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We study the balanced detection of broadband incoherent optical signals-signals characterized by high-intensity noise. We consider signals generated from a single incoherent source with two types of correlation: identical spectra, but delayed in time, and overlapping, nonidentical spectra but zero time delay. Our statistical analysis yields equations for the probability density function (pdf) of the balanced detector output for partially correlated input signals based on easily measured system parameters (power spectral densities in one case, relative time delay in the other). Using analytical tools we derive expressions for output pdfs giving extremely good prediction of measured pdfs for signals with correlation coefficient up to 95%. The analytic expressions can be used to characterize system performance, in particular, bit error rate for communications systems.