Extraction of signals buried in noise. Part I: Fundamentals

In the first part of this series, we derive conditions under which the periodogram power spectral estimate can be used without any sort of averaging or smoothing in the time or frequency domain for extraction of buried signals independently of the nature of noise (white or colored, Gaussian or not) and locations of its spectral extent superimposed to them. Two denoising methods called, respectively “modified frequency extent denoising (MFED)” and “constant frequency extent denoising (CFED)” are proposed. It is shown that signal-to-noise ratio of buried signals and standard-deviation of noisy spectral estimates are, respectively, enhanced and reduced by the same proportion. In the second part of this series, extraction performances and comparative results with other denoising techniques (modified periodogram method, wavelet denoising and bispectrum estimation) are demonstrated via simulated and experimental Doppler velocimetry processes.