Coherent extraction of signals from turbulent noise

This paper reports the results of some theoretical and experimental studies of the extraction of signals from convecting and decaying fluid dynamic turbulent noise employing an analog correlation receiver. In addition, it presents an extension of the theory of correlator analysis for finite observation times to the case of a linear time-varying delay. Detailed study of the mean and variance of the output signal from a correlation receiver permits a prediction of the gain in signal-to-noise ratio in the receiver and its dependence upon various fluid dynamic fluctuation, signal, and correlator parameters. The gain in signal-to-noise ratio for periodic and Gaussian random signals in extraction from turbulent noise is found to depend upon 1) a ratio of correlation lengths involving several statistical properties of the turbulence obtained from a model of the space-time correlations, 2) a ratio of a characteristic signal frequency to a characteristic frequency of the turbulence and 3) a time bandwidth product associated with the effective finite averaging time of the correlator and a characteristic frequency of the convolution of the signal and noise spectra. Experimental studies in a subsonic wind tunnel employing acoustic signals are in good agreement with theoretical predictions of the gain in signal-to-noise ratio. Some receiver design considerations emerge from the analysis. Of special interest are the influence of linear scanning and ranging and the finite lifetime of the turbulence on the required averaging process.