Algorithm for the Complex Discrete Cosine Transform

Abstract

The main way to represent an audio signal in the frequency domain is the fast Fourier transform (FFT). When analyzing short signal sequences, the FFT often cannot provide the necessary resolution and accuracy in the formation of estimates of the amplitude and phase of the coefficients. The discrete cosine transform (DCT) is known and widely used, the coefficients of which are placed twice as often on the frequency scale. The disadvantage of DCT is the dependence of the estimate on the initial phase position of the signal; nevertheless, DCT is widely used to eliminate the statistical redundancy of signals. An algorithm for complex DCT is proposed that provides an increase in the resolution and accuracy of the estimate.