The discrete Fourier transform (DFT) often is used instead of the optimum Karhunen-Lo\grave{e}ve 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. We address the problem of this performance degradation by deriving a simple and easily applied upper bound on the increase in the distortion-rate function (DRF) for the mean-squared error criterion incurred by substitution of the DFT for the KLT.