A nonlinear joint transform image correlator is investigated. The Fourier transform interference intensity is thresholded to provide higher correlation peak intensity and better defined correlation spot. Analytical expressions for the thresholded joint power spectrum is provided. The effects of the nonlinearity at the Fourier plane on the correlation signals at the output plane is investigated. The correlation signals are determined in terms of the nonlinear characteristics of the spatial light modulator (SLM) at the Fourier plane. We show that thresholding the interference intensity results in a sum of infinite harmonic terms. Each harmonic term is envelope modulated due to the nonlinear characteristics of the device, and phase modulated by m times the phase modulation of the nonthresholded joint power spectrum. The correct phase information about the correlation signal is recovered for the first order harmonic of the thresholded interference intensity. We show that various types of correlation signals can be produced simply by varying the severity of the nonlinearity and without the need to synthesize the specific matched filter. For example, a phase-only correlation signal is produced by selecting the appropriate nonlinearity.