MDCTn

MDCTn refers to a family of Modified Discrete Cosine Transform variants parameterized by an integer n, intended to generalize the standard MDCT by varying the block size and overlap characteristics. In this usage, the transform operates on blocks of 2n input samples with a 50 percent overlap, producing n frequency coefficients per block. As a result, MDCTn inherits the lapped, critically sampled nature of the MDCT and remains a linear, time-domain to frequency-domain transform.

Key properties of MDCTn include its potential for perfect reconstruction when paired with a suitable synthesis window that satisfies the time-domain aliasing cancellation condition. Like the conventional MDCT, it is typically implemented with a window function and an overlap-add synthesis stage, making it well suited for streaming or block-based applications. The choice of n directly influences frequency resolution, latency, and computational load: larger n provides finer spectral detail but increases block size and latency, while smaller n reduces latency at the cost of resolution.

Applications of MDCTn are primarily in audio and multimedia coding, where side information and scalable bitstreams may benefit from different block sizes. MDCT variants are used to reduce redundancy and to enable efficient perceptual coding, often in conjunction with psychoacoustic models and multiple window types. In practice, MDCTn can leverage FFT-based algorithms for speed, sharing implementation principles with the standard MDCT.

See also: MDCT, DCT-IV, time-domain aliasing cancellation, windowed overlapped transforms.