Comments on "Discrete Cosine Transform"

In the above correspondence,1 Ahmed et al. proposed a discrete cosine transform (DCT) and compared its performance with the Karhunen-Loeve transform (KLT). They offered empirical evidence showing that the DCT and the KLT compare closely for a number of digital signal processing applications. The purpose of this note is to show that the DCT and the KLT are indeed asymptotically equivalent if the data covariance matrix is a Toeplitz matrix.