In a data processing system, a method and system employing high fidelity inverse discrete cosine transform (IDCT) and discrete cosine transform (DCT) algorithms are provided. The values of the coefficients in a two-dimensional (2D) transform utilized in the IDCT and DCT algorithms may approximate the ideal integer output with sufficient visual quality. The transform coefficients may match a portion of the most significant bits (MSBs) or properly rounded bits of the coefficients of a reference transform matrix within an upper bound. The IDCT and DCT algorithms may specify constraints based on separating the 2D transform operation into two 1D transform operations in order to determine a minimum-bit width for each of the transform coefficients. The minimum-bit width may also be based on integer-bit precision of the data to be processed by the IDCT and DCT algorithms.