This brief exhibits the relationship between the analog click modulator, which produces a binary pulse width modulation (PWM) signal with separated baseband, and recently reported fully digital, baseband distortion-free PWM algorithms (BBDFPWM). We show that BBDFPWM not only is a discretetime version of the click modulator but also can operate in real-time without any shortcoming of other implementations. The method can also be used for developing low distortion and efficient arbitrary signal generators. In this case, we show a procedure for the offline computation of the duty-cycles of the PWM signal with zero distortion.