MFCCk

MFCCk is a family of speech features that extends the conventional Mel-frequency cepstral coefficients (MFCCs) by introducing a parameter k to incorporate additional spectral-temporal information. In common interpretations, k denotes either the amount of temporal context or the order of higher-order information included in the feature vector.

In the standard MFCC pipeline, per-frame estimates are obtained by applying a Fourier transform, mapping to a mel filterbank, taking logarithms, and applying a discrete cosine transform to produce cepstral coefficients. MFCCk modifies this pipeline in one of two ways. First, temporal context extension uses k neighboring frames, either by concatenating their MFCCs or by applying a lightweight temporal model, producing a higher-dimensional feature that captures short-term dynamics. Second, higher-order extensions incorporate additional statistics or derivatives up to order k, such as higher-order moments of the mel energies or higher-order finite differences, to capture rapid spectral changes.

MFCCk aims to improve robustness to noise, speaker variation, and dynamic speech patterns, with reported benefits in automatic speech recognition and related tasks, particularly under challenging acoustic conditions. However, the increased feature dimensionality can demand more data and stronger regularization, and may incur higher computational cost. Practitioners often balance k to achieve a favorable trade-off between information content and complexity.

Relation to standard MFCC is one of compatibility and extension: MFCCk preserves the core ideas of mel-scale filtering, log-energy, and cepstral analysis while offering a tunable mechanism to capture richer temporal or spectral structure. Further empirical comparisons with MFCCs and delta features are common in studies evaluating MFCCk for specific applications.