Abstract: A new estimator for evolutionary spectrum (ES) based
on short time Fourier transform (STFT) and modified group delay
function (MGDF) by signal decomposition (SD) is proposed. The
STFT due to its built-in averaging, suppresses the cross terms and the
MGDF preserves the frequency resolution of the rectangular window
with the reduction in the Gibbs ripple. The present work overcomes
the magnitude distortion observed in multi-component non-stationary
signals with STFT and MGDF estimation of ES using SD. The SD is
achieved either through discrete cosine transform based harmonic
wavelet transform (DCTHWT) or perfect reconstruction filter banks
(PRFB). The MGDF also improves the signal to noise ratio by
removing associated noise. The performance of the present method is
illustrated for cross chirp and frequency shift keying (FSK) signals,
which indicates that its performance is better than STFT-MGDF
(STFT-GD) alone. Further its noise immunity is better than STFT.
The SD based methods, however cannot bring out the frequency
transition path from band to band clearly, as there will be gap in the
contour plot at the transition. The PRFB based STFT-SD shows good
performance than DCTHWT decomposition method for STFT-GD.
Abstract: Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine 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).