Recursive Wiener-Khintchine Theorem

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (WienerKhintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N). Keywords— Power Spectral Density (PSD), Wiener-Khintchine Theorem, Periodogram, Short Time Fourier Transform (STFT), The Sliding DFT.