation zeroing all coefficients except the coefficients along the diagonal of the matrix given a matrix input, off (...) denotes a matrix operation zeroing all coefficients on the diagonal of the matrix and ∥...∥ F denotes the Frobenius norm. a downmix matrix determiner configured to determine for each frequency bin j of a plurality of frequency bins a downmix matrix (D U) with j being an integer in the range from 1 to N, wherein for a given frequency bin j the downmix matrix (Du) maps a plurality of Fourier coefficients associated with the plurality of input channels of the input audio signal into a plurality of Fourier coefficients of the primary output channels of the output audio signal, wherein for frequency bins with j being smaller than or equal to a cutoff frequency bin k the downmix matrix (D U) is determined by determining eigenvectors of a discrete Laplace-Beltrami operator defined by the plurality of spatial positions where the plurality of input channels are recorded, and wherein for frequency bins with j being larger than the cutoff frequency bin k the downmix matrix (D U) is determined by determining a first subset of eigenvectors of a covariance matrix defined by the plurality of input channels of the input audio signal; and a processor configured to process the input audio signal using the downmix matrix (Du) into the output audio signal;