Roundoff noise generated by orthogonal building blocks in signal processing structures

The statistics of roundoff errors produced by the multiplication of a random input vector with an orthogonal matrix can be expressed in terms of the characteristic function of the input vector. The case of a 2*2 orthogonal matrix is analyzed by assuming that the input probability mass function follows a jointly Gaussian envelope. It is found that for small dynamic ranges the two errors are not necessarily uncorrelated. However, they are uncorrelated for large dynamic range. The lossless FIR (finite-impulse-response) lattice with quantizers is considered as an example.<>