A limit on optimum performance degradation in fixed-rate coding of the discrete Fourier transform

The discrete Fourier transform (DFT) often is used instead of the optimum Karhunen-Loeve transform (KLT) in encoding a stationary normal time series, because the recursive FFT is computationally efficient and yields 'nearly' uncorrelated components. Substituting the DFT for the KLT and then treating its components as if they were uncorrelated reduces the ultimate performance attainable in fixed-rate source coding. The problem of this performance degradation is addressed by deriving a simple and easily applied upper bound on the increase in the distortion-rate function for the mean-squared error criterion incurred by substitution of the DFT for the KLT.