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FCT-Based Convolution , Filtering and Correlation of Signals ' Unified Structure

This paper focuses on constructing efficient algorithms of the main DSP discrete procedures: convolution, correlation functions and filtering of signals based on discrete cosine transform (DCTII) and presenting them using unified structure. This structure is very useful in reducing the computational complexity by 3 N 2 − real multiplications and 2 N − real additions in comparison with indirect fast Fourier transforms (FFT) based algorithms calculated through fast cosine transform (FCT). The DCT and its fast calculation ways effectively can be used to calculate convolution, filtering and correlation of signals. For their calculating, the classic schema (two DCT + product of cosine spectrums + IDCT) will be saved.