Recursive Algorithms for Computing Sliding DCT With Arbitrary Step

Discrete cosine transform (DCT) is one of the most popular transforms in digital signal processing. Its close approximation to the Karhunen-Loeve transform implies a high degree of energy compaction. Therefore, it can be used in a wide range of applications such as sensor noise removal, spectral analysis, linear filtering, feature extraction and pattern recognition. When it is required to estimate the spectrum of a nonstationary process such as radar, speech, biomedical and communication signals, a short-time (sliding) transform can be used. Basically, the sliding transform means that the transform is calculated on a fixed-length window of the signal, which is constantly updated with new samples while the oldest ones are discarded. In some engineering applications, when the spectral content changes slowly, the window can slide more than one sample at a time to speed up the spectral analysis. In this paper, second-order recursive algorithms are proposed for fast computing the DCT in windows that are located at a given equal distance from each other. The computational complexity of the algorithms is compared with that of common fast and sliding DCT algorithms.