Spectrum of the lagged product in cross correlation
Henry M. Beisner
Abstract
Henry M. Beisner
Abstract
Cross correlation has been used for detection and parameter estimation of moving targets. Various correlation techniques consist, essentially, of methods to estimate the spectrum of the correlation product. The power spectrum of the lagged product is derived. The time-lag dependence of the spectrum is found to be proportional to the squared magnitude of the signal autocorrelation function. It is shown that, if the bandwidth of the modulation noise is small compared to the signal bandwidth, considerable gain can be obtained by correlation.
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Cross correlation has been used for detection and parameter estimation of moving targets. Various correlation techniques consist, essentially, of methods to estimate the spectrum of the correlation product. The power spectrum of the lagged product is derived. The time-lag dependence of the spectrum is found to be proportional to the squared magnitude of the signal autocorrelation function. It is shown that, if the bandwidth of the modulation noise is small compared to the signal bandwidth, considerable gain can be obtained by correlation.
Key concepts: Autocorrelation, Spectral density, Correlation, Bandwidth (computing), Correlation function (quantum field theory), Cross-correlation, Mathematics, Lag