Methods and apparatus are disclosed for approximating an MDCT coefficient of a block of windowed sinusoid having a defined frequency, the block being multiplied by a window sequence and having a block length and a block index. A finite trigonometric series is employed to approximate the window sequence. A window summation table is pre-computed using the finite trigonometric series and the defined frequency of the sinusoid. A block phase is computed for each block with the defined frequency, the block length and the block index. An MDCT coefficient is approximated by the dot product of a phase vector computed using the block phase with a corresponding row of the window summation table.