The discrete cosine transform (DCT), a type of transform coding for lossy compression, was proposed by Nasir Ahmed in 1972, and developed by Ahmed with T. Natarajan and K. R. Rao in 1973, publishing their results in 1974.[9][10][11] This led to the development of the modified discrete cosine transform (MDCT), proposed by J. P. Princen, A. W. Johnson and A. B. Bradley in 1987,[12] following earlier