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An alias-free, discrete-time click modulator is developed in this paper. Previous approaches rely on translating the continuous-time click modulator to a discrete-time setting, although a key component in the click modulator - the analytic exponential modulator-cannot be exactly transformed to the discrete domain. Every discrete-time version of the click modulator reported in the literature is prone to aliasing effects that are ameliorated, but not eliminated, using interpolation techniques. The precision of the switching times of the output square wave is critical to click modulation because uncertainties in their determination adversely affect the performance and SNR of the modulator. A novel method that uses frequency domain information to compute these switching times without error is also presented. This two techniques are used to develop an off-line discrete-time click modulator that achieves a SNR larger than 180 dB for both multitonal and bandpass signals.