IDCT

IDCT stands for inverse discrete cosine transform. It is the operation that reconstructs a signal from its frequency-domain coefficients when the forward transform used is a discrete cosine transform. In most practical contexts the forward transform is the DCT of type II, and the IDCT is the corresponding inverse transform of type III under the same normalization. There are several DCT/I variants (types I–IV), with IDCT usually referring to the inverse of the DCT-II in standard forms.

In the 1-D case, the IDCT expresses each time-domain sample as a weighted sum of cosine basis functions, with the input coefficients acting as weights. In higher dimensions, the transform is separable: a 2-D IDCT is obtained by applying 1-D IDCTs along the rows and then along the columns. This separability enables efficient implementation and is widely exploited in software and hardware.

IDCT is central to many lossy compression schemes. In image compression such as JPEG, blocks are transformed with a DCT-II, quantized, and later reconstructed by applying the IDCT-III inverse to the quantized coefficients. It is also used in video codecs and other signal-processing pipelines, where it serves as part of the reconstruction stage after coefficient coding.

Computationally, fast IDCT algorithms reduce complexity and often share structure with fast DCT algorithms. Implementations exist for one- and multi-dimensional transforms, in floating-point and fixed-point arithmetic, with attention to numerical scaling and stability.